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ardupilot/libraries/AP_Scripting/examples/quadruped.lua

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Lua
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-- Lua "motor driver" for a four legged (aka quadruped) walking robot
--
-- This script consumes controller outputs (i.e. roll, pitch, yaw/steering, throttle, lateral) from
-- the vehicle code and then calculates the outputs for 12 servos controlling four legs
--
-- AutoPilot servo connections:
-- Output1: front right coxa (hip) servo
-- Output2: front right femur (thigh) servo
-- Output3: front right tibia (shin) servo
-- Output4: front left coxa (hip) servo
-- Output5: front left femur (thigh) servo
-- Output6: front left tibia (shin) servo
-- Output7: back left coxa (hip) servo
-- Output8: back left femur (thigh) servo
-- Output9: back left tibia (shin) servo
-- Output10: back right coxa (hip) servo
-- Output11: back right femur (thigh) servo
-- Output12: back right tibia (shin) servo
--
-- CAUTION: This script should only be used with ArduPilot Rover's firmware
local FRAME_LEN = 80 -- frame length in mm
local FRAME_WIDTH = 150 -- frame width in mm
local COXA_LEN = 30 -- distance (in mm) from coxa (aka hip) servo to femur servo
local FEMUR_LEN = 85 -- distance (in mm) from femur servo to tibia servo
local TIBIA_LEN = 125 -- distance (in mm) from tibia servo to foot
--body position and rotation parameters
local body_rot_max = 10 -- body rotation maximum for any individual axis
local body_rot_x = 0 -- body rotation about the X axis (i.e. roll rotation)
local body_rot_y = 0 -- body rotation about the Y axis (i.e. pitch rotation)
local body_rot_z = 0 -- body rotation about the Z axis (i.e. yaw rotation)
local body_pos_x = 0 -- body position in the X axis (i.e. forward, back). should be -40mm to +40mm
local body_pos_y = 0 -- body position in the Y axis (i.e. right, left). should be -40mm to +40mm
local body_pos_z = 0 -- body position in the Z axis (i.e. up, down). should be -40mm to +40mm
-- starting positions of the legs
local endpoint_LB = {math.cos(math.rad(45))*(COXA_LEN + FEMUR_LEN), math.sin(math.rad(45))*(COXA_LEN + FEMUR_LEN), TIBIA_LEN}
local endpoint_LF = {math.cos(math.rad(45))*(COXA_LEN + FEMUR_LEN), math.sin(math.rad(-45))*(COXA_LEN + FEMUR_LEN), TIBIA_LEN}
local endpoint_RF = {-math.cos(math.rad(45))*(COXA_LEN + FEMUR_LEN), math.sin(math.rad(-45))*(COXA_LEN + FEMUR_LEN), TIBIA_LEN}
local endpoint_RB = {-math.cos(math.rad(45))*(COXA_LEN + FEMUR_LEN), math.sin(math.rad(45))*(COXA_LEN + FEMUR_LEN), TIBIA_LEN}
-- control input enum
local control_input_roll = 1
local control_input_pitch = 2
local control_input_throttle = 3
local control_input_yaw = 4
local control_input_height = 8
local xy_travel_max = 80 -- x and y axis travel max (used to convert control input) in mm
local yaw_travel_max = 10 -- yaw travel maximum (used to convert control input)
local height_max = 40 -- height maximum (used to convert control input)
local travel_dz = 5 -- travel deadzone. x, y and yaw travel requests are ignored if their absolute value is less than this number
local x_travel = 0 -- target lenght of gait along x
local y_travel = 0 -- target travel of gait along y
local yaw_travel = 0 -- yaw rotation travel target
local leg_lift_height = 50 -- leg lift height (in mm) while walking
-- gait definition parameters
local gait_type = 0 -- gait pattern. 0 = alternating gait, 1 = wave gait.
