ardupilot/libraries/AP_Scripting/applets/Aerobatics/FixedWing/plane_aerobatics.lua

--[[
   trajectory tracking aerobatic control
   See README.md for usage
   Written by Matthew Hampsey, Andy Palmer and Andrew Tridgell, with controller
   assistance from Paul Riseborough, testing by Henry Wurzburg
]]--
-- luacheck: ignore 212 (Unused argument)

-- setup param block for aerobatics, reserving 35 params beginning with AERO_
local PARAM_TABLE_KEY = 70
local PARAM_TABLE_PREFIX = 'AEROM_'
assert(param:add_table(PARAM_TABLE_KEY, "AEROM_", 40), 'could not add param table')

local MAV_SEVERITY = {EMERGENCY=0, ALERT=1, CRITICAL=2, ERROR=3, WARNING=4, NOTICE=5, INFO=6, DEBUG=7}

-- add a parameter and bind it to a variable
function bind_add_param(name, idx, default_value)
    assert(param:add_param(PARAM_TABLE_KEY, idx, name, default_value), string.format('could not add param %s', name))
    return Parameter(PARAM_TABLE_PREFIX .. name)
end


--[[
  // @Param: AEROM_ANG_ACCEL
  // @DisplayName: Angular acceleration limit
  // @Description: Maximum angular acceleration in maneuvers
  // @Units: deg/s/s
--]]
AEROM_ANG_ACCEL = bind_add_param('ANG_ACCEL', 1, 6000)


--[[
  // @Param: AEROM_ANG_TC
  // @DisplayName: Roll control filtertime constant
  // @Description: This is the time over which we filter the desired roll to smooth it
  // @Units: s
--]]
AEROM_ANG_TC = bind_add_param('ANG_TC', 2, 0.1)

-- 3 was AEROM_KE_ANG

--[[
  // @Param: AEROM_THR_PIT_FF
  // @DisplayName: Throttle feed forward from pitch
  // @Description: This controls how much extra throttle to add based on pitch ange. The value is for 90 degrees and is applied in proportion to pitch
  // @Units: %
--]]
THR_PIT_FF = bind_add_param('THR_PIT_FF', 4, 80)

--[[
  // @Param: AEROM_SPD_P
  // @DisplayName: P gain for speed controller
  // @Description: This controls how rapidly the throttle is raised to compensate for a speed error
  // @Units: %
--]]
SPD_P = bind_add_param('SPD_P', 5, 5)

--[[
  // @Param: AEROM_SPD_I
  // @DisplayName: I gain for speed controller
  // @Description: This controls how rapidly the throttle is raised to compensate for a speed error
  // @Units: %
--]]
SPD_I = bind_add_param('SPD_I', 6, 25)

--[[
  // @Param: AEROM_ROL_COR_TC
  // @DisplayName: Roll control time constant
  // @Description: This is the time constant for correcting roll errors. A smaller value leads to faster roll corrections
  // @Units: s
--]]
ROLL_CORR_TC = bind_add_param('ROL_COR_TC', 8, 0.25)

-- removed 9 and 10

--[[
  // @Param: AEROM_TIME_COR_P
  // @DisplayName: Time constant for correction of our distance along the path
  // @Description: This is the time constant for correcting path position errors
  // @Units: s
--]]
TIME_CORR_P = bind_add_param('TIME_COR_P', 11, 1.0)

--[[
  // @Param: AEROM_ERR_COR_P
  // @DisplayName: P gain for path error corrections
  // @Description: This controls how rapidly we correct back onto the desired path
--]]
ERR_CORR_P = bind_add_param('ERR_COR_P', 12, 2.0)

--[[
  // @Param: AEROM_ERR_COR_D
  // @DisplayName: D gain for path error corrections
  // @Description: This controls how rapidly we correct back onto the desired path
--]]
ERR_CORR_D = bind_add_param('ERR_COR_D', 13, 2.8)

--[[
  // @Param: AEROM_ENTRY_RATE
  // @DisplayName: The roll rate to use when entering a roll maneuver
  // @Description: This controls how rapidly we roll into a new orientation
  // @Units: deg/s
--]]
AEROM_ENTRY_RATE = bind_add_param('ENTRY_RATE', 14, 60)

--[[
  // @Param: AEROM_THR_LKAHD
  // @DisplayName: The lookahead for throttle control
  // @Description: This controls how far ahead we look in time along the path for the target throttle
  // @Units: s
--]]
AEROM_THR_LKAHD = bind_add_param('THR_LKAHD', 15, 1)

--[[
  // @Param: AEROM_DEBUG
  // @DisplayName: Debug control
  // @Description: This controls the printing of extra debug information on paths
--]]
AEROM_DEBUG = bind_add_param('DEBUG', 16, 0)

--[[
  // @Param: AEROM_THR_MIN
  // @DisplayName: Minimum Throttle
  // @Description: Lowest throttle used during maneuvers
  // @Units: %
--]]
AEROM_THR_MIN = bind_add_param('THR_MIN', 17, 0)

--[[
  // @Param: AEROM_THR_BOOST
  // @DisplayName: Throttle boost
  // @Description: This is the extra throttle added in schedule elements marked as needing a throttle boost
  // @Units: %
--]]
AEROM_THR_BOOST = bind_add_param('THR_BOOST', 18, 50)

--[[
  // @Param: AEROM_YAW_ACCEL
  // @DisplayName: Yaw acceleration
  // @Description: This is maximum yaw acceleration to use
  // @Units: deg/s/s
--]]
AEROM_YAW_ACCEL = bind_add_param('YAW_ACCEL', 19, 1500)

--[[
  // @Param: AEROM_LKAHD
  // @DisplayName: Lookahead
  // @Description: This is how much time to look ahead in the path for calculating path rates
  // @Units: s
--]]
AEROM_LKAHD = bind_add_param('LKAHD', 20, 0.5)

--[[
    // @Param: AEROM_PATH_SCALE
    // @DisplayName: Path Scale
    // @Description: Scale factor for Path/Box size. 0.5 would half the distances in maneuvers. Radii are unaffected.
    // @Range: 0.1 100
--]]
AEROM_PATH_SCALE = bind_add_param('PATH_SCALE', 21, 1.0)

--[[
    // @Param: AEROM_BOX_WIDTH
    // @DisplayName: Box Width
    // @Description: Length of aerobatic "box" 
    // @Units: m
--]]
AEROM_BOX_WIDTH = bind_add_param('BOX_WIDTH', 22, 400)

--[[
    // @Param: AEROM_STALL_THR
    // @DisplayName: Stall turn throttle
    // @Description: Amount of throttle to reduce to for a stall turn
    // @Units: %
--]]
AEROM_STALL_THR = bind_add_param('STALL_THR', 23, 40)

--[[
    // @Param: AEROM_STALL_PIT
    // @DisplayName: Stall turn pitch threshold
    // @Description: Pitch threashold for moving to final stage of stall turn
    // @Units: deg
--]]
AEROM_STALL_PIT = bind_add_param('STALL_PIT', 24, -20)

-- 25 was AEROM_KE_TC

--[[
    // @Param: AEROM_KE_RUDD
    // @DisplayName: KnifeEdge Rudder
    // @Description: Percent of rudder normally uses to sustain knife-edge at trick speed
    // @Units: %
--]]
AEROM_KE_RUDD = bind_add_param('KE_RUDD', 26, 25)

--[[
    // @Param: AEROM_KE_RUDD_LK
    // @DisplayName: KnifeEdge Rudder lookahead
    // @Description: Time to look ahead in the path to calculate rudder correction for bank angle
    // @Units: s
--]]
AEROM_KE_RUDD_LK = bind_add_param('KE_RUDD_LK', 27, 0.25)

--[[
    // @Param: AEROM_ALT_ABORT
    // @DisplayName: Altitude Abort
    // @Description: Maximum allowable loss in altitude during a trick or sequence from its starting altitude.
    // @Units: m
--]]
AEROM_ALT_ABORT = bind_add_param('ALT_ABORT',28,15)

--[[
    // @Param: AEROM_TS_P
    // @DisplayName: Timesync P gain
    // @Description: This controls how rapidly two aircraft are brought back into time sync
--]]
AEROM_TS_P = bind_add_param('TS_P', 29, 0.33)

--[[
    // @Param: AEROM_TS_I
    // @DisplayName: Timesync I gain
    // @Description: This controls how rapidly two aircraft are brought back into time sync
--]]
AEROM_TS_I = bind_add_param('TS_I', 30, 0.33)

--[[
    // @Param: AEROM_TS_SPDMAX
    // @DisplayName: Timesync speed max
    // @Description: This sets the maximum speed adjustment for time sync between aircraft
    // @Units: m/s
--]]
AEROM_TS_SPDMAX = bind_add_param('TS_SPDMAX', 31, 0.0)

--[[
    // @Param: AEROM_TS_RATE
    // @DisplayName: Timesync rate of send of NAMED_VALUE_FLOAT data
    // @Description: This sets the rate we send data for time sync between aircraft
    // @Units: Hz
--]]
AEROM_TS_RATE = bind_add_param('TS_RATE', 32, 4.0)

--[[
    // @Param: AEROM_MIS_ANGLE
    // @DisplayName: Mission angle
    // @Description: When set to a non-zero value, this is the assumed direction of the mission. Otherwise the waypoint angle is used
    // @Units: deg
--]]
AEROM_MIS_ANGLE = bind_add_param('MIS_ANGLE', 33, 0.0)

--[[
    // @Param: AEROM_OPTIONS
    // @DisplayName: Aerobatic options
    // @Description: Options to control aerobatic behavior
    // @Bitmask: 0:UseRTLOnAbort, 1:AddAtToMessages, 2:DualAircraftSynchronised
    // @Units: deg
--]]
AEROM_OPTIONS = bind_add_param('OPTIONS', 34, 0.0)

local OPTIONS = { ABORT_RTL=(1<<0), MSG_ADD_AT=(1<<1), DUAL_AIRCRAFT=(1<<2) }

--[[
   return true if an option is set
--]]
function option_set(option)
   local options = math.floor(AEROM_OPTIONS:get())
   return options & option ~= 0
end


-- cope with old param values
if AEROM_ANG_ACCEL:get() < 100 and AEROM_ANG_ACCEL:get() > 0 then
   AEROM_ANG_ACCEL:set_and_save(3000)
end
if AEROM_ANG_TC:get() > 1.0 then
   AEROM_ANG_TC:set_and_save(0.2)
end

ACRO_ROLL_RATE = Parameter("ACRO_ROLL_RATE")
ACRO_YAW_RATE = Parameter('ACRO_YAW_RATE')
ARSPD_FBW_MIN = Parameter("ARSPD_FBW_MIN")
SCALING_SPEED = Parameter("SCALING_SPEED")
SYSID_THISMAV = Parameter("SYSID_THISMAV")

GRAVITY_MSS = 9.80665

--[[
   list of attributes that can be added to a path element
--]]
local path_attribs = { "roll_ref", "set_orient", "rate_override", "thr_boost", "pos_corr", "message", "shift_xy", "timestamp", "pos_gain_mul" }

--[[
   Aerobatic tricks on a switch support - allows for tricks to be initiated outside AUTO mode
--]]
-- 2nd param table for tricks on a switch
local PARAM_TABLE_KEY2 = 71
local PARAM_TABLE_PREFIX2 = "TRIK"
assert(param:add_table(PARAM_TABLE_KEY2, PARAM_TABLE_PREFIX2, 63), 'could not add param table2')

-- add a parameter and bind it to a variable in table2
function bind_add_param2(name, idx, default_value)
    assert(param:add_param(PARAM_TABLE_KEY2, idx, name, default_value), string.format('could not add param %s', name))
    return Parameter(PARAM_TABLE_PREFIX2 .. name)
end
--[[
    // @Param: TRIK_ENABLE
    // @DisplayName: Tricks on Switch Enable
    // @Description: Enables Tricks on Switch. TRIK params hidden until enabled
--]]
local TRIK_ENABLE = bind_add_param2("_ENABLE", 1, 0)
local TRICKS = nil
local TRIK_SEL_FN = nil
local TRIK_ACT_FN = nil
local TRIK_COUNT  = nil


local function TrickDef(id, arg1, arg2, arg3, arg4)
   local self = {}
   self.id = id
   self.args = {arg1, arg2, arg3, arg4}
   return self
end

-- constrain a value between limits
local function constrain(v, vmin, vmax)
   if v < vmin then
      v = vmin
   end
   if v > vmax then
      v = vmax
   end
   return v
end

local function sq(x)
   return x*x
end

if TRIK_ENABLE:get() > 0 then
--[[
    // @Param: TRIK_SEL_FN
    // @DisplayName: Trik Selection Scripting Function
    // @Description: Setting an RC channel's _OPTION to this value will use it for trick selection
    // @Range: 301 307
--]]
   TRIK_SEL_FN = bind_add_param2("_SEL_FN", 2, 301)
--[[
    // @Param: TRIK_ACT_FN
    // @DisplayName: Trik Action Scripting Function
    // @Description: Setting an RC channel's _OPTION to this value will use it for trick action (abort,announce,execute)
    // @Range: 301 307
--]]
   TRIK_ACT_FN = bind_add_param2("_ACT_FN", 3, 300)
--[[
    // @Param: TRIK_COUNT
    // @DisplayName: Trik Count
    // @Description: Number of tricks which can be selected over the range of the trik selection RC channel
    // @Range: 1 11
--]]
   TRIK_COUNT  = bind_add_param2("_COUNT",  4, 3)
   TRICKS = {}

