Ardupilot2/libraries/SITL/examples/JSON/MATLAB/Copter/SIM_multicopter.m

clc
clearvars
close all
addpath(genpath('../../MATLAB'))

% Physics of a multi copter

% load in the parameters for a frame, generated by Copter.m
try
    state = load('Hexsoon','copter');
catch
    run('Copter.m')
    fprintf('Could not find Hexsoon.mat file, running copter.m\n')
    return
end

% Setup environmental conditions
state.environment.density = 1.225; % (kg/m^3)
state.gravity_mss = 9.80665; % (m/s^2)

% Setup the time step size for the Physics model
delta_t = 1/400;

% This is the ip that SITL is running at
target_ip = '127.0.0.1';
target_ip = '192.168.194.97';

% define init and time setup functions
init_function = @(state)init(state);
physics_function = @(pwm_in,state)physics_step(pwm_in,state,delta_t);

% setup connection
SITL_connector(target_ip,state,init_function,physics_function,delta_t);

% Simulator model must take and return a structure with the felids: 
% gyro(roll, pitch, yaw) (radians/sec) body frame
% attitude(roll, pitch yaw) (radians)
% accel(north, east, down) (m/s^2) body frame
% velocity(north, east,down) (m/s) earth frame
% position(north, east, down) (m) earth frame 
% the structure can have any other felids required for the physics model

% init values
function state = init(state)
for i = 1:numel(state.copter.motors)
    state.copter.motors(i).rpm = 0;
    state.copter.motors(i).current = 0;
end
state.gyro = [0,0,0]; % (rad/sec)
state.attitude = [0,0,0]; % (radians) (roll, pitch, yaw)
state.accel = [0,0,0]; % (m/s^2) body frame
state.velocity = [0,0,0]; % (m/s) earth frame
state.position = [0,0,0]; % (m) earth frame
state.drag = [0,0,0]; % (N) body frame drag
state.rotational_drag = [0,0,0]; % (N/m) body frame rotational drag
end

% Take a physics time step
function state = physics_step(pwm_in,state,delta_t)

% Calculate the dropped battery voltage, assume current draw from last step
state.copter.battery.current = sum([state.copter.motors.current]);
state.copter.battery.dropped_voltage = state.copter.battery.voltage - state.copter.battery.resistance * state.copter.battery.current;

% Calculate the torque and thrust, assume RPM is last step value
for i = 1:numel(state.copter.motors)
    motor = state.copter.motors(i);

    % Calculate the throttle
    throttle = (pwm_in(motor.channel) - 1100) / 800;
    throttle = max(throttle,0);
    throttle = min(throttle,1);

    % effective voltage
    voltage = throttle * state.copter.battery.dropped_voltage;

    % Take the RPM from the last step to calculate the new
    % torque and current
    Kt = 1/(motor.electrical.kv * ( (2*pi)/60) );

    % rpm equation rearranged for current
    current = ((motor.electrical.kv * voltage) - motor.rpm) / ((motor.electrical.resistance + motor.esc.resistance) * motor.electrical.kv);
    torque = current * Kt;

    prop_drag = motor.prop.PConst * state.environment.density * (motor.rpm/60)^2 * motor.prop.diameter^5;

    w = motor.rpm * ((2*pi)/60); % convert to rad/sec

    w1 = w + ((torque-prop_drag) / motor.prop.inertia) * delta_t;

    rps = w1 * (1/(2*pi));

    % can never have negative rps
    rps = max(rps,0);

    % Calculate the thrust (with fudge factor!)
    thrust = 2.2 * motor.prop.TConst * state.environment.density * rps^2 * motor.prop.diameter^4;

    % calculate resulting moments
    moment_roll = thrust * motor.location(1);
    moment_pitch = thrust * motor.location(2);
    moment_yaw = -torque * motor.direction;

    % Update main structure
    state.copter.motors(i).torque = torque;
    state.copter.motors(i).current = current;
    state.copter.motors(i).rpm = rps * 60;
    state.copter.motors(i).thrust = thrust;
    state.copter.motors(i).moment_roll = moment_roll;
    state.copter.motors(i).moment_pitch = moment_pitch;
    state.copter.motors(i).moment_yaw = moment_yaw;
end

% Update attitude, moments to rotational acceleration to rotational velocity to attitude
moments = [-sum([state.copter.motors.moment_roll]),sum([state.copter.motors.moment_pitch]),sum([state.copter.motors.moment_yaw])] - state.rotational_drag;
ang_acel = moments / state.copter.inertia;
state.gyro = state.gyro + ang_acel * delta_t;
state.attitude = state.attitude + state.gyro * delta_t;

% Calculate a dcm, see https://github.com/ArduPilot/ardupilot/blob/f5320e88161a17e78ffc969bf7ce0bec48adbe7a/libraries/AP_Math/matrix3.cpp#L26
cp = cos(state.attitude(2));
sp = sin(state.attitude(2));
sr = sin(state.attitude(1));
cr = cos(state.attitude(1));
sy = sin(state.attitude(3));
cy = cos(state.attitude(3));

dcm = [cp * cy,                   cp * sy,                    -sp;...
      (sr * sp * cy) - (cr * sy), (sr * sp * sy) + (cr * cy), sr * cp;...
      (cr * sp * cy) + (sr * sy), (cr * sp * sy) - (sr * cy), cr * cp;];

% Calculate the forces about the CG (N,E,D) (body frame)
force = [0,0,-sum([state.copter.motors.thrust])] - state.drag;

% body frame accelerations (NED)
state.accel = force / state.copter.mass;

% earth frame accelerations (NED)
acel_ef = state.accel * dcm;
acel_ef(3) = acel_ef(3) + state.gravity_mss;

state.velocity = state.velocity + acel_ef * delta_t;
state.position = state.position + state.velocity * delta_t;

% make sure we can't go underground (NED so underground is positive)
if state.position(3) >= 0
    state.position(3) = 0;
    state.velocity = [0,0,0];
    state.accel = [0,0,-state.gravity_mss];
    state.gyro = [0,0,0];
end

% caculate the body frame velocity and resulting drag
bf_velo = (state.velocity / dcm);
state.drag = sign(bf_velo) .* state.copter.cd .* state.copter.cd_ref_area .* 0.5 .* state.environment.density .* bf_velo.^2;

% estimate rotational drag (mostly for yaw)
state.rotational_drag = 0.3 * sign(state.gyro) .* state.gyro.^2; % estimated to give a reasonable max rotation rate

end