local gait_step = 0 -- gait step in execution
local gait_step_total = 0 -- number of steps in gait
local gait_step_leg_start = {0,0,0,0} -- leg starts moving on this gait step (front-right, front-left, back-left, back-right)
local gait_lifted_steps = 0 -- number of steps that a leg is lifted for
local gait_down_steps = 0 -- number of steps that the leg lifted needs to be put down for
local gait_lift_divisor = 0 -- when a leg is lifted and brought back down the action is divided into 2 or multiple steps, so the travel distance also need to be split in between the steps to make the transition natural
local gait_half_lift_height = 0 -- used to split lift across two steps
local gait_travel_divisor = 0 -- number of steps in the gait the leg is touching the floor, this is used as a factor to split the travel distance between the steps
local gait_pos_x = {0,0,0,0} -- X-axis position for each leg (back-right, front-right, back-left, front-left)
local gait_pos_y = {0,0,0,0} -- Y-axis position for each leg (back-right, front-right, back-left, front-left)
local gait_pos_z = {0,0,0,0} -- Z-axis position for each leg (back-right, front-right, back-left, front-left)
local gait_rot_z = {0,0,0,0} -- Z-axis rotation for each leg (back-right, front-right, back-left, front-left)
local last_angle = {0,0,0,0,0,0,0,0,0,0,0,0}
local start_time = 0
local curr_target = 0
function Gaitselect()
if (gait_type == 0) then
-- alternating gait
gait_step_total = 6
gait_step_leg_start = {1,4,4,1}
gait_lifted_steps = 2
gait_down_steps = 1
gait_lift_divisor = 2
gait_half_lift_height = 1
gait_travel_divisor = 4
elseif (gait_type == 1) then
-- wave gait with 28 steps
gait_step_total = 28
gait_step_leg_start = {8,15,1,22}
gait_lifted_steps = 3
gait_down_steps = 2
gait_lift_divisor = 2
gait_half_lift_height = 3
gait_travel_divisor = 24
end
end
-- Calculate Gait sequence
function calc_gait_sequence()
local move_requested = (math.abs(x_travel) > travel_dz) or (math.abs(y_travel) > travel_dz) or (math.abs(yaw_travel) > travel_dz)
if move_requested then
for leg_index=1, 4 do
update_leg(leg_index,move_requested)
end
gait_step = gait_step + 1
if (gait_step>gait_step_total) then
gait_step = 1
end
else
gait_pos_x = {0,0,0,0}
gait_pos_y = {0,0,0,0}
gait_pos_z = {0,0,0,0}
gait_rot_z = {0,0,0,0}
end
end
-- in order for the robot to move forward it needs to move its legs in a
-- specific order and this is repeated over and over to attain linear motion. when a
-- specific leg number is passed the update_leg() produces the set of values for the
-- given leg at that step, for each cycle of the gait each leg will move to a set
-- distance which is decided by the x_travel, yaw_travel, y_travel
function update_leg(moving_leg,move_requested)
local leg_step = gait_step - gait_step_leg_start[moving_leg]
if ((move_requested and (gait_lifted_steps > 0) and leg_step==0) or
(not move_requested and leg_step==0 and ((gait_pos_x[moving_leg]>2) or
(gait_pos_y[moving_leg]>2) or (gait_rot_z[moving_leg] >2)))) then
gait_pos_x[moving_leg] = 0
gait_pos_z[moving_leg] = -leg_lift_height
gait_pos_y[moving_leg] = 0
gait_rot_z[moving_leg] = 0
elseif (((gait_lifted_steps==2 and leg_step==0) or (gait_lifted_steps>=3 and
(leg_step==-1 or leg_step==(gait_step_total-1)))) and move_requested) then
gait_pos_x[moving_leg] = -x_travel/gait_lift_divisor
gait_pos_z[moving_leg] = -3*leg_lift_height/(3+gait_half_lift_height)
gait_pos_y[moving_leg] = -y_travel/gait_lift_divisor
gait_rot_z[moving_leg] = -yaw_travel/gait_lift_divisor
elseif ((gait_lifted_steps>=2) and (leg_step==1 or leg_step==-(gait_step_total-1)) and move_requested) then
gait_pos_x[moving_leg] = x_travel/gait_lift_divisor
gait_pos_z[moving_leg] = -3*leg_lift_height/(3+gait_half_lift_height)
gait_pos_y[moving_leg] = y_travel/gait_lift_divisor
gait_rot_z[moving_leg] = yaw_travel/gait_lift_divisor
elseif (((gait_lifted_steps==5 and (leg_step==-2 ))) and move_requested) then
gait_pos_x[moving_leg] = -x_travel * 0.5
gait_pos_z[moving_leg] = -leg_lift_height * 0.5
gait_pos_y[moving_leg] = -y_travel * 0.5
gait_rot_z[moving_leg] = -yaw_travel * 0.5
elseif ((gait_lifted_steps==5) and (leg_step==2 or leg_step==-(gait_step_total-2)) and move_requested) then
gait_pos_x[moving_leg] = x_travel * 0.5
gait_pos_z[moving_leg] = -leg_lift_height * 0.5
gait_pos_y[moving_leg] = y_travel * 0.5
gait_rot_z[moving_leg] = yaw_travel * 0.5
elseif ((leg_step==gait_down_steps or leg_step==-(gait_step_total-gait_down_steps)) and gait_pos_y[moving_leg]<0) then
gait_pos_x[moving_leg] = x_travel * 0.5
gait_pos_z[moving_leg] = 0
gait_pos_y[moving_leg] = y_travel * 0.5
gait_rot_z[moving_leg] = yaw_travel * 0.5
else
gait_pos_x[moving_leg] = gait_pos_x[moving_leg] - (x_travel/gait_travel_divisor)
gait_pos_z[moving_leg] = 0
gait_pos_y[moving_leg] = gait_pos_y[moving_leg] - (y_travel/gait_travel_divisor)
gait_rot_z[moving_leg] = gait_rot_z[moving_leg] - (yaw_travel/gait_travel_divisor)
end
end
-- Body Forward Kinematics calculates where each leg should be.