   -- setup parameters for tricks
   local count = math.floor(constrain(TRIK_COUNT:get(),1,11))
   for i = 1, count do
      local k = 5*i
      local prefix = string.format("%u", i)
      TRICKS[i] = TrickDef(bind_add_param2(prefix .. "_ID",   k+0, -1),
                           bind_add_param2(prefix .. "_ARG1", k+1, 30),
                           bind_add_param2(prefix .. "_ARG2", k+2, 0),
                           bind_add_param2(prefix .. "_ARG3", k+3, 0),
                           bind_add_param2(prefix .. "_ARG4", k+4, 0))
   end
   gcs:send_text(MAV_SEVERITY.ALERT, string.format("Enabled %u aerobatic tricks", TRIK_COUNT:get()))
end

local NAV_SCRIPT_TIME = 42702

local MODE_AUTO = 10
local MODE_RTL = 11

local LOOP_RATE = 40
local DO_JUMP = 177
local k_throttle = 70
local NAME_FLOAT_RATE = 2

local TRIM_ARSPD_CM = Parameter("TRIM_ARSPD_CM")

local last_id = 0
local current_task = nil
local last_named_float_t = 0
local last_named_float_send_t = 0

local path_var = {}

local function wrap_360(angle)
   local res = math.fmod(angle, 360.0)
    if res < 0 then
        res = res + 360.0
    end
    return res
end

local function wrap_180(angle)
    local res = wrap_360(angle)
    if res > 180 then
       res = res - 360
    end
    return res
end

local function wrap_pi(angle)
   local angle_deg = math.deg(angle)
   local angle_wrapped = wrap_180(angle_deg)
   return math.rad(angle_wrapped)
end

local function wrap_2pi(angle)
   local angle_deg = math.deg(angle)
   local angle_wrapped = wrap_360(angle_deg)
   return math.rad(angle_wrapped)
end


--[[
   calculate an alpha for a first order low pass filter
--]]
local function calc_lowpass_alpha(dt, time_constant)
   local rc = time_constant/(math.pi*2)
   return dt/(dt+rc)
end

--[[ get the c.y element of a quaternion, which gives
   the projection of the vehicle y axis in the down direction
   This is equal to sin(roll)*cos(pitch)
--]]
local function get_quat_dcm_c_y(q)
   local q1 = q:q1()
   local q2 = q:q2()
   local q3 = q:q3()
   local q4 = q:q4()
   local q3q4 = q3 * q4
   local q1q2 = q1 * q2
   return 2*(q3q4 + q1q2)
end

--[[ get the c.y element of the DCM body to earth matrix, which gives
   the projection of the vehicle y axis in the down direction
   This is equal to sin(roll)*cos(pitch)
--]]
local function get_ahrs_dcm_c_y()
   return get_quat_dcm_c_y(ahrs:get_quaternion())
end

-- a PI controller implemented as a Lua object
local function PI_controller(kP,kI,iMax,min,max)
   -- the new instance. You can put public variables inside this self
   -- declaration if you want to
   local self = {}

   -- private fields as locals
   local _kP = kP or 0.0
   local _kI = kI or 0.0
   local _iMax = iMax
   local _min = min
   local _max = max
   local _last_t = nil
   local _I = 0
   local _P = 0
   local _total = 0
   local _counter = 0
   local _target = 0
   local _current = 0

   -- update the controller.
   function self.update(target, current)
      local now = millis():tofloat() * 0.001
      if not _last_t then
         _last_t = now
      end
      local dt = now - _last_t
      _last_t = now
      local err = target - current
      _counter = _counter + 1

      local P = _kP * err
      if ((_total < _max and _total > _min) or (_total >= _max and err < 0) or (_total <= _min and err > 0)) then
         _I = _I + _kI * err * dt
      end
      if _iMax then
         _I = constrain(_I, -_iMax, iMax)
      end
      local I = _I
      local ret = P + I

      _target = target
      _current = current
      _P = P

      ret = constrain(ret, _min, _max)
      _total = ret
      return ret
   end

   -- reset integrator to an initial value
   function self.reset(integrator)
      _I = integrator
   end

   function self.set_I(I)
      _kI = I
   end

   function self.set_P(P)
      _kP = P
   end
   
   function self.set_Imax(Imax)
      _iMax = Imax
   end
   
   -- log the controller internals
   function self.log(name, add_total)
      -- allow for an external addition to total
      logger.write(name,'Targ,Curr,P,I,Total,Add','ffffff',_target,_current,_P,_I,_total,add_total)
   end
   -- return the instance
   return self
end

local function speed_controller(kP_param,kI_param, kFF_pitch_param, Imax, min, max)
   local self = {}
   local kFF_pitch = kFF_pitch_param
   local PI = PI_controller(kP_param:get(), kI_param:get(), Imax, min, max)

   function self.update(target, anticipated_pitch_rad)
      local current_speed = ahrs:get_velocity_NED():length()
      local throttle = PI.update(target, current_speed)
      local FF = math.sin(anticipated_pitch_rad)*kFF_pitch:get()
      PI.log("AESP", FF)
      return throttle + FF
   end

   function self.reset()
      PI.reset(0)
      local temp_throttle = self.update(ahrs:get_velocity_NED():length(), 0)
      local current_throttle = SRV_Channels:get_output_scaled(k_throttle)
      PI.reset(current_throttle-temp_throttle)
   end

   return self
end

local speed_PI = speed_controller(SPD_P, SPD_I, THR_PIT_FF, 100.0, 0.0, 100.0)

local function speed_adjust_controller(kP_param, kI_param)
   local self = {}
   local spd_max = AEROM_TS_SPDMAX:get()
   local PI = PI_controller(kP_param:get(), kI_param:get(), spd_max, -spd_max, spd_max)

   function self.update(spd_error)
      local adjustment = PI.update(0, spd_error)
      PI.log("AESA", 0)
      return adjustment
   end

   function self.reset()
      PI.reset(0)
   end

   return self
end

local speed_adjustment_PI = speed_adjust_controller(AEROM_TS_P, AEROM_TS_I)

function sgn(x)
   local eps = 0.000001
   if (x > eps) then
      return 1.0
   elseif x < eps then
      return -1.0
   else
      return 0.0
   end
end

local function get_wp_location(i)
   local m = mission:get_item(i)
   local loc = Location()
   loc:lat(m:x())
   loc:lng(m:y())
   loc:relative_alt(true)
   loc:terrain_alt(false)
   loc:origin_alt(false)
   loc:alt(math.floor(m:z()*100))
   return loc
end

local function resolve_jump(i)
   local m = mission:get_item(i)
   while m:command() == DO_JUMP do
      i = math.floor(m:param1())
      m = mission:get_item(i)
   end
   return i
end

--[[
   Wrapper to construct a Vector3f{x, y, z} from (x, y, z)
--]]
local function makeVector3f(x, y, z)
   local vec = Vector3f()
   vec:x(x)
   vec:y(y)
   vec:z(z)
   return vec
end

--[[
   get quaternion rotation between vector1 and vector2
   with thanks to https://stackoverflow.com/questions/1171849/finding-quaternion-representing-the-rotation-from-one-vector-to-another
--]]
local function vectors_to_quat_rotation(vector1, vector2)
   local v1 = vector1:copy()
   local v2 = vector2:copy()
   v1:normalize()
   v2:normalize()
   local dot = v1:dot(v2)
   local a = v1:cross(v2)
   local w = 1.0 + dot
   local q = Quaternion()
   q:q1(w)
   q:q2(a:x())
   q:q3(a:y())
   q:q4(a:z())
   q:normalize()
   return q
end

--[[
   get path rate from two tangents and delta time
--]]
local function tangents_to_rate(t1, t2, dt)
   local q_delta = vectors_to_quat_rotation(t1, t2)
   local rate_rads = Vector3f()
   q_delta:to_axis_angle(rate_rads)
   rate_rads = rate_rads:scale(1.0/dt)
   return rate_rads
end

--[[
   create a class that inherits from a base class
--]]
local function inheritsFrom(baseClass, _name)
    local new_class = { name = _name }
    local class_mt = { __index = new_class }

    function new_class:create()
        local newinst = {}
        setmetatable( newinst, class_mt )
        return newinst
    end

    if nil ~= baseClass then
        setmetatable( new_class, { __index = baseClass } )
    end

    return new_class
end

--[[
   return a quaternion for a roll, pitch, yaw (321 euler sequence) attitude
--]]
function qorient(roll_deg, pitch_deg, yaw_deg)
   local q = Quaternion()
   q:from_euler(math.rad(roll_deg), math.rad(pitch_deg), math.rad(yaw_deg))
   return q
end

--[[
   rotate a vector by a quaternion
--]]
local function quat_earth_to_body(quat, v)
   local v2 = v:copy()
   quat:earth_to_body(v2)
   return v2
end

--[[
   rotate a vector by a inverse quaternion
--]]
local function quat_body_to_earth(quat, v)
   local v2 = v:copy()
   quat:inverse():earth_to_body(v2)
   return v2
end

--[[
   copy a quaternion
--]]
local function quat_copy(q)
   return q:inverse():inverse()
end


--[[
   trajectory building blocks. We have two types of building blocks,
   roll blocks and path blocks. These are combined to give composite paths
--]]


--[[
  roll component that goes through a fixed total angle at a fixed roll rate
--]]
local _roll_angle = inheritsFrom(nil, 'roll_angle')
function _roll_angle:get_roll(t)
   if self.angle == nil then
      return 0
   end
   return self.angle * t
end
function roll_angle(angle)
   local self = _roll_angle:create()
   if angle ~= 0 then
      self.angle = angle
   end
   return self
end

--[[
   roll component that banks to _angle over AEROM_ENTRY_RATE
   degrees/s, then holds that angle, then banks back to zero at
   AEROM_ENTRY_RATE degrees/s
--]]
local _roll_angle_entry_exit = inheritsFrom(nil, "roll_angle_entry_exit")
function _roll_angle_entry_exit:get_roll(t, time_s)
   local entry_s = math.abs(self.angle) / AEROM_ENTRY_RATE:get()
   local entry_t = entry_s / time_s
   if entry_t > 0.5 then
      entry_t = 0.5
   end
   if t <= 0 then
      return 0
   end
   if t < entry_t then
      return self.angle * t / entry_t
   end
   if t < 1.0 - entry_t then
      return self.angle
   end
   if self.angle == 0 or t >= 1.0 then
      return 0
   end
   return (1.0 - ((t - (1.0 - entry_t)) / entry_t)) * self.angle
end

function roll_angle_entry_exit(angle)
   local self = _roll_angle_entry_exit:create()
   self.angle = angle
   return self
end

--[[
   roll component that banks to _angle over AEROM_ENTRY_RATE
   degrees/s, then holds that angle
--]]
local _roll_angle_entry = inheritsFrom(nil, "roll_angle_entry")
function _roll_angle_entry:get_roll(t, time_s)
   local entry_s = math.abs(self.angle) / AEROM_ENTRY_RATE:get()
   local entry_t = entry_s / time_s
   if entry_t > 0.5 then
      entry_t = 0.5
   end
   if t < entry_t then
      return self.angle * t / entry_t
   end
   return self.angle
end

function roll_angle_entry(angle)
   local self = _roll_angle_entry:create()
   self.angle = angle
   return self
end

--[[
   roll component that holds angle until the end of the subpath, then
   rolls back to 0 at the AEROM_ENTRY_RATE
--]]
local _roll_angle_exit = inheritsFrom(nil, "roll_angle_exit")
function _roll_angle_exit:get_roll(t, time_s)
   local entry_s = math.abs(self.angle) / AEROM_ENTRY_RATE:get()
   local entry_t = entry_s / time_s
   if t < 1.0 - entry_t then
      return 0
   end
   if self.angle == 0 then
      return 0
   end
   return ((t - (1.0 - entry_t)) / entry_t) * self.angle
end

function roll_angle_exit(angle)
   local self = _roll_angle_exit:create()
   self.angle = angle
   return self
end

--[[
   implement a sequence of rolls, specified as a list of {proportion, roll_angle} pairs
--]]
local _roll_sequence = inheritsFrom(nil, "roll_sequence")
function _roll_sequence:get_roll(t)
   for i = 1, #self.seq do
      if t <= self.end_t[i] then
         local t2 = (t - self.start_t[i])/(self.seq[i][1]/self.total)
         return self.start_ang[i] + t2 * self.seq[i][2]
      end
   end
   -- we've gone past the end
   return self.start_ang[#self.seq] + self.seq[#self.seq][2]
end

function roll_sequence(seq)
   local self = _roll_sequence:create()
   self.seq = seq
   self.total = 0.0
   self.end_t = {}
   self.start_t = {}
   self.start_ang = {}
   for i = 1, #seq do
      self.total = self.total + seq[i][1]
   end
   local t = 0.0
   local angle = 0.0
   for i = 1, #seq do
      self.start_t[i] = t
      self.start_ang[i] = angle
      angle = angle + seq[i][2]
      t = t + seq[i][1]/self.total
      self.end_t[i] = t
   end
   return self
end

--[[ given a path function get_pos() calculate the extents of the path
   along the X axis as a tuple
--]]
local function get_extents_x(obj)
   local p = obj:get_pos(0)
   local min_x = p:x()
   local max_x = min_x
   for t=0, 1, 0.02 do
      p = obj:get_pos(t)
      min_x = math.min(min_x, p:x())
      max_x = math.max(max_x, p:x())
   end
   return { min_x, max_x }
end


--[[
  all path components inherit from PathComponent
--]]
local _PathComponent = inheritsFrom(nil)
function _PathComponent:get_pos(t)
   return makeVector3f(0, 0, 0)
end
function _PathComponent:get_length()
   return 0
end
function _PathComponent:get_final_orientation()
   return Quaternion()
end
function _PathComponent:get_roll_correction(t)
   return 0
end
function _PathComponent:get_attribute(t, attrib)
   return self[attrib]
end
function _PathComponent:get_extents_x()
   if self.extents ~= nil then
      return self.extents
   end
   self.extents = get_extents_x(self)
   return self.extents
end

--[[
   path component that does a straight horizontal line
--]]
local _path_straight = inheritsFrom(_PathComponent, "path_straight")
function _path_straight:get_pos(t)
   return makeVector3f(self.distance*t, 0, 0)
end
function _path_straight:get_length()
   return self.distance
end
function path_straight(distance)
   local self = _path_straight:create()
   self.distance = distance
   return self
end

--[[
   path component that does a straight line then reverses direction
--]]
local _path_reverse = inheritsFrom(_PathComponent, "path_reverse")
function _path_reverse:get_pos(t)
   if t < 0.5 then
      return makeVector3f(self.distance*t*2, 0, 0)
   else
      return makeVector3f(self.distance-(self.distance*(t-0.5)*2), 0, 0)
   end
end
function _path_reverse:get_length()
      return self.distance*2
end
function path_reverse(distance)
   local self = _path_reverse:create()
   self.distance = distance
   return self
end

