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196 lines
6.7 KiB
196 lines
6.7 KiB
clc |
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clearvars |
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close all |
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addpath(genpath('../../MATLAB')) |
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% Physics of a multi copter |
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% load in the parameters for a frame, generated by Copter.m |
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try |
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state = load('Hexsoon','copter'); |
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catch |
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run('Copter.m') |
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fprintf('Could not find Hexsoon.mat file, running copter.m\n') |
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return |
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end |
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% Setup environmental conditions |
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state.environment.density = 1.225; % (kg/m^3) |
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state.gravity_mss = 9.80665; % (m/s^2) |
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% Setup the time step size for the Physics model |
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max_timestep = 1/50; |
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% define init and time setup functions |
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init_function = @init; |
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physics_function = @physics_step; |
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% setup connection |
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SITL_connector(state,init_function,physics_function,max_timestep); |
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% Simulator model must take and return a structure with the felids: |
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% gyro(roll, pitch, yaw) (radians/sec) body frame |
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% attitude(roll, pitch yaw) (radians) |
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% accel(north, east, down) (m/s^2) body frame |
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% velocity(north, east,down) (m/s) earth frame |
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% position(north, east, down) (m) earth frame |
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% the structure can have any other felids required for the physics model |
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% init values |
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function state = init(state) |
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for i = 1:numel(state.copter.motors) |
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state.copter.motors(i).rpm = 0; |
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state.copter.motors(i).current = 0; |
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end |
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state.gyro = [0;0;0]; % (rad/sec) |
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state.dcm = diag([1,1,1]); % direction cosine matrix |
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state.attitude = [0;0;0]; % (radians) (roll, pitch, yaw) |
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state.accel = [0;0;0]; % (m/s^2) body frame |
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state.velocity = [0;0;0]; % (m/s) earth frame |
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state.position = [0;0;0]; % (m) earth frame |
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state.bf_velo = [0;0;0]; % (m/s) body frame |
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end |
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% Take a physics time step |
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function state = physics_step(pwm_in,state) |
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% Calculate the dropped battery voltage, assume current draw from last step |
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state.copter.battery.current = sum([state.copter.motors.current]); |
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state.copter.battery.dropped_voltage = state.copter.battery.voltage - state.copter.battery.resistance * state.copter.battery.current; |
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% Calculate the torque and thrust, assume RPM is last step value |
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for i = 1:numel(state.copter.motors) |
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motor = state.copter.motors(i); |
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% Calculate the throttle |
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throttle = (pwm_in(motor.channel) - 1100) / 800; |
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throttle = max(throttle,0); |
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throttle = min(throttle,1); |
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% effective voltage |
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voltage = throttle * state.copter.battery.dropped_voltage; |
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% Take the RPM from the last step to calculate the new |
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% torque and current |
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Kt = 1/(motor.electrical.kv * ( (2*pi)/60) ); |
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% rpm equation rearranged for current |
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current = ((motor.electrical.kv * voltage) - motor.rpm) / ((motor.electrical.resistance + motor.esc.resistance) * motor.electrical.kv); |
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torque = current * Kt; |
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prop_drag = motor.prop.PConst * state.environment.density * (motor.rpm/60)^2 * motor.prop.diameter^5; |
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w = motor.rpm * ((2*pi)/60); % convert to rad/sec |
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w1 = w + ((torque-prop_drag) / motor.prop.inertia) * state.delta_t; |
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rps = w1 * (1/(2*pi)); |
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% can never have negative rps |
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rps = max(rps,0); |
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% Calculate the thrust (with fudge factor!) |
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thrust = 2.2 * motor.prop.TConst * state.environment.density * rps^2 * motor.prop.diameter^4; |
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% calculate resulting moments |
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moment_roll = thrust * motor.location(1); |
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moment_pitch = thrust * motor.location(2); |
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moment_yaw = -torque * motor.direction; |
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% Update main structure |
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state.copter.motors(i).torque = torque; |
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state.copter.motors(i).current = current; |
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state.copter.motors(i).rpm = rps * 60; |
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state.copter.motors(i).thrust = thrust; |
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state.copter.motors(i).moment_roll = moment_roll; |
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state.copter.motors(i).moment_pitch = moment_pitch; |
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state.copter.motors(i).moment_yaw = moment_yaw; |
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end |
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drag = sign(state.bf_velo) .* state.copter.cd .* state.copter.cd_ref_area .* 0.5 .* state.environment.density .* state.bf_velo.^2; |
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% Calculate the forces about the CG (N,E,D) (body frame) |
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force = [0;0;-sum([state.copter.motors.thrust])] - drag; |
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% estimate rotational drag |
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rotational_drag = 0.2 * sign(state.gyro) .* state.gyro.^2; % estimated to give a reasonable max rotation rate |
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% Update attitude, moments to rotational acceleration to rotational velocity to attitude |
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moments = [-sum([state.copter.motors.moment_roll]);sum([