-- inputs are
-- a) body rotations: body_rot_x, body_rot_y, body_rot_z
-- b) body position: body_pos_x, body_pos_y, body_pos_z
-- c) offset of the center of body
function body_forward_kinematics(X, Y, Z, Xdist, Ydist, Zrot)
local totaldist_x = X + Xdist + body_pos_x
local totaldist_y = Y + Ydist + body_pos_y
local distBodyCenterFeet = math.sqrt(totaldist_x^2 + totaldist_y^2)
local AngleBodyCenter = math.atan(totaldist_y, totaldist_x)
local rolly = math.tan(math.rad(body_rot_y)) * totaldist_x
local pitchy = math.tan(math.rad(body_rot_x)) * totaldist_y
local ansx = math.cos(AngleBodyCenter + math.rad(body_rot_z+Zrot)) * distBodyCenterFeet - totaldist_x + body_pos_x
local ansy = math.sin(AngleBodyCenter + math.rad(body_rot_z+Zrot)) * distBodyCenterFeet - totaldist_y + body_pos_y
local ansz = rolly + pitchy + body_pos_z
return {ansx, ansy, ansz}
end
-- Leg Inverse Kinematics calculates the angles for each servo of each joint using the output of the
-- body_forward_kinematics() function which gives the origin of each leg on the body frame
function leg_inverse_kinematics(x, y, z)
local coxa = math.deg(math.atan(x, y))
local trueX = math.sqrt(x^2 + y^2) - COXA_LEN
local im = math.sqrt(trueX^2 + z^2)
local q1 = -math.atan(z, trueX)
local d1 = FEMUR_LEN^2 - TIBIA_LEN^2 + im^2
local d2 = 2*FEMUR_LEN*im
local q2 = math.acos(d1/d2)
local femur = math.deg(q1+q2)
d1 = FEMUR_LEN^2 - im^2 + TIBIA_LEN^2
d2 = 2*TIBIA_LEN*FEMUR_LEN
local tibia = math.deg(math.acos(d1/d2)-math.rad(90))
return {coxa, -femur, -tibia}
end
-- checks if the servo has moved to its expected position
function servo_estimate(current_angle)
local target = 0
for j = 1, 12 do
curr_target = math.abs(current_angle[j] - last_angle[j])
if curr_target > target then
target = curr_target
end
end
local target_time = target * (0.24/60) * 1000
return (millis() - start_time) > target_time
end
-- main_inverse_kinematics produces the inverse kinematic solution for each
-- leg joint servo by taking into consideration the initial_pos, gait offset and the body inverse kinematic values.