--[[
   path component that aligns to within the aerobatic box
--]]
local _path_align_box = inheritsFrom(_PathComponent, "path_align_box")
function _path_align_box:get_pos(t)
   return makeVector3f(self.distance*t, 0, 0)
end
function _path_align_box:get_length()
   return self.distance
end
function _path_align_box:set_next_extents(extents, start_pos, start_orientation)
   local box_half = AEROM_BOX_WIDTH:get()/2
   local start_x = start_pos:x()
   local next_max_x = extents[2]
   if math.abs(math.deg(start_orientation:get_euler_yaw())) > 90 then
      -- we are on a reverse path
      self.distance = (box_half * self.alignment) + start_x - next_max_x
   else
      -- we are on a forward path
      self.distance = (box_half * self.alignment) - start_x - next_max_x
   end
   self.distance = math.max(self.distance, 0.01)
end
function path_align_box(alignment)
   local self = _path_align_box:create()
   self.distance = nil
   self.alignment = alignment
   return self
end

--[[
   path component that aligns so the center of the next maneuver is
   centered within the aerobatic box
--]]
local _path_align_center = inheritsFrom(_PathComponent, "path_align_center")
function _path_align_center:get_pos(t)
   return makeVector3f(self.distance*t, 0, 0)
end
function _path_align_center:get_length()
   return self.distance
end
function _path_align_center:set_next_extents(extents, start_pos, start_orientation)
   local start_x = start_pos:x()
   local next_mid_x = (extents[1]+extents[2])*0.5
   if math.abs(math.deg(start_orientation:get_euler_yaw())) > 90 then
      -- we are on a reverse path
      self.distance = start_x - next_mid_x
   else
      -- we are on a forward path
      self.distance = - start_x - next_mid_x
   end
   self.distance = math.max(self.distance, 0.01)
end

function path_align_center()
   local self = _path_align_center:create()
   self.distance = nil
   return self
end

--[[
   path component that does a vertical arc over a given angle
--]]
local _path_vertical_arc = inheritsFrom(_PathComponent, "path_vertical_arc")
function _path_vertical_arc:get_pos(t)
   local t2ang = wrap_2pi(t * math.rad(self.angle))
   return makeVector3f(math.abs(self.radius)*math.sin(t2ang), 0, -self.radius*(1.0 - math.cos(t2ang)))
end
function _path_vertical_arc:get_length()
   return math.abs(self.radius) * 2 * math.pi * math.abs(self.angle) / 360.0
end
function _path_vertical_arc:get_final_orientation()
   local q = Quaternion()
   q:from_axis_angle(makeVector3f(0,1,0), sgn(self.radius)*math.rad(wrap_180(self.angle)))
   q:normalize()
   return q
end
function path_vertical_arc(radius, angle)
   local self = _path_vertical_arc:create()
   self.radius = radius
   self.angle = angle
   return self
end

--[[
   path component that does a horizontal arc over a given angle
--]]
local _path_horizontal_arc = inheritsFrom(_PathComponent, "path_horizontal_arc")
function _path_horizontal_arc:get_pos(t)
   local t2ang = t * math.rad(self.angle)
   return makeVector3f(math.abs(self.radius)*math.sin(t2ang), self.radius*(1.0 - math.cos(t2ang)), -self.height_gain*t)
end
function _path_horizontal_arc:get_length()
   local circumference = 2 * math.pi * math.abs(self.radius)
   local full_circle_height_gain = self.height_gain * 360.0 / math.abs(self.angle)
   local helix_length = math.sqrt(full_circle_height_gain*full_circle_height_gain + circumference*circumference)
   return helix_length * math.abs(self.angle) / 360.0
end
function _path_horizontal_arc:get_final_orientation()
   local q = Quaternion()
   q:from_axis_angle(makeVector3f(0,0,1), sgn(self.radius)*math.rad(self.angle))
   return q
end

--[[
   roll correction for the rotation caused by height gain
--]]
function _path_horizontal_arc:get_roll_correction(t)
   if self.height_gain == 0 then
      return 0
   end
   local gamma=math.atan(self.height_gain*(360/self.angle)/(2*math.pi*self.radius))
   return -t*self.angle*math.sin(gamma)
end

function path_horizontal_arc(radius, angle, height_gain)
   local self = _path_horizontal_arc:create()
   self.radius = radius
   self.angle = angle
   self.height_gain = height_gain or 0
   return self
end

--[[
   path component that does a cylinder for a barrel roll
--]]
local _path_cylinder = inheritsFrom(_PathComponent, "path_cylinder")
function _path_cylinder:get_pos(t)
   local t2ang = t * self.num_spirals * math.pi * 2
   local v = makeVector3f(self.length*t, math.abs(self.radius)*math.sin(t2ang+math.pi), -math.abs(self.radius)*(1.0 - math.cos(t2ang)))
   local qrot = Quaternion()
   qrot:from_axis_angle(makeVector3f(0,0,1), (0.5*math.pi)-self.gamma)
   v = quat_earth_to_body(qrot, v)
   if self.radius < 0 then
      -- mirror for reverse radius
      v:y(-v:y())
   end
   return v
end

function _path_cylinder:get_length()
   local circumference = 2 * math.pi * math.abs(self.radius)
   local length_per_spiral = self.length / self.num_spirals
   local helix_length = math.sqrt(length_per_spiral*length_per_spiral + circumference*circumference)
   return helix_length * self.num_spirals
end

--[[
   roll correction for the rotation caused by the path
--]]
function _path_cylinder:get_roll_correction(t)
   return sgn(self.radius)*t*360*math.sin(self.gamma)*self.num_spirals
end

function path_cylinder(radius, length, num_spirals)
   local self = _path_cylinder:create()
   self.radius = radius
   self.length = length
   self.num_spirals = num_spirals
   self.gamma = math.atan((length/num_spirals)/(2*math.pi*math.abs(radius)))
   return self
end

--[[
   a Path has the methods of both RollComponent and
   PathComponent allowing for a complete description of a subpath
--]]
local _Path = inheritsFrom(nil)
function _Path:get_roll(t, time_s)
   return wrap_180(self.roll_component:get_roll(t, time_s))
end
function _Path:get_roll_correction(t)
   return self.path_component:get_roll_correction(t)
end
function _Path:get_pos(t)
   return self.path_component:get_pos(t)
end
function _Path:get_length()
   return self.path_component:get_length()
end
function _Path:get_final_orientation()
   return self.path_component:get_final_orientation()
end
function _Path:get_attribute(t, attrib)
   return self[attrib]
end
function _Path:set_next_extents(extents, start_pos, start_orientation)
   self.path_component:set_next_extents(extents, start_pos, start_orientation)
end
local function Path(path_component, roll_component)
   local self = _Path:create()
   self.name = string.format("%s|%s", path_component.name, roll_component.name)
   assert(path_component)
   assert(roll_component)
   self.path_component = path_component
   self.roll_component = roll_component
   return self
end


--[[
   componse multiple sub-paths together to create a full trajectory
--]]
local _path_composer = inheritsFrom(nil)
-- return the subpath with index i. Used to cope with two ways of calling path_composer
function _path_composer:subpath(i)
   if i == self.cache_i then
      return self.cache_sp
   end
   self.cache_i = i
   local sp = self.subpaths[i]
   if sp.name then
      -- we are being called with a list of Path objects
      self.cache_sp = sp
   else
      -- we are being called with a list function/argument tuples
      local args = self.subpaths[i][2]
      self.cache_sp = self.subpaths[i][1](args[1], args[2], args[3], args[4], self.start_pos[i], self.start_orientation[i])
      -- copy over path attributes
      for _, v in pairs(path_attribs) do
         self.cache_sp[v] = self.subpaths[i][v]
      end
   end
   return self.cache_sp
end

function _path_composer:end_time(i)
   local proportion = self.lengths[i] / self.total_length
   return self.start_time[i] + proportion
end

function _path_composer:get_subpath_t(t)
   if self.last_subpath_t[1] == t then
      -- use cached value
      return self.last_subpath_t[2], self.last_subpath_t[3]
   end
   local i = 1
   while t >= self:end_time(i) and i < self.num_sub_paths do
      i = i + 1
   end
   local proportion = self.lengths[i]/self.total_length
   local subpath_t = (t - self.start_time[i]) / proportion
   self.last_subpath_t = { t, subpath_t, i }
   local sp = self:subpath(i)
   if i > self.highest_i and t < 1.0 and t > 0 then
      self.highest_i = i
      if sp.message ~= nil then
         local msg = sp.message
         if option_set(OPTIONS.MSG_ADD_AT) then
            msg = "@" .. msg
         end
         gcs:send_text(MAV_SEVERITY.ALERT, msg)
      end
      if AEROM_DEBUG:get() > 0 then
         gcs:send_text(MAV_SEVERITY.ALERT, string.format("starting %s[%d] %s", self.name, i, sp.name))
      end
   end
   return subpath_t, i
end

-- return position at time t
function _path_composer:get_pos(t)
   local subpath_t, i = self:get_subpath_t(t)
   local sp = self:subpath(i)
   return quat_earth_to_body(self.start_orientation[i], sp:get_pos(subpath_t)) + self.start_pos[i]
end

-- return angle for the composed path at time t
function _path_composer:get_roll(t, time_s)
   local subpath_t, i = self:get_subpath_t(t)
   local speed = target_groundspeed()
   local sp = self:subpath(i)
   local angle = sp:get_roll(subpath_t, self.lengths[i]/speed)
   return angle + self.start_angle[i]
end

function _path_composer:get_roll_correction(t)
   local subpath_t, i = self:get_subpath_t(t)
   local sp = self:subpath(i)
   return sp:get_roll_correction(subpath_t) + (self.start_roll_correction[i] or 0)
end
   
function _path_composer:get_length()
   return self.total_length
end

function _path_composer:get_final_orientation()
   return self.final_orientation
end

function _path_composer:get_attribute(t, attrib)
   local subpath_t, i = self:get_subpath_t(t)
   local sp = self:subpath(i)
   return sp[attrib] or sp:get_attribute(subpath_t, attrib)
end

function _path_composer:get_extents_x()
   if self.extents ~= nil then
      return self.extents
   end
   self.extents = get_extents_x(self)
   return self.extents
end

function _path_composer:calculate_timestamps()
   self.timestamp_start = {}
   self.timestamp_start[1] = 0.0
   self.have_timestamps = false
   for i = 1, self.num_sub_paths do
      local sp = self:subpath(i)
      local timestamp = sp.timestamp
      if timestamp then
         self.timestamp_start[i] = timestamp
         self.have_timestamps = true
      end
   end
   if self.have_timestamps then
      local tstart = 0.0
      for i = 2, self.num_sub_paths do
         if not self.timestamp_start[i] then
            -- find the next element with a timestamp, getting total length
            local length_sum = self:subpath(i-1):get_length()
            for j = i, self.num_sub_paths do
               if self.timestamp_start[j] then
                  --gcs:send_text(MAV_SEVERITY.ALERT, string.format("found %u %u %.3f ts=%.3f", i, j, length_sum, tstart))
                  for k = i, j-1 do
                     local len = self:subpath(k):get_length()
                     self.timestamp_start[k] = tstart +  len / length_sum
                     --gcs:send_text(MAV_SEVERITY.ALERT, string.format("ts[%u] %.3f %.2f/%.2f", k, self.timestamp_start[k], len, length_sum))
                  end
                  break
               end
               length_sum = length_sum + self:subpath(j):get_length()
            end
         else
            tstart = self.timestamp_start[i]
         end
      end
      self.timestamp_start[self.num_sub_paths+1] = self.timestamp_start[self.num_sub_paths]+1.0
   end

   self.patht_start = {}
   self.patht_start[1] = 0.0
   self.patht_start[self.num_sub_paths+1] = 1.0
   local total_length = self:get_length()
   for i = 2, self.num_sub_paths do
      self.patht_start[i] = self.patht_start[i-1] + self:subpath(i-1):get_length() / total_length
   end

   if self.have_timestamps then
      gcs:send_text(MAV_SEVERITY.INFO,"Calculated timestamps")
   end
end

function _path_composer:patht_to_timestamp(path_t)
   path_t = constrain(path_t, 0.0, 1.0)
   if not self.have_timestamps then
      return path_t
   end
   for i = 1, self.num_sub_paths do
      if self.patht_start[i+1] >= path_t then
         local dt = path_t - self.patht_start[i]
         local p = dt / (self.patht_start[i+1] - self.patht_start[i])
         return self.timestamp_start[i] + p * (self.timestamp_start[i+1] - self.timestamp_start[i])
      end
   end
   return self.timestamp_start[self.num_sub_paths+1]
end

function _path_composer:timestamp_to_patht(tstamp)
   if not self.have_timestamps then
      return tstamp
   end
   tstamp = constrain(tstamp, 0.0, self.timestamp_start[self.num_sub_paths+1])
   for i = 1, self.num_sub_paths do
      if self.timestamp_start[i+1] >= tstamp then
         local dt = tstamp - self.timestamp_start[i]
         local p = dt / (self.timestamp_start[i+1] - self.timestamp_start[i])
         return self.patht_start[i] + p * (self.patht_start[i+1] - self.patht_start[i])
      end
   end
   return 1.0
end

--[[
   get the time that the next segment starts
--]]
function _path_composer:get_next_segment_start(t)
   local subpath_t, i = self:get_subpath_t(t)
   local sp = self:subpath(i)
   if sp.get_next_segment_start ~= nil then
      return self.start_time[i] + (sp:get_next_segment_start(subpath_t) * (self:end_time(i) - self.start_time[i]))
   end
   return self:end_time(i)
end

local function path_composer(name, subpaths)
   local self = _path_composer:create()
   self.name = name
   self.subpaths = subpaths
   self.lengths = {}
   self.start_time = {}
   self.start_orientation = {}
   self.start_pos = {}
   self.start_angle = {}
   self.start_roll_correction = {}
   self.total_length = 0
   self.num_sub_paths = #subpaths
   self.last_subpath_t = { -1, 0, 0 }
   self.highest_i = 0

   local orientation = Quaternion()
   local pos = makeVector3f(0,0,0)
   local angle = 0
   local roll_correction = 0
   local speed = target_groundspeed()

   for i = 1, self.num_sub_paths do
      -- accumulate orientation, position and angle
      self.start_orientation[i] = quat_copy(orientation)
      self.start_pos[i] = pos:copy()
      self.start_angle[i] = angle
      if roll_correction ~= 0 then
         self.start_roll_correction[i] = roll_correction
      end

      local sp = self:subpath(i)

      self.lengths[i] = sp:get_length()
      if self.lengths[i] == nil and i < self.num_sub_paths then
         local sp2 = self:subpath(i+1)
         local next_extents = sp2:get_extents_x()
         if next_extents ~= nil then
            sp:set_next_extents(next_extents, self.start_pos[i], self.start_orientation[i])
            self.lengths[i] = sp:get_length()
            -- solidify this subpath now that it has its length calculated
            self.subpaths[i] = sp
         end
      end

      self.total_length = self.total_length + self.lengths[i]

      local spos = quat_earth_to_body(orientation, sp:get_pos(1.0))

      pos = pos + spos
      orientation = sp:get_final_orientation() * orientation
      orientation:normalize()

      angle = angle + sp:get_roll(1.0, self.lengths[i]/speed)
      roll_correction = roll_correction + sp:get_roll_correction(1.0)

      if sp.set_orient ~= nil then
         -- override orientation at this point in the sequence
         orientation = sp.set_orient
      end

      if sp.roll_ref ~= nil then
         local q = Quaternion()
         q:from_axis_angle(makeVector3f(1,0,0), math.rad(sp.roll_ref))
         orientation = orientation * q
         orientation:normalize()
      end
   end

   -- get our final orientation, including roll
   self.final_orientation = quat_copy(orientation)
   local q = Quaternion()
   q:from_axis_angle(makeVector3f(1,0,0), math.rad(wrap_180(angle)))
   self.final_orientation = q * self.final_orientation

   -- work out the proportion of the total time we will spend in each sub path
   local total_time = 0
   for i = 1, self.num_sub_paths do
      self.start_time[i] = total_time
      local proportion = self.lengths[i]/self.total_length
      total_time = total_time + proportion
   end
   return self
end


--[[
   make a list of Path() objects from a list of PathComponent, RollComponent pairs
--]]
function make_paths(name, paths)
   local p = {}
   for i = 1, #paths do
      if paths[i][2] == nil then
         p[i] = paths[i][1]
      else
         p[i] = Path(paths[i][1], paths[i][2])
      end
      -- copy over path attributes
      for _, v in pairs(path_attribs) do
         if paths[i][v] ~= nil then
            p[i][v] = paths[i][v]
         end
      end
   end
   return path_composer(name, p)
end

--[[
   composed trajectories, does as individual aerobatic maneuvers
--]]

function climbing_circle(radius, height, bank_angle, arg4)
   return make_paths("climbing_circle", {
         { path_horizontal_arc(radius, 360, height), roll_angle_entry_exit(bank_angle) },
   })
end

function half_climbing_circle(radius, height, bank_angle, arg4)
   return make_paths("half_climbing_circle", {
         { path_horizontal_arc(radius, 180, height), roll_angle_entry_exit(bank_angle) },
   })
end

function partial_circle(radius, bank_angle, angle)
   return make_paths("partial_circle", {
         { path_horizontal_arc(radius, angle, 0), roll_angle_entry_exit(bank_angle) },
   })
end

function loop(radius, bank_angle, num_loops, arg4)
   if not num_loops or num_loops <= 0 then
      num_loops = 1
   end
   return make_paths("loop", {
         { path_vertical_arc(radius, 360*num_loops), roll_angle_entry_exit(bank_angle) },
   })
end

function straight_roll(length, num_rolls, arg3, arg4)
   return make_paths("straight_roll", {
         { path_straight(length), roll_angle(num_rolls*360) },
   })
end

--[[
   fly straight until we are distance meters from the composite path
   origin in the maneuver frame along the X axis. If we are already
   past that position then return immediately
--]]
function straight_align(distance, arg2, arg3, arg4, start_pos, start_orientation)
   local d2 = distance - start_pos:x()
   local v = quat_earth_to_body(start_orientation, makeVector3f(d2, 0, 0))
   local len = math.max(v:x(),0.01)
   return make_paths("straight_align", {
         { path_straight(len), roll_angle(0) },
   })
end

--[[
   fly straight so that the next maneuver in the sequence ends at
   the given proportion of the aerobatic box
--]]
function align_box(alignment, arg2, arg3, arg4)
   return Path(path_align_box(alignment), roll_angle(0))
end

--[[
   fly straight so that the next maneuver in the sequence is centered
   in the aerobatic box
--]]
function align_center(arg1, arg2, arg3, arg4)
   return Path(path_align_center(), roll_angle(0))
end

function immelmann_turn(r, arg2, arg3, arg4)
   local rabs = math.abs(r)
   return make_paths("immelmann_turn", {
         { path_vertical_arc(r, 180),      roll_angle(0) },
         { path_straight(rabs),            roll_angle(180) },
   })
end

-- immelmann with max roll rate
function immelmann_turn_fast(r, arg2, arg3, arg4)
   local roll_time = 180.0 / ACRO_ROLL_RATE:get()
   local roll_dist = target_groundspeed() * roll_time
   return make_paths("immelmann_turn_fast", {
         { path_vertical_arc(r, 180),      roll_angle(0) },
         { path_straight(roll_dist),       roll_angle(180) },
   })
end

function humpty_bump(r, h, arg3, arg4)
   assert(h >= 2*r)
   local rabs = math.abs(r)
   return make_paths("humpty_bump", {
            { path_vertical_arc(r, 90),             roll_angle(0) },
            { path_straight((h-2*rabs)/3),          roll_angle(0) },
            { path_straight((h-2*rabs)/3),          roll_angle(180) },
            { path_straight((h-2*rabs)/3),          roll_angle(0) },
            { path_vertical_arc(-r, 180),           roll_angle(0) },
            { path_straight(h-2*rabs),              roll_angle(0) },
            { path_vertical_arc(-r, 90),            roll_angle(0) },
            { path_straight(2*rabs),                roll_angle(0) },
   })
end

function laydown_humpty(r, h, arg3, arg4)
   assert(h >= 2*r)
   local rabs = math.abs(r)
   return make_paths("laydown_humpty", {
            { path_vertical_arc(r, 45),          roll_angle(0) },
            { path_straight((h-2*rabs)/3),       roll_angle(0) },
            { path_straight((h-2*rabs)/3),       roll_angle(-90), roll_ref=90 },
            { path_straight((h-2*rabs)/3),       roll_angle(0) },
            { path_vertical_arc(r, 180),         roll_angle(0) },
            { path_straight((h-2*rabs)/3),       roll_angle(0) },
            { path_straight((h-2*rabs)/3),       roll_angle(90),  roll_ref=-90 },
            { path_straight((h-2*rabs)/3),       roll_angle(0) },
            { path_vertical_arc(-r, 45),         roll_angle(0), roll_ref=180},
   })
end

function split_s(r, arg2, arg3, arg4)
   local rabs = math.abs(r)
   return make_paths("split_s", {
         { path_straight(rabs/2),                roll_angle(180) },
         { path_vertical_arc(-r, 180),           roll_angle(0) },
   })
end

function upline_45(r, height_gain, arg3, arg4)
   --local h = (height_gain - 2*r*(1.0-math.cos(math.rad(45))))/math.sin(math.rad(45))
   local h = (height_gain - (2 * r) + (2 * r * math.cos(math.rad(45)))) / math.cos(math.rad(45))
  assert(h >= 0)
   return make_paths("upline_45", {
         { path_vertical_arc(r, 45),  roll_angle(0) },
         { path_straight(h),          roll_angle(0) },
         { path_vertical_arc(-r, 45), roll_angle(0) },
   })
end

function upline_20(r, height_gain, arg3, arg4)
   local h = (height_gain - 2*r*(1.0-math.cos(math.rad(20))))/math.sin(math.rad(20))
   assert(h >= 0)
   return make_paths("upline_45", {
         { path_vertical_arc(r, 20),  roll_angle(0) },
         { path_straight(h),          roll_angle(0) },
         { path_vertical_arc(-r, 20), roll_angle(0) },
   })
end

function downline_45(r, height_loss, arg3, arg4)
   local h = (height_loss - 2*r*(1.0-math.cos(math.rad(45))))/math.sin(math.rad(45))
   assert(h >= 0)
   return make_paths("downline_45", {
         { path_vertical_arc(-r, 45),  roll_angle(0) },
         { path_straight(h),           roll_angle(0) },
         { path_vertical_arc(r, 45),   roll_angle(0) },
   })
end

function rolling_circle(radius, num_rolls, arg3, arg4)
   return make_paths("rolling_circle", {
         { path_horizontal_arc(radius, 360), roll_angle(360*num_rolls), thr_boost=true },
   })
end

function barrel_roll(radius, length, num_spirals, arg4)
   local gamma_deg = math.deg(math.atan((length/num_spirals)/(2*math.pi*math.abs(radius))))
   local speed = target_groundspeed()
   local bank = math.deg(math.atan((speed*speed) / (radius * GRAVITY_MSS)))
   local radius2 = radius/(1.0 - math.cos(math.rad(90-gamma_deg)))

   return make_paths("barrel_roll", {
         { path_horizontal_arc(-radius2, 90-gamma_deg, 0), roll_angle_entry_exit(-bank) },
         { path_cylinder(radius, length, num_spirals),    roll_angle(0) },
         { path_horizontal_arc(radius2, 90-gamma_deg, 0),  roll_angle_entry_exit(bank) },
   })
end

function side_step(displacement, length, arg3, arg4)
   local speed = target_groundspeed()
   local radius = (displacement*displacement + length*length)/(4*displacement)
   local angle = math.deg(2*math.atan(displacement, length))
   local sign = sgn(displacement)
   local bank = math.deg(math.atan((speed*speed) / (radius * GRAVITY_MSS)))

   return make_paths("side_step",{
      {path_horizontal_arc(sign*radius, angle, 0), roll_angle_entry_exit(sign*bank)},
      {path_horizontal_arc(-sign*radius, angle, 0) , roll_angle_entry_exit(-sign*bank)},
   })
end

function straight_flight(length, bank_angle, arg3, arg4)
   return make_paths("straight_flight", {
         { path_straight(length), roll_angle_entry_exit(bank_angle) },
   })
end

function straight_hold(length, bank_angle, arg3, arg4)
   return make_paths("straight_hold", {
         { path_straight(length), roll_angle_entry(bank_angle) },
   })
end

function scale_figure_eight(r, bank_angle, arg3, arg4)
   local rabs = math.abs(r)
   return make_paths("scale_figure_eight", {
         { path_straight(rabs),             roll_angle(0) },
         { path_horizontal_arc(r,  90),     roll_angle_entry_exit(bank_angle) },
         { path_horizontal_arc(-r, 360),    roll_angle_entry_exit(-bank_angle) },
         { path_horizontal_arc(r,  270),    roll_angle_entry_exit(bank_angle) },
         { path_straight(3*rabs),           roll_angle(0) },
   })
end

function figure_eight(r, bank_angle, arg3, arg4)
   local rabs = math.abs(r)
   return make_paths("figure_eight", {
         { path_straight(rabs*math.sqrt(2)), roll_angle(0) },
         { path_horizontal_arc(r,  225),     roll_angle_entry_exit(bank_angle) },
         { path_straight(2*rabs),            roll_angle(0) },
         { path_horizontal_arc(-r,  270),    roll_angle_entry_exit(-bank_angle) },
         { path_straight(2*rabs),            roll_angle(0) },
         { path_horizontal_arc(r,    45),    roll_angle_entry_exit(bank_angle) },
   })
end


--[[
   perform a rudder over maneuver
--]]
function rudder_over(_direction, _min_speed)
   local self = {}
   local direction = _direction
   local min_speed = _min_speed
   local reached_speed = false
   local kick_started = false
   local pitch2_done = false
   local descent_done = false
   local target_q = nil
   local initial_q = nil
   local last_t = nil
   local initial_z = nil
   local desired_direction = nil

   --[[
      the update() method is called during the rudder over, it
      should return true when the maneuver is completed
   --]]
   function self.update(path, t, target_speed)
      if descent_done then
         -- we're all done
         return true
      end

      local ahrs_quat = ahrs:get_quaternion()
      local ahrs_pos = ahrs:get_relative_position_NED_origin()
      local ahrs_gyro = ahrs:get_gyro()
      local now = millis():tofloat() * 0.001

      if target_q == nil then
         -- initialising
         initial_z = ahrs_pos:z()
         target_q = quat_copy(ahrs_quat)
         initial_q = quat_copy(target_q)
         last_t = now
      end

      local dt = now - last_t
      last_t = now

      local error_quat = ahrs_quat:inverse() * target_q
      local rate_rads = Vector3f()
      error_quat:to_axis_angle(rate_rads)
      local tc = ROLL_CORR_TC:get()
      local rate_dps = rate_rads:scale(math.deg(1)/tc)

      -- use user set throttle for achieving the stall
      local throttle = AEROM_STALL_THR:get()
      local pitch_deg = math.deg(ahrs:get_pitch())
      if reached_speed and not kick_started and math.abs(math.deg(ahrs_gyro:z())) > ACRO_YAW_RATE:get()/3 then
         kick_started = true
      end
      if kick_started then
         -- when we have established some yaw rate cut the throttle to minimum
         throttle = AEROM_THR_MIN:get()
      end

      vehicle:set_target_throttle_rate_rpy(throttle, rate_dps:x(), rate_dps:y(), rate_dps:z())

      log_pose('POSM', ahrs_pos, ahrs:get_quaternion())
      log_pose('POST', ahrs_pos, target_q)

      local current_speed_up = -ahrs:get_velocity_NED():z()
      if not reached_speed and current_speed_up <= min_speed then
         reached_speed = true
      end

      if not reached_speed then
         return false
      end

      -- integrate desired attitude through yaw
      local q_rate_rads = makeVector3f(0,0,ahrs_gyro:z())
      if pitch2_done then
         -- stop adding yaw
         q_rate_rads:z(0)
      end
      local rotation = Quaternion()
      rotation:from_angular_velocity(q_rate_rads, dt)
      target_q = target_q * rotation
      target_q:normalize()

      --[[
         override rudder to maximum, basing PWM on the MIN/MAX of the channel
         according to the desired direction
      --]]
      if desired_direction == nil then
         desired_direction = direction
         if desired_direction == 0 then
            local c_y = get_ahrs_dcm_c_y()
            if c_y > 0 then
               desired_direction = 1
            else
               desired_direction = -1
            end
         end
      end
      if not pitch2_done then
         vehicle:set_rudder_offset(desired_direction * 100, false)
      else
         vehicle:set_rudder_offset(0, true)
      end
      if not kick_started then
         return false
      end