function main_inverse_kinematics()
local ans_RB = body_forward_kinematics(endpoint_RB[1]+gait_pos_x[1],
endpoint_RB[2]+gait_pos_y[1],
endpoint_RB[3]+gait_pos_z[1],
-FRAME_LEN*0.5, FRAME_WIDTH*0.5,
gait_rot_z[1])
local angles_RB = leg_inverse_kinematics(endpoint_RB[1]+ans_RB[1]+gait_pos_x[1],
endpoint_RB[2]+ans_RB[2]+gait_pos_y[1],
endpoint_RB[3]+ans_RB[3]+gait_pos_z[1])
angles_RB[1] = 45 + angles_RB[1]
local ans_RF = body_forward_kinematics(endpoint_RF[1]+gait_pos_x[2],
endpoint_RF[2]+gait_pos_y[2],
endpoint_RF[3]+gait_pos_z[2],
-FRAME_LEN*0.5, -FRAME_WIDTH*0.5,
gait_rot_z[2])
local angles_RF = leg_inverse_kinematics(endpoint_RF[1]-ans_RF[1]+gait_pos_x[2],
endpoint_RF[2]-ans_RF[2]-gait_pos_y[2],
endpoint_RF[3]+ans_RF[3]+gait_pos_z[2])
angles_RF[1] = 135 + angles_RF[1]
local ans_LB = body_forward_kinematics(endpoint_LB[1]+gait_pos_x[3],
endpoint_LB[2]+gait_pos_y[3],
endpoint_LB[3]+gait_pos_z[3],
FRAME_LEN*0.5, FRAME_WIDTH*0.5,
gait_rot_z[3])
local angles_LB = leg_inverse_kinematics(endpoint_LB[1]+ans_LB[1]+gait_pos_x[3],
endpoint_LB[2]+ans_LB[2]+gait_pos_y[3],
endpoint_LB[3]+ans_LB[3]+gait_pos_z[3])
angles_LB[1] = -45 + angles_LB[1]
local ans_LF = body_forward_kinematics(endpoint_LF[1]+gait_pos_x[4],
endpoint_LF[2]+gait_pos_y[4],
endpoint_LF[3]+gait_pos_z[4],
FRAME_LEN*0.5, -FRAME_WIDTH*0.5,
gait_rot_z[4])
local angles_LF = leg_inverse_kinematics(endpoint_LF[1]-ans_LF[1]+gait_pos_x[4],
endpoint_LF[2]-ans_LF[2]-gait_pos_y[4],
endpoint_LF[3]+ans_LF[3]+gait_pos_z[4])
angles_LF[1] = -135 + angles_LF[1]
Gaitselect()
local current_angle = {angles_RF[1],angles_RF[2],angles_RF[3],
angles_LF[1],angles_LF[2],angles_LF[3],
angles_LB[1],angles_LB[2],angles_LB[3],
angles_RB[1],angles_RB[2],angles_RB[3]}
if servo_estimate(current_angle) then
start_time = millis()
calc_gait_sequence()
last_angle = current_angle
end
return current_angle
end
-- servo angles when robot is disarmed and resting body on the ground
local rest_angles = { 45, -90, 40, -- front right leg (coxa, femur, tibia)
-45, -90, 40, -- front left leg (coxa, femur, tibia)
-45, -90, 40, -- back left leg (coxa, femur, tibia)
45, -90, 40} -- back right leg (coxa, femur, tibia)
function update()
local throttle = vehicle:get_control_output(control_input_throttle) * xy_travel_max
local gait_direction
if throttle > 0 then
gait_direction = -1
y_travel = throttle
elseif throttle < 0 then
gait_direction = 1
y_travel = -throttle
elseif throttle == 0 then
gait_direction = 1
y_travel = 0
end
yaw_travel = -vehicle:get_control_output(control_input_yaw) * yaw_travel_max
body_rot_x = -vehicle:get_control_output(control_input_roll) * body_rot_max
body_rot_y = -vehicle:get_control_output(control_input_pitch) * body_rot_max
body_pos_z = vehicle:get_control_output(control_input_height) * height_max
local servo_direction = { gait_direction * 1, -1, 1, -- front right leg (coxa, femur, tibia)
gait_direction * 1, 1, -1, -- front left leg (coxa, femur, tibia)
gait_direction * -1, -1, 1, -- back left leg (coxa, femur, tibia)
gait_direction * -1, 1, -1} -- back right leg (coxa, femur, tibia)
local angles
if arming:is_armed() then
angles = main_inverse_kinematics()
else
angles = rest_angles
end
for i = 1, 12 do
SRV_Channels:set_output_pwm_chan_timeout(i-1, math.floor(((angles[i] * servo_direction[i] * 1000)/90) + 1500), 1000)
end
return update,10
end
-- turn off rudder based arming/disarming
param:set_and_save('ARMING_RUDDER', 0)
gcs:send_text(0, "quadruped simulation")
return update()
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