      -- see if we are nose down
      if kick_started and pitch_deg < AEROM_STALL_PIT:get() and not pitch2_done then
         -- lock onto a descent path
         pitch2_done = true
         target_q = initial_q * qorient(0, 0, 180)
         --[[ correct the attitude to the opposite correction that we
            had at the start of the slowdown, so we fight the wind on
            the way down
         --]]
         local error_q = initial_q:inverse() * qorient(0, 90, math.deg(initial_q:get_euler_yaw()))
         local error_pitch = error_q:get_euler_pitch()
         local error_yaw = error_q:get_euler_yaw()
         target_q = target_q * qorient(0, math.deg(-2*error_pitch), math.deg(2*error_yaw))
         target_q:normalize()
         return false
      end

      if not pitch2_done or ahrs_pos:z() < initial_z then
         -- haven't finished the descent
         return false
      end

      -- all done, update state
      descent_done = true
      path_var.tangent = path_var.tangent:scale(-1)
      path_var.path_t = path:get_next_segment_start(t)
      path_var.accumulated_orientation_rel_ef = path_var.accumulated_orientation_rel_ef * qorient(0,0,180)
      path_var.last_time = now
      path_var.last_ang_rate_dps = ahrs_gyro:scale(math.deg(1))
      path_var.pos = rotate_path(path, path_var.path_t, path_var.initial_ori, path_var.initial_ef_pos)
      -- ensure that the path will move fwd on the next step
      path_var.pos:z(path_var.pos:z()-10)

      return false
   end

   return self
end

--[[
   stall turn is not really correct, as we don't fully stall. Needs to be
   reworked
--]]
function stall_turn(radius, height, direction, min_speed)
   local h = height - radius
   assert(h >= 0)
   return make_paths("stall_turn", {
         { path_vertical_arc(radius, 90),          roll_angle(0) },
         { path_straight(h),                       roll_angle(0) },
         { path_reverse(h/4),                      roll_angle(0), rate_override=rudder_over(direction,min_speed), set_orient=qorient(0,-90,0) },
         { path_straight(h),                       roll_angle(0), pos_corr=0.5, shift_xy=true },
         { path_vertical_arc(-radius, 90),         roll_angle(0), set_orient=qorient(0,0,180) },
   })
end

--[[
   takeoff controller
--]]
function takeoff_controller(_distance, _thr_slew)
   local self = {}
   local start_time = 0
   local start_pos = nil
   local thr_slew = _thr_slew
   local distance = _distance
   local all_done = false
   local initial_yaw_deg = math.deg(ahrs:get_yaw())
   local yaw_correction_tconst = 1.0
   gcs:send_text(MAV_SEVERITY.INFO,string.format("Takeoff init"))

   --[[
      the update() method is called during the rudder over, it
      should return true when the maneuver is completed
   --]]
   function self.update(path, t, target_speed)
      if all_done then
         return true
      end
      local now = millis():tofloat() * 0.001
      local ahrs_pos = ahrs:get_relative_position_NED_origin()
      if start_time == 0 then
         gcs:send_text(MAV_SEVERITY.INFO,string.format("Takeoff start"))
         start_time = now
         start_pos = ahrs_pos
      end
      local throttle = constrain(thr_slew * (now - start_time), 0, 100)

      local yaw_deg = math.deg(ahrs:get_yaw())
      local yaw_err_deg = wrap_180(yaw_deg - initial_yaw_deg)
      local targ_yaw_rate = -yaw_err_deg / yaw_correction_tconst

      vehicle:set_target_throttle_rate_rpy(throttle, 0, 0, targ_yaw_rate)
      vehicle:set_rudder_offset(0, true)
      local dist_moved = (ahrs_pos - start_pos):length()
      if dist_moved > distance then
         gcs:send_text(MAV_SEVERITY.INFO,string.format("Takeoff complete dist=%.1f", dist_moved))

         path_var.path_t = path:get_next_segment_start(t)
         path_var.last_time = now
         path_var.last_ang_rate_dps = ahrs:get_gyro():scale(math.deg(1))
         path_var.pos = rotate_path(path, path_var.path_t, path_var.initial_ori, path_var.initial_ef_pos)
         all_done = true
      end
      return false
   end

   return self
end

--[[
   stall turn is not really correct, as we don't fully stall. Needs to be
   reworked
--]]
function takeoff(dist, height, thr_slew)
   local angle_deg = 20
   local dist_per_arc = 3*dist/8
   local radius = dist_per_arc / math.sin(math.rad(angle_deg))
   local h1 = dist_per_arc * (1.0 - math.cos(math.rad(angle_deg)))
   local line_h = constrain(height - 2*h1, 0, height)
   local line_len = (line_h - 2*radius*(1.0-math.cos(math.rad(angle_deg))))/math.sin(math.rad(angle_deg))

   return make_paths("takeoff", {
         { path_straight(dist/4), roll_angle(0), rate_override=takeoff_controller(dist/4, thr_slew) },
         { path_vertical_arc(radius, 20),  roll_angle(0), pos_gain_mul=0.3 },
         { path_straight(line_len), roll_angle(0), pos_gain_mul=0.5 },
         { path_vertical_arc(-radius, 20),  roll_angle(0), pos_gain_mul=0.5 },
   })
end

function half_cuban_eight(r, arg2, arg3, arg4)
   local rabs = math.abs(r)
   return make_paths("half_cuban_eight", {
         { path_straight(2*rabs*math.sqrt(2)), roll_angle(0) },
         { path_vertical_arc(r,  225),         roll_angle(0) },
         { path_straight(2*rabs/3),            roll_angle(0) },
         { path_straight(2*rabs/3),            roll_angle(180) },
         { path_straight(2*rabs/3),            roll_angle(0) },
         { path_vertical_arc(-r, 45),          roll_angle(0) },
   })
end

function cuban_eight(r, arg2, arg3, arg4)
   local rabs = math.abs(r)
   return make_paths("cuban_eight", {
         { path_straight(rabs*math.sqrt(2)), roll_angle(0) },
         { path_vertical_arc(r,  225),       roll_angle(0) },
         { path_straight(2*rabs/3),          roll_angle(0) },
         { path_straight(2*rabs/3),          roll_angle(180) },
         { path_straight(2*rabs/3),          roll_angle(0) },
         { path_vertical_arc(-r, 270),       roll_angle(0) },
         { path_straight(2*rabs/3),          roll_angle(0) },
         { path_straight(2*rabs/3),          roll_angle(180) },
         { path_straight(2*rabs/3),          roll_angle(0) },
         { path_vertical_arc(r, 45),         roll_angle(0) },
   })
end

function half_reverse_cuban_eight(r, arg2, arg3, arg4)
   local rabs = math.abs(r)
   return make_paths("half_reverse_cuban_eight", {
         { path_vertical_arc(r,  45),   roll_angle(0) },
         { path_straight(2*rabs/3),     roll_angle(0) },
         { path_straight(2*rabs/3),     roll_angle(180) },
         { path_straight(2*rabs/3),     roll_angle(0) },
         { path_vertical_arc(-r, 225),  roll_angle(0) },
   })
end

function horizontal_rectangle(total_length, total_width, r, bank_angle)
   local l = total_length - 2*r
   local w = total_width - 2*r
      
   return make_paths("horizontal_rectangle", {
         { path_straight(0.5*l),        roll_angle(0) },
         { path_horizontal_arc(r, 90),  roll_angle_entry_exit(bank_angle)},
         { path_straight(w),            roll_angle(0) },
         { path_horizontal_arc(r, 90),  roll_angle_entry_exit(bank_angle) },
         { path_straight(l),            roll_angle(0) },
         { path_horizontal_arc(r, 90),  roll_angle_entry_exit(bank_angle) },
         { path_straight(w),            roll_angle(0) },
         { path_horizontal_arc(r, 90),  roll_angle_entry_exit(bank_angle) },
         { path_straight(0.5*l),        roll_angle(0) },
   })
end

function vertical_aerobatic_box(total_length, total_width, r, bank_angle)
   local l = total_length - 2*r
   local w = total_width - 2*r
      
   return make_paths("vertical_aerobatic_box", {
         { path_straight(0.5*l),       roll_angle_entry(bank_angle) },
         { path_vertical_arc(r, 90),   roll_angle(0) },
         { path_straight(w),           roll_angle(0) },
         { path_vertical_arc(r, 90),   roll_angle(0) },
         { path_straight(l),           roll_angle(0) },
         { path_vertical_arc(r, 90),   roll_angle(0) },
         { path_straight(w),           roll_angle(0) },
         { path_vertical_arc(r, 90),   roll_angle(0) },
         { path_straight(0.5*l),       roll_angle_exit(-bank_angle) },
   })
end

--[[
   a multi-point roll
     - length = total length of straight flight
     - N = number of points of roll for full 360
     - hold_frac = proportion of each segment to hold attitude, will use 0.2 if 0
     - num_points = number of points of the N point roll to do, will use N if 0

   Note that num_points can be greater than N, for example do 6 points
   of a 4 point roll, resulting in inverted flight
--]]
function multi_point_roll(length, N, hold_frac, num_points)
   if hold_frac <= 0 then
      hold_frac = 0.2
   end
   if num_points <= 0 then
      num_points = N
   end
   --[[
      construct a roll sequence to use over the full length
   --]]
   local seq = {}
   local roll_frac = 1.0 - hold_frac
   for i = 1, num_points do
      seq[#seq+1] = { roll_frac, 360 / N }
      if i < num_points then
         seq[#seq+1] = { hold_frac, 0 }
      end
   end
   return make_paths("multi_point_roll", {{ path_straight(length), roll_sequence(seq) }})
end

function eight_point_roll(length, arg2, arg3, arg4)
   return multi_point_roll(length, 8, 0.5)
end

function procedure_turn(radius, bank_angle, step_out, arg4)
   local rabs = math.abs(radius)
   return make_paths("procedure_turn", {
            { path_horizontal_arc(radius,  90),     roll_angle_entry_exit(bank_angle) },
            { path_straight(step_out),              roll_angle(0) },
            { path_horizontal_arc(-radius,  270),   roll_angle_entry_exit(-bank_angle) },
            { path_straight(3*rabs),                roll_angle(0) },
      })
end

---------------------------------------------------

--[[
   target speed is taken as max of target airspeed and current 3D
   velocity at the start of the maneuver
--]]
function target_groundspeed()
   return math.max(ahrs:get_EAS2TAS()*TRIM_ARSPD_CM:get()*0.01, ahrs:get_velocity_NED():length())
end

--[[
   get ground course from AHRS
--]]
function get_ground_course_deg()
   local vned = ahrs:get_velocity_NED()
   return wrap_180(math.deg(math.atan(vned:y(), vned:x())))
end


--args:
--  path_f: path function returning position 
--  t: normalised [0, 1] time
--  arg1, arg2: arguments for path function
--  orientation: maneuver frame orientation
--returns: requested position, angle and speed in maneuver frame
function rotate_path(path_f, t0, orientation, offset)
   local t = constrain(t0, 0, 1)
   local point = path_f:get_pos(t)
   local angle = path_f:get_roll(t)
   local roll_correction = path_f:get_roll_correction(t)

   local attrib = {}
   for _, v in pairs(path_attribs) do
      attrib[v] = path_f:get_attribute(t, v)
   end
   point = point + path_var.path_shift
   point = quat_earth_to_body(orientation, point)

   local scale = AEROM_PATH_SCALE:get()
   point = point:scale(math.abs(scale))
   if scale < 0 then
      -- we need to mirror the path
      point:y(-point:y())
      roll_correction = -roll_correction
      angle = -angle
      -- compensate path orientation for the mirroring
      local orient = orientation:inverse()
      point = quat_body_to_earth((orient * orient), point)
   end

   return point+offset, math.rad(angle+roll_correction), attrib
end

--Given vec1, vec2, returns an (rotation axis, angle) tuple that rotates vec1 to be parallel to vec2
--If vec1 and vec2 are already parallel, returns a zero vector and zero angle
--Note that the rotation will not be unique.
function vectors_to_rotation(vector1, vector2)
   local axis = vector1:cross(vector2)
   if axis:length() < 0.00001 then
      local vec = Vector3f()
      vec:x(1)
      return vec, 0
   end
   axis:normalize()
   local angle = vector1:angle(vector2)
   return axis, angle
end

--returns Quaternion
function vectors_to_rotation_w_roll(vector1, vector2, roll)
   local axis, angle = vectors_to_rotation(vector1, vector2)
   local vector_rotation = Quaternion()
   vector_rotation:from_axis_angle(axis, angle)

   local roll_rotation = Quaternion()
   roll_rotation:from_euler(roll, 0, 0)
   
   local total_rot = vector_rotation*roll_rotation
   return to_axis_and_angle(total_rot)
end

--Given vec1, vec2, returns an angular velocity  tuple that rotates vec1 to be parallel to vec2
--If vec1 and vec2 are already parallel, returns a zero vector and zero angle 
function vectors_to_angular_rate(vector1, vector2, time_constant)
   local axis, angle = vectors_to_rotation(vector1, vector2)
   local angular_velocity = angle/time_constant
   return axis:scale(angular_velocity)
end

function vectors_to_angular_rate_w_roll(vector1, vector2, time_constant, roll)
   local axis, angle = vectors_to_rotation_w_roll(vector1, vector2, roll)
   local angular_velocity = angle/time_constant
   return axis:scale(angular_velocity)
end

-- convert a quaternion to axis angle form
function to_axis_and_angle(quat)
   local axis_angle = Vector3f()
   quat:to_axis_angle(axis_angle)
   local angle = axis_angle:length()
   if angle < 0.00001 then
      return makeVector3f(1.0, 0.0, 0.0), 0.0
   end
   return axis_angle:scale(1.0/angle), angle
end

--projects x onto the othogonal subspace of span(unit_v)
function ortho_proj(x, unit_v)
   local temp_x = unit_v:cross(x)
   return unit_v:cross(temp_x)
end

-- log a pose from position and quaternion attitude
function log_pose(logname, pos, quat)
   logger.write(logname, 'px,py,pz,q1,q2,q3,q4,r,p,y', 'ffffffffff',
                pos:x(),
                pos:y(),
                pos:z(),
                quat:q1(),
                quat:q2(),
                quat:q3(),
                quat:q4(),
                math.deg(quat:get_euler_roll()),
                math.deg(quat:get_euler_pitch()),
                math.deg(quat:get_euler_yaw()))
end


function log_position(logname, loc, quat)
   local gps_last_fix_ms1 = gps:last_fix_time_ms(0)
   local gps_week = gps:time_week(0)
   local gps_week_ms = gps:time_week_ms(0)
   local gps_last_fix_ms2 = gps:last_fix_time_ms(0)
   local now_ms = millis()
   if gps_last_fix_ms2 ~= gps_last_fix_ms1 then
      -- we got a new fix while requesting the values. fetch again,
      -- and assume we won't get another fix during these calls
      gps_week = gps:time_week(0)
      gps_week_ms = gps:time_week_ms(0)
   end
   gps_week_ms = gps_week_ms + (now_ms - gps_last_fix_ms2)

   logger.write(logname, 'I,GWk,GMS,Lat,Lon,Alt,R,P,Y',
                'BHILLffff',
                '#--DU----',
                '---GG----',
                SYSID_THISMAV:get(),
                gps_week,
                gps_week_ms,
                loc:lat(),
                loc:lng(),
                loc:alt()*0.01,
                math.deg(quat:get_euler_roll()),
                math.deg(quat:get_euler_pitch()),
                math.deg(quat:get_euler_yaw()))
end

--[[
   check if a number is Nan.
--]]
function isNaN(value)
   -- NaN is lua is not equal to itself
   return value ~= value
end

function Vec3IsNaN(v)
   return isNaN(v:x()) or isNaN(v:y()) or isNaN(v:z())
end

function qIsNaN(q)
   return isNaN(q:q1()) or isNaN(q:q2()) or isNaN(q:q3()) or isNaN(q:q4())
end

--[[
   return the body y projection down, this is the c.y element of the equivalent rotation matrix
--]]
function quat_projection_ground_plane(q)
   local q1q2 = q:q1() * q:q2()
   local q3q4 = q:q3() * q:q4()
   return 2.0 * (q3q4 + q1q2)
end


--[[
   calculate rudder offset
--]]
function calculate_rudder_offset(ahrs_quat, ahrs_gyro, airspeed_constrained)
   --[[
      look ahead for what our y projection will be at AEROM_KE_RUDD_LK
      seconds forward in time
   --]]
   local qchange = Quaternion()
   qchange:from_angular_velocity(ahrs_gyro, -AEROM_KE_RUDD_LK:get())
   local qnew = qchange * ahrs_quat

   local airspeed_scaling = SCALING_SPEED:get()/airspeed_constrained
   local y_projection = get_quat_dcm_c_y(qnew:inverse())
   local rudder_ofs = -y_projection * AEROM_KE_RUDD:get() * sq(airspeed_scaling)
   rudder_ofs = constrain(rudder_ofs, -100, 100)

   return rudder_ofs
end

--[[
   convert a table of bytes to a lua string
--]]
function bytes_to_string(bytes)
   local ret = {}
   for _, b in ipairs(bytes) do
      if b == 0 then
         break
      end
      table.insert(ret, string.char(b))
   end
   return table.concat(ret)
end

--[[
   a lua implementation of the jitter correction algorithm from libraries/AP_RTC

   note that the use of a 32 bit float lua number for a uint32_t
   milliseconds means we lose accuracy over time. At 9 hours we have
   an accuracy of about 1 millisecond
--]]
local function JitterCorrection(_max_lag_ms, _convergence_loops)
   local self = {}

   local max_lag_ms = _max_lag_ms
   local convergence_loops = _convergence_loops
   local link_offset_ms = 0
   local min_sample_ms = 0
   local initialised = false
   local min_sample_counter = 0

   function self.correct_offboard_timestamp_msec(offboard_ms, local_ms)
      local diff_ms = local_ms - offboard_ms
      if not initialised or diff_ms < link_offset_ms then
         --[[
            this message arrived from the remote system with a
            timestamp that would imply the message was from the
            future. We know that isn't possible, so we adjust down the
            correction value
         --]]
        link_offset_ms = diff_ms
        initialised = true
      end

      local estimate_ms = offboard_ms + link_offset_ms

      if estimate_ms + max_lag_ms < local_ms then
         --[[
            this implies the message came from too far in the past. clamp the lag estimate
            to assume the message had maximum lag
         --]]
         estimate_ms = local_ms - max_lag_ms
         link_offset_ms = estimate_ms - offboard_ms
      end

      if min_sample_counter == 0 then
         min_sample_ms = diff_ms
      end

      min_sample_counter = (min_sample_counter+1)
      if diff_ms < min_sample_ms then
         min_sample_ms = diff_ms
      end
      if min_sample_counter == convergence_loops then
         --[[
            we have the requested number of samples of the transport
            lag for convergence. To account for long term clock drift
            we set the diff we will use in future to this value
         --]]
         link_offset_ms = min_sample_ms
         min_sample_counter = 0
      end
    
      return estimate_ms
   end

   return self
end

--[[
   import mavlink support for NAMED_VALUE_FLOAT, only used for
   DUAL_AIRCRAFT operation
--]]
local function mavlink_receiver()
   local self = {}
   local mavlink_msgs = require("mavlink_msgs")
   local NAMED_VALUE_FLOAT_msgid = mavlink_msgs.get_msgid("NAMED_VALUE_FLOAT")
   local msg_map = {}
   local jitter_correction = JitterCorrection(5000, 100)

   msg_map[NAMED_VALUE_FLOAT_msgid] = "NAMED_VALUE_FLOAT"

   -- initialise mavlink rx with number of messages, and buffer depth
   mavlink.init(1, 10)

   -- register message id to receive
   mavlink.register_rx_msgid(NAMED_VALUE_FLOAT_msgid)

   --[[
      get a NAMED_VALUE_FLOAT incoming message, handling jitter correction
   --]]
   function self.get_named_value_float()
      local msg,_,timestamp_ms = mavlink.receive_chan()
      if msg then
         local parsed_msg = mavlink_msgs.decode(msg, msg_map)
         if (parsed_msg ~= nil) and (parsed_msg.msgid == NAMED_VALUE_FLOAT_msgid) then
            -- convert remote timestamp to local timestamp with jitter correction
            local time_boot_ms = jitter_correction.correct_offboard_timestamp_msec(parsed_msg.time_boot_ms, timestamp_ms:toint())
            local value = parsed_msg.value
            local name = bytes_to_string(parsed_msg.name)
            return time_boot_ms, name, value, parsed_msg.sysid
         end
      end
      return nil
   end

   return self
end

local mavlink_handler = nil
if option_set(OPTIONS.DUAL_AIRCRAFT) then
   mavlink_handler = mavlink_receiver()
end

--[[
   handle NAMED_VALUE_FLOAT from another vehicle to sync our schedules
--]]
function handle_speed_adjustment()
   local local_t = millis():tofloat() * 0.001
   local named_float_rate = AEROM_TS_RATE:get()
   local loc_timestamp = current_task.fn:patht_to_timestamp(path_var.path_t)
   if named_float_rate > 0 and loc_timestamp > 1 and local_t - last_named_float_send_t > 1.0/named_float_rate then
      last_named_float_send_t = local_t
      gcs:send_named_float("PATHT", loc_timestamp)
   end
   local time_boot_ms, name, remote_timestamp, sysid = mavlink_handler.get_named_value_float()
   if not time_boot_ms then
      return
   end
   -- gcs:send_text(MAV_SEVERITY.INFO, string.format("NVF: name='%s' value=%f sysid=%d tbm=%f", name, remote_timestamp, sysid, time_boot_ms))
   if name == "PATHT" and sysid ~= SYSID_THISMAV:get() then
      local remote_t = time_boot_ms * 0.001
      local dt = local_t - remote_t
      local rem_patht = current_task.fn:timestamp_to_patht(remote_timestamp)
      local adjusted_rem_path_t = rem_patht + dt / path_var.total_time
      local dist_err = (path_var.path_t - adjusted_rem_path_t) * path_var.total_time * path_var.target_speed

      if loc_timestamp > 1 and remote_timestamp > 1 then
         path_var.speed_adjustment = speed_adjustment_PI.update(dist_err)
      else
         path_var.speed_adjustment = 0.0
      end

      logger.write("PTHT",'SysID,RemT,LocT,TS,RemTS,PathT,RemPathT,Dt,ARPT,DE,SA','Bffffffffff',
                   sysid, remote_t, local_t,
                   loc_timestamp,
                   remote_timestamp,
                   path_var.path_t, rem_patht,
                   dt, adjusted_rem_path_t, dist_err, path_var.speed_adjustment)
   end
end

path_var.count = 0

function do_path()
   local now = millis():tofloat() * 0.001
   local ahrs_pos_NED = ahrs:get_relative_position_NED_origin()
   local ahrs_pos = ahrs:get_position()
   local ahrs_gyro = ahrs:get_gyro()
   local ahrs_velned = ahrs:get_velocity_NED()
   local ahrs_airspeed = ahrs:airspeed_estimate()
   --[[
      ahrs_quat is the quaterion which when used with quat_earth_to_body() rotates a vector
      from earth to body frame. It needs to be the inverse of ahrs:get_quaternion()
   --]]
   local ahrs_quat = ahrs:get_quaternion():inverse()

   path_var.count = path_var.count + 1
   local path = current_task.fn

   if not current_task.started then
      local initial_yaw_deg = current_task.initial_yaw_deg
      current_task.started = true

      local speed = target_groundspeed()
      path_var.target_speed = speed
      path_var.speed_adjustment = 0.0

      path_var.length = path:get_length() * math.abs(AEROM_PATH_SCALE:get())

      path_var.total_rate_rads_ef = makeVector3f(0.0, 0.0, 0.0)

      --assuming constant velocity
      path_var.total_time = path_var.length/speed

      --deliberately only want yaw component, because the maneuver should be performed relative to the earth, not relative to the initial orientation
      path_var.initial_ori = Quaternion()
      path_var.initial_ori:from_euler(0, 0, math.rad(initial_yaw_deg))
      path_var.initial_ori = path_var.initial_ori
      path_var.initial_ori:normalize()

      path_var.initial_ef_pos = ahrs_pos_NED:copy()

      path_var.start_pos = ahrs_pos:copy()
      path_var.path_int = path_var.start_pos:copy()

      speed_PI.reset()

      path_var.accumulated_orientation_rel_ef = path_var.initial_ori

      path_var.time_correction = 0.0 

      path_var.filtered_angular_velocity = Vector3f()

      path_var.last_time = now - 1.0/LOOP_RATE
      path_var.last_ang_rate_dps = ahrs_gyro:scale(math.deg(1))

      path_var.path_t = 0.0

      path_var.pos = path_var.initial_ef_pos:copy()
      path_var.roll = 0.0
      path_var.last_shift_xy = nil
      path_var.path_shift = Vector3f()

      path_var.ss_angle = 0.0
      path_var.ss_angle_filt = 0.0
      path_var.last_rate_override = 0

      -- get initial tangent
      local p1, _ = rotate_path(path, path_var.path_t + 0.1/(path_var.total_time*LOOP_RATE),
                                 path_var.initial_ori, path_var.initial_ef_pos)
      path_var.tangent = p1 - path_var.pos
      return true
   end
   
   local vel_length = ahrs_velned:length()

   local actual_dt = now - path_var.last_time
   if actual_dt < 0.25 / LOOP_RATE then
      -- the update has been executed too soon
      return true
   end

   path_var.last_time = now

   local local_n_dt = (1.0/LOOP_RATE)/path_var.total_time

   if path_var.path_t + local_n_dt > 1.0 then
      -- all done
      return false
   end

   if option_set(OPTIONS.DUAL_AIRCRAFT) then
      handle_speed_adjustment()
   end

   -- airspeed, assume we don't go below min
   local airspeed_constrained = math.max(ARSPD_FBW_MIN:get(), ahrs_airspeed)

   --[[
      calculate positions and angles at previous, current and next time steps
   --]]

   local p0 = path_var.pos:copy()
   local r0 = path_var.roll
   local p1, _, attrib = rotate_path(path, path_var.path_t + local_n_dt,
                                      path_var.initial_ori, path_var.initial_ef_pos)

   local current_measured_pos_ef = ahrs_pos_NED:copy()

   if attrib.rate_override ~= nil then
      if not attrib.rate_override.update(path, path_var.path_t + local_n_dt, path_var.target_speed) then
         -- not done yet
         path_var.pos = current_measured_pos_ef
         path_var.last_rate_override = now
         return true
      end
   end

   --[[
      see if this path element has a shift_xy attribute
   --]]
   local shift_xy = attrib.shift_xy
   if shift_xy and not path_var.last_shift_xy then
      --[[
         we have entered a new sub-element with a shift_xy
      --]]
      local curpos_mf = quat_body_to_earth(path_var.initial_ori, current_measured_pos_ef)
      local pathpos_mf = quat_body_to_earth(path_var.initial_ori, p1)
      local shift = curpos_mf - pathpos_mf
      shift:z(0)
      path_var.path_shift = path_var.path_shift + shift
      local shift_ef = quat_earth_to_body(path_var.initial_ori, shift)
      p1 = p1 + shift_ef
      p0:y(p1:y())
      p0:x(p1:x())
   end
   path_var.last_shift_xy = shift_xy

   --[[
      get tangents to the path
   --]]
   local tangent1_ef = path_var.tangent:copy()
   local tangent2_ef = p1 - p0

   local tv_unit = tangent2_ef:copy()
   if tv_unit:length() < 0.00001 then
      gcs:send_text(MAV_SEVERITY.EMERGENCY, string.format("path not advancing %f", tv_unit:length()))
   end
   tv_unit:normalize()

   --[[
      use actual vehicle velocity to calculate how far along the
      path we have progressed
   --]]
   local v = ahrs_velned:copy()
   local path_dist = v:dot(tv_unit)*actual_dt
   if path_dist < 0 and path_var.last_rate_override > 0 and now - path_var.last_rate_override > 1 then
      gcs:send_text(MAV_SEVERITY.EMERGENCY, string.format("aborting %.2f at %d tv=(%.2f,%.2f,%.2f) vx=%.2f adt=%.2f",
                                     path_dist, path_var.count,
                                     tangent2_ef:x(),
                                     tangent2_ef:y(),
                                     tangent2_ef:z(),
                                     v:x(), actual_dt))
      if option_set(OPTIONS.ABORT_RTL) and vehicle:get_mode() == MODE_AUTO then
         vehicle:set_mode(MODE_RTL)
      end
      path_var.last_rate_override = 0
      return false
   end
   local path_t_delta = constrain(path_dist/path_var.length, 0.2*local_n_dt, 4*local_n_dt)

   --[[
      recalculate the current path position and angle based on actual delta time
   --]]
   p1, _, _ = rotate_path(path,
                          constrain(path_var.path_t + path_t_delta, 0, 1),
                          path_var.initial_ori, path_var.initial_ef_pos)
   local last_path_t = path_var.path_t
   path_var.path_t = path_var.path_t + path_t_delta

   -- tangents needs to be recalculated
   tangent2_ef = p1 - p0
   tv_unit = tangent2_ef:copy()
   tv_unit:normalize()

   -- error in position versus current point on the path
   local pos_error_ef = current_measured_pos_ef - p1

   --[[
      calculate a time correction. We first get the projection of
      the position error onto the track. This tells us how far we
      are ahead or behind on the track
   --]]
   local path_dist_err_m = tv_unit:dot(pos_error_ef)

   -- normalize against the total path length
   local path_err_t = path_dist_err_m / path_var.length

   -- don't allow the path to go backwards in time, or faster than twice the actual rate
   path_err_t = constrain(path_err_t, -0.9*path_t_delta, 2*path_t_delta)

   -- correct time to bring us back into sync
   path_var.path_t = path_var.path_t + TIME_CORR_P:get() * path_err_t

   -- get the path again with the corrected time
   local r1
   p1, r1, attrib = rotate_path(path,
                                constrain(path_var.path_t, 0, 1),
                                path_var.initial_ori, path_var.initial_ef_pos)
   -- recalculate the tangent to match the amount we advanced the path time
   tangent2_ef = p1 - p0

   -- get the real world time corresponding to the quaternion change
   local q_change_t = (path_var.path_t - last_path_t) * path_var.total_time

   -- low pass filter the demanded roll angle
   r1 = path_var.roll + wrap_pi(r1 - path_var.roll)
   local alpha = calc_lowpass_alpha(q_change_t, AEROM_ANG_TC:get())
   r1 = (1.0 - alpha) * path_var.roll + alpha * r1
   r1 = wrap_pi(r1)

   path_var.tangent = tangent2_ef:copy()
   path_var.pos = p1:copy()
   path_var.roll = r1

   
   --[[
      calculation of error correction, calculating acceleration
      needed to bring us back on the path, and body rates in pitch and
      yaw to achieve those accelerations
   --]]
   
   -- component of pos_err perpendicular to the current path tangent
   local B = ortho_proj(pos_error_ef, tv_unit)

   -- derivative of pos_err perpendicular to the current path tangent, assuming tangent is constant
   local B_dot = ortho_proj(v, tv_unit)

   -- gains for error correction.
   local acc_err_ef = B:scale(ERR_CORR_P:get()) + B_dot:scale(ERR_CORR_D:get())

   if attrib.pos_gain_mul then
      -- allow for reduced gains during some maneuvers like takeoff
      acc_err_ef = acc_err_ef:scale(attrib.pos_gain_mul)
   end

   -- scale by per-maneuver error correction scale factor
   acc_err_ef = acc_err_ef:scale(attrib.pos_corr or 1.0)

   local acc_err_bf = quat_earth_to_body(ahrs_quat, acc_err_ef)

   local TAS = constrain(ahrs:get_EAS2TAS()*airspeed_constrained, 3, 100)
   local corr_rate_bf_y_rads = -acc_err_bf:z()/TAS
   local corr_rate_bf_z_rads = acc_err_bf:y()/TAS

   local cor_ang_vel_bf_rads = makeVector3f(0.0, corr_rate_bf_y_rads, corr_rate_bf_z_rads)
   if Vec3IsNaN(cor_ang_vel_bf_rads) then
      cor_ang_vel_bf_rads = makeVector3f(0,0,0)
   end
   local cor_ang_vel_bf_dps = cor_ang_vel_bf_rads:scale(math.deg(1))

   if path_var.count < 2 then
      cor_ang_vel_bf_dps = Vector3f()
   end

   --[[
      work out body frame path rate, this is based on two adjacent tangents on the path
   --]]
   local path_rate_ef_rads = tangents_to_rate(tangent1_ef, tangent2_ef, actual_dt)
   if Vec3IsNaN(path_rate_ef_rads) then
      gcs:send_text(MAV_SEVERITY.EMERGENCY,string.format("path_rate_ef_rads: NaN"))
      path_rate_ef_rads = makeVector3f(0,0,0)
   end
   local path_rate_ef_dps = path_rate_ef_rads:scale(math.deg(1))
   if path_var.count < 3 then
      -- cope with small initial misalignment
      path_rate_ef_dps:z(0)
   end
   local path_rate_bf_dps = quat_earth_to_body(ahrs_quat, path_rate_ef_dps)

   -- set the path roll rate
   path_rate_bf_dps:x(math.deg(wrap_pi(r1 - r0)/actual_dt))


   --[[
      calculate body frame roll rate to achieved the desired roll
      angle relative to the maneuver path
   --]]
   local zero_roll_angle_delta = Quaternion()
   zero_roll_angle_delta:from_angular_velocity(path_rate_ef_rads, actual_dt)
   path_var.accumulated_orientation_rel_ef = zero_roll_angle_delta*path_var.accumulated_orientation_rel_ef
   path_var.accumulated_orientation_rel_ef:normalize()

   local mf_axis = quat_earth_to_body(path_var.accumulated_orientation_rel_ef, makeVector3f(1, 0, 0))

   local orientation_rel_mf_with_roll_angle = Quaternion()
   orientation_rel_mf_with_roll_angle:from_axis_angle(mf_axis, r1)
   orientation_rel_ef_with_roll_angle = orientation_rel_mf_with_roll_angle*path_var.accumulated_orientation_rel_ef

   --[[
      calculate the error correction for the roll versus the desired roll
   --]]
   local roll_error = orientation_rel_ef_with_roll_angle * ahrs_quat
   roll_error:normalize()
   local err_axis_ef, err_angle_rad = to_axis_and_angle(roll_error)
   local time_const_roll = ROLL_CORR_TC:get()
   local err_angle_rate_ef_rads = err_axis_ef:scale(err_angle_rad/time_const_roll)
   local err_angle_rate_bf_dps = quat_earth_to_body(ahrs_quat,err_angle_rate_ef_rads):scale(math.deg(1))
   -- zero any non-roll components
   err_angle_rate_bf_dps:y(0)
   err_angle_rate_bf_dps:z(0)

   --[[
      implement lookahead for path rates
   --]]
   if AEROM_LKAHD:get() > 0 then
      local lookahead = AEROM_LKAHD:get()
      local lookahead_vt = lookahead / path_var.total_time
      p2 = rotate_path(path,
                       constrain(path_var.path_t+lookahead_vt, 0, 1),
                       path_var.initial_ori, path_var.initial_ef_pos)
      local tangent3_ef = p2 - p1
      local lk_ef_rads = tangents_to_rate(tangent2_ef, tangent3_ef, 0.5*(lookahead+(1.0/LOOP_RATE)))

      -- scale for airspeed
      lk_ef_rads = lk_ef_rads:scale(sq(vel_length/path_var.target_speed))

      local lookahead_bf_rads = quat_earth_to_body(ahrs_quat, lk_ef_rads)
      local lookahead_bf_dps = lookahead_bf_rads:scale(math.deg(1))
      logger.write('AELK','Py,Ly,Pz,Lz', 'ffff',
                   path_rate_bf_dps:y(),
                   lookahead_bf_dps:y(),
                   path_rate_bf_dps:z(),
                   lookahead_bf_dps:z())
      path_rate_bf_dps:y(lookahead_bf_dps:y())
      path_rate_bf_dps:z(lookahead_bf_dps:z())
   end
   
   --[[
      calculate an additional yaw rate to get us to the right angle of sideslip for knifeedge
   --]]
   -- local sideslip_rate_bf_dps = calculate_side_slip_aoa(path_rate_bf_dps, ahrs_quat, airspeed_constrained, tv_unit, ahrs_velned, actual_dt)
   local sideslip_rate_bf_dps = Vector3f()

   --[[
      total angular rate is sum of path rate, correction rate and roll correction rate
   --]]
   local tot_ang_vel_bf_dps = path_rate_bf_dps + cor_ang_vel_bf_dps + err_angle_rate_bf_dps + sideslip_rate_bf_dps

   --[[
      apply angular accel limit
   --]]
   local ang_rate_diff_dps = tot_ang_vel_bf_dps - path_var.last_ang_rate_dps
   local max_delta_dps = AEROM_ANG_ACCEL:get() * actual_dt
   local max_delta_yaw_dps = max_delta_dps
   if AEROM_YAW_ACCEL:get() > 0 and
      (AEROM_YAW_ACCEL:get() < AEROM_ANG_ACCEL:get() or AEROM_ANG_ACCEL:get() <= 0) then
      max_delta_yaw_dps = AEROM_YAW_ACCEL:get() * actual_dt
   end
   if max_delta_dps > 0 then
      ang_rate_diff_dps:x(constrain(ang_rate_diff_dps:x(), -max_delta_dps, max_delta_dps))
      ang_rate_diff_dps:y(constrain(ang_rate_diff_dps:y(), -max_delta_dps, max_delta_dps))
   end
   if max_delta_yaw_dps > 0 then
      ang_rate_diff_dps:z(constrain(ang_rate_diff_dps:z(), -max_delta_yaw_dps, max_delta_yaw_dps))
   end

   tot_ang_vel_bf_dps = path_var.last_ang_rate_dps + ang_rate_diff_dps
   path_var.last_ang_rate_dps = tot_ang_vel_bf_dps

   --[[
      calculate a rudder offset for knife-edge
   --]]
   local rudder_offset_pct = 0
   if AEROM_KE_RUDD:get() > 0 then
      rudder_offset_pct = calculate_rudder_offset(ahrs_quat, ahrs_gyro, airspeed_constrained)
   end

   --[[
      log POSM is pose-measured, POST is pose-track, POSB is pose-track without the roll
   --]]
   log_pose('POSM', current_measured_pos_ef, ahrs_quat:inverse())
   log_pose('POST', p1, orientation_rel_ef_with_roll_angle)

   logger.write('AETM', 'T,Terr,QCt,Adt','ffff',
                path_var.path_t,
                path_err_t,
                q_change_t,
                actual_dt)

   logger.write('AERT','Cx,Cy,Cz,Px,Py,Pz,Ex,Tx,Ty,Tz,Perr,Aerr,Yff,Rofs', 'ffffffffffffff',
                cor_ang_vel_bf_dps:x(), cor_ang_vel_bf_dps:y(), cor_ang_vel_bf_dps:z(),
                path_rate_bf_dps:x(), path_rate_bf_dps:y(), path_rate_bf_dps:z(),
                err_angle_rate_bf_dps:x(),
                tot_ang_vel_bf_dps:x(), tot_ang_vel_bf_dps:y(), tot_ang_vel_bf_dps:z(),
                pos_error_ef:length(),
                wrap_180(math.deg(err_angle_rad)),
                sideslip_rate_bf_dps:z(),
                rudder_offset_pct)

   --log_pose('POSB', p1, path_var.accumulated_orientation_rel_ef)

   --[[
      run the throttle based speed controller

      get the anticipated pitch at the throttle lookahead time
      we use the maximum of the current path pitch and the anticipated pitch
   --]]
   local qchange = Quaternion()
   qchange:from_angular_velocity(path_rate_ef_rads, AEROM_THR_LKAHD:get())
   local qnew = qchange * orientation_rel_ef_with_roll_angle
   local anticipated_pitch_rad = math.max(qnew:get_euler_pitch(), orientation_rel_ef_with_roll_angle:get_euler_pitch())

   local throttle = speed_PI.update(path_var.target_speed + path_var.speed_adjustment, anticipated_pitch_rad)
   local thr_min = AEROM_THR_MIN:get()
   if attrib.thr_boost then
      thr_min = math.max(thr_min, AEROM_THR_BOOST:get())
   end
   throttle = constrain(throttle, thr_min, 100.0)

   if isNaN(throttle) or Vec3IsNaN(tot_ang_vel_bf_dps) then
      gcs:send_text(MAV_SEVERITY.EMERGENCY,string.format("Path NaN - aborting"))
      return false
   end

   vehicle:set_target_throttle_rate_rpy(throttle, tot_ang_vel_bf_dps:x(), tot_ang_vel_bf_dps:y(), tot_ang_vel_bf_dps:z())
   vehicle:set_rudder_offset(rudder_offset_pct, true)

   if now - last_named_float_t > 1.0 / NAME_FLOAT_RATE then
      last_named_float_t = now
      gcs:send_named_float("PERR", pos_error_ef:length())
   end

   local alt_error = (current_measured_pos_ef - path_var.initial_ef_pos):z()
   if alt_error > AEROM_ALT_ABORT:get() then
     gcs:send_text(MAV_SEVERITY.EMERGENCY,"Too low altitude, aborting")
     return false
   end

   return true
end

--[[
   an object defining a path
--]]
function PathFunction(fn, name)
   local self = {}
   self.fn = fn
   self.name = name
   return self
end

local last_preload = nil

local command_table = {}
command_table[1] = PathFunction(figure_eight, "Figure Eight")
command_table[2] = PathFunction(loop, "Loop")
command_table[3] = PathFunction(horizontal_rectangle, "Horizontal Rectangle")
command_table[4] = PathFunction(climbing_circle, "Climbing Circle")
command_table[5] = PathFunction(vertical_aerobatic_box, "Vertical Box")
command_table[6] = PathFunction(immelmann_turn_fast, "Immelmann Fast")
command_table[7] = PathFunction(straight_roll, "Axial Roll")
command_table[8] = PathFunction(rolling_circle, "Rolling Circle")
command_table[9] = PathFunction(half_cuban_eight, "Half Cuban Eight")
command_table[10]= PathFunction(half_reverse_cuban_eight, "Half Reverse Cuban Eight")
command_table[11]= PathFunction(cuban_eight, "Cuban Eight")
command_table[12]= PathFunction(humpty_bump, "Humpty Bump")
command_table[13]= PathFunction(straight_flight, "Straight Flight")
command_table[14]= PathFunction(scale_figure_eight, "Scale Figure Eight")
command_table[15]= PathFunction(immelmann_turn, "Immelmann Turn")
command_table[16]= PathFunction(split_s, "Split-S")
command_table[17]= PathFunction(upline_45, "Upline-45")
command_table[18]= PathFunction(downline_45, "Downline-45")
command_table[19]= PathFunction(stall_turn, "Stall Turn")
command_table[20]= PathFunction(procedure_turn, "Procedure Turn")
command_table[23]= PathFunction(half_climbing_circle, "Half Climbing Circle")
command_table[25]= PathFunction(laydown_humpty, "Laydown Humpty")
command_table[26]= PathFunction(barrel_roll, "Barrel Roll")
command_table[27]= PathFunction(straight_flight, "Straight Hold")
command_table[28]= PathFunction(partial_circle, "Partial Circle")
command_table[31]= PathFunction(multi_point_roll, "Multi Point Roll")
command_table[32]= PathFunction(side_step, "Side Step")

--[[
   a table of function available in loadable tricks
--]]
local load_table = {}
load_table["loop"] = loop
load_table["horizontal_rectangle"] = horizontal_rectangle
load_table["climbing_circle"] = climbing_circle
load_table["vertical_aerobatic_box"] = vertical_aerobatic_box
load_table["immelmann_turn_fast"] = immelmann_turn_fast
load_table["straight_roll"] = straight_roll
load_table["rolling_circle"] = rolling_circle
load_table["half_cuban_eight"] = half_cuban_eight
load_table["half_reverse_cuban_eight"] = half_reverse_cuban_eight
load_table["cuban_eight"] = cuban_eight
load_table["humpty_bump"] = humpty_bump
load_table["straight_flight"] = straight_flight
load_table["scale_figure_eight"] = scale_figure_eight
load_table["immelmann_turn"] = immelmann_turn
load_table["split_s"] = split_s
load_table["upline_45"] = upline_45
load_table["upline_20"] = upline_20
load_table["takeoff"] = takeoff
load_table["downline_45"] = downline_45
load_table["stall_turn"] = stall_turn
load_table["procedure_turn"] = procedure_turn
load_table["two_point_roll"] = two_point_roll
load_table["half_climbing_circle"] = half_climbing_circle
load_table["laydown_humpty"] = laydown_humpty
load_table["straight_align"] = straight_align
load_table["figure_eight"] = figure_eight
load_table["barrel_roll"] = barrel_roll
load_table["straight_hold"] = straight_hold
load_table["partial_circle"] = partial_circle
load_table["multi_point_roll"] = multi_point_roll
load_table["side_step"] = side_step
load_table["align_box"] = align_box
load_table["align_center"] = align_center

--[[
   interpret an attribute value, coping with special cases
--]]
function interpret_attrib(v)
   if v == "true" then
      return true
   end
   if v == "false" then
      return false
   end
   -- could be a number
   local n = tonumber(v)
   if n ~= nil then
      return n
   end
   -- assume a string
   return v
end

--[[
   parse a function definition in a txt load file, adding it to the load table so
   it can be used in schedules
--]]
function parse_function(line, file)
   _, _, funcname = string.find(line, "^function%s*([%w_]+).*$")
   if not funcname then
      gcs:send_text(MAV_SEVERITY.ERROR, string.format("Parse error: %s", line))
      return
   end
   local funcstr = line .. "\n"
   while true do
      line = file:read()
      if not line then
         gcs:send_text(MAV_SEVERITY.ERROR, string.format("Error: end of file in %s", funcname))
         break
      end
      funcstr = funcstr .. line .. "\n"
      if string.sub(line,1,3) == "end" then
         break
      end
   end
   local f, errloc, err = load(funcstr, funcname, "t", _ENV)
   if not f then
      gcs:send_text(MAV_SEVERITY.ERROR,string.format("Error %s: %s", errloc, err))
      return
   end
   -- fun the function code, which creates the function
   local success
   success, err = pcall(f)
   if not success then
      gcs:send_text(MAV_SEVERITY.ERROR,string.format("Error %s: %s", funcname, err))
   end
   load_table[funcname] = _ENV[funcname]
end

--[[
   load a trick description from a text file
--]]
function load_trick(id)
   if command_table[id] ~= nil then
      -- already have it
      return
   end
   -- look in 3 possible locations for the trick, coping with SITL and real boards
   local trickdirs = { "APM/scripts/", "scripts/", "./" }
   local file = nil
   local fname = string.format("trick%u.txt", id)
   local filename = nil
   for i = 1, #trickdirs do
      filename = trickdirs[i] .. fname
      file = io.open(filename, "r")
      if file then
         break
      end
   end
   if file == nil then
      gcs:send_text(MAV_SEVERITY.ERROR,string.format("Failed to open %s", fname))
      return
   end
   local name = string.format("Trick%u", id)
   local attrib = {}
   local paths = {}
   while true do
      local line = file:read()
      if not line then
         break
      end
      -- trim trailing spaces
      line = string.gsub(line, '^(.-)%s*$', '%1')
      local _, _, cmd, arg1, arg2, arg3, arg4 = string.find(line, "^([%w_:]+)%s*([-.%d]*)%s*([-.%d]*)%s*([-.%d]*)%s*([-.%d]*)")
      if cmd == "" or cmd == nil or string.sub(cmd,1,1) == "#" then
         -- ignore comments
         goto continue
      elseif cmd == "name:" then
         _, _, name = string.find(line, "^name:%s*([%w_]+)$")
      elseif string.sub(cmd,-1) == ":" then
         _, _, a, s = string.find(line, "^([%w_]+):%s*([%w_:%s-]+)$")
         if a ~= nil then
            attrib[a] = interpret_attrib(s)
         else
            gcs:send_text(MAV_SEVERITY.ERROR, string.format("Bad line: '%s'", line))
         end
      elseif cmd == "function" then
         parse_function(line, file)
      elseif cmd ~= nil then
         arg1 = tonumber(arg1) or 0
         arg2 = tonumber(arg2) or 0
         arg3 = tonumber(arg3) or 0
         arg4 = tonumber(arg4) or 0
         local f = load_table[cmd]
         if f == nil then
            gcs:send_text(MAV_SEVERITY.ERROR,string.format("Unknown command '%s' in %s", cmd, fname))
         else
            paths[#paths+1] = { f, { arg1, arg2, arg3, arg4 }}
            for k, v in pairs(attrib) do
               paths[#paths][k] = v
            end
            attrib = {}
         end
      end
      ::continue::
   end
   local pc = path_composer(name, paths)
   gcs:send_text(MAV_SEVERITY.INFO, string.format("Loaded trick%u '%s'", id, name))
   command_table[id] = PathFunction(pc, name)
   logger:log_file_content(filename)

   calculate_timestamps(command_table[id])
end

function calculate_timestamps(pc)
   pc.fn:calculate_timestamps()
end

function PathTask(fn, name, id, initial_yaw_deg, arg1, arg2, arg3, arg4)
   local self = {}
   if type(fn) == "table" then
      self.fn = fn
   else
      self.fn = fn(arg1, arg2, arg3, arg4)
   end
   self.name = name
   self.id = id
   self.initial_yaw_deg = initial_yaw_deg
   self.started = false
   return self
end

--[[
   see if we should prepare for an upcoming trick
--]]
function check_preload_trick()
   local idx = mission:get_current_nav_index()
   if idx == last_preload then
      return
   end
   last_preload = idx
   local m = mission:get_item(idx+1)
   if not m then
      return
   end
   if m:command() ~= NAV_SCRIPT_TIME then
      return
   end
   cmdid = m:param1()
   if command_table[cmdid] == nil then
      load_trick(cmdid)
   end
end

-- see if an auto mission item needs to be run
function check_auto_mission()
   id, cmd, arg1, arg2, arg3, arg4 = vehicle:nav_script_time()
   if not id then
      check_preload_trick()
      return
   end
   if id ~= last_id then
      -- we've started a new command
      current_task = nil
      last_id = id
      local initial_yaw_deg = get_ground_course_deg()
      load_trick(cmd)
      if command_table[cmd] == nil then
         gcs:send_text(MAV_SEVERITY.ERROR, string.format("Trick %u not found", cmd))
         return
      end
      gcs:send_text(MAV_SEVERITY.INFO, string.format("Starting %s!", command_table[cmd].name ))

      -- work out yaw between previous WP and next WP
      local cnum = mission:get_current_nav_index()

      if AEROM_MIS_ANGLE:get() == 0 then
         -- find previous nav waypoint
         local loc_prev = ahrs:get_location()
         if cnum > 1 then
            loc_prev = get_wp_location(cnum-1)
            local i= cnum-1
            while get_wp_location(i):lat() == 0 and get_wp_location(i):lng() == 0 do
               i = i-1
               loc_prev = get_wp_location(i)
            end
         end

         -- find next nav waypoint
         local loc_next = get_wp_location(cnum+1)
         i = cnum+1
         while get_wp_location(i):lat() == 0 and get_wp_location(i):lng() == 0 do
            i = i+1
            loc_next = get_wp_location(resolve_jump(i))
         end
         local wp_yaw_deg = math.deg(loc_prev:get_bearing(loc_next))
         if math.abs(wrap_180(initial_yaw_deg - wp_yaw_deg)) > 90 and cnum > 1 then
            gcs:send_text(MAV_SEVERITY.INFO, string.format("Doing turnaround! iyaw=%.1f wyaw=%.1f", initial_yaw_deg, wp_yaw_deg))
            wp_yaw_deg = wrap_180(wp_yaw_deg + 180)
         end
         initial_yaw_deg = wp_yaw_deg
      else
         initial_yaw_deg = AEROM_MIS_ANGLE:get()
      end
      current_task = PathTask(command_table[cmd].fn, command_table[cmd].name,
                              id, initial_yaw_deg, arg1, arg2, arg3, arg4)
   end
end

local last_trick_action_state = rc:get_aux_cached(TRIK_ACT_FN:get())
local trick_sel_chan = nil
local last_trick_selection = nil

--[[
   get selected trick. Trick numbers are 1 .. TRIK_COUNT. A value of 0 is invalid
--]]
function get_trick_selection()
   if trick_sel_chan == nil then
      trick_sel_chan = rc:find_channel_for_option(TRIK_SEL_FN:get())
      if trick_sel_chan == nil then
         return 0
      end
   end
   -- get trick selection based on selection channel input and number of tricks
   local i = math.floor(TRIK_COUNT:get() * constrain(0.5*(trick_sel_chan:norm_input_ignore_trim()+1),0,0.999)+1)
   if TRICKS[i] == nil then
      return 0
   end
   return i
end

--[[
   check for running a trick
--]]
function check_trick()
   local selection = get_trick_selection()
   local action = rc:get_aux_cached(TRIK_ACT_FN:get())
   if action == 0 and current_task ~= nil then
      gcs:send_text(MAV_SEVERITY.ALERT,string.format("Trick aborted"))
      current_task = nil
      last_trick_selection = nil
      -- use invalid mode to disable script control
      vehicle:nav_scripting_enable(255)
      return
   end
   if selection == 0 then
      return
   end
   if action == 1 and selection ~= last_trick_selection then
      local id = TRICKS[selection].id:get()
         if id == -1 then
            gcs:send_text(MAV_SEVERITY.ERROR,string.format("Trick %u not setup",selection))
            last_trick_selection = selection
            return
         end
      load_trick(id)
      if command_table[id] ~= nil then
         local cmd = command_table[id]
         gcs:send_text(MAV_SEVERITY.INFO, string.format("Trick %u selected (%s)", selection, cmd.name))
         last_trick_selection = selection
         return
      end
   end
   if current_task ~= nil then
      -- let the task finish
      return
   end
   if action ~= last_trick_action_state then
      last_trick_selection = selection
      last_trick_action_state = action
      if selection == 0 then
         gcs:send_text(MAV_SEVERITY.ALERT, string.format("No trick selected"))
         return
      end
      local id = TRICKS[selection].id:get()
      if id == -1 then
         gcs:send_text(MAV_SEVERITY.ALERT,string.format("Trick %u not setup",selection))
         last_trick_selection = selection
         return
      end
      load_trick(id)
      if command_table[id] == nil then
         gcs:send_text(MAV_SEVERITY.ALERT, string.format("Invalid trick ID %u", id))
         return
      end
      local cmd = command_table[id]
      if action == 1 then
         gcs:send_text(MAV_SEVERITY.INFO, string.format("Trick %u selected (%s)", selection, cmd.name))
      end
      if action == 2 then
         last_trick_selection = nil
         local current_mode = vehicle:get_mode()
         if not vehicle:nav_scripting_enable(current_mode) then
            gcs:send_text(MAV_SEVERITY.ALERT, string.format("Tricks not available in mode"))
            return
         end
         gcs:send_text(MAV_SEVERITY.INFO, string.format("Trick %u started (%s)", selection, cmd.name))
         local initial_yaw_deg = get_ground_course_deg()
         current_task = PathTask(cmd.fn,
                                 cmd.name,
                                 nil,
                                 initial_yaw_deg,
                                 TRICKS[selection].args[1]:get(),
                                 TRICKS[selection].args[2]:get(),
                                 TRICKS[selection].args[3]:get(),
                                 TRICKS[selection].args[4]:get())
      end
   end

end

function update()
   if ahrs:get_velocity_NED() == nil  or ahrs:get_EAS2TAS() == nil or ahrs:get_relative_position_NED_origin() == nil then
      -- don't start till we have valid ahrs estimates
      return update, 1000.0/LOOP_RATE
   end
   if vehicle:get_mode() == MODE_AUTO then
      if arming:is_armed() then
         log_position("VEH", ahrs:get_location(), ahrs:get_quaternion())
      end
      check_auto_mission()
   elseif TRICKS ~= nil then
      check_trick()
   end

   if current_task ~= nil then
      if not do_path() then
         gcs:send_text(MAV_SEVERITY.INFO, string.format("Finishing %s!", current_task.name))
         if current_task.id ~= nil then
            vehicle:nav_script_time_done(current_task.id)
         else
            -- use invalid mode to disable script control
            vehicle:nav_scripting_enable(255)
         end
         current_task = nil
      end
   end
   
   return update, 1000.0/LOOP_RATE
end

gcs:send_text(MAV_SEVERITY.INFO, string.format("Loaded plane_aerobatics.lua"))
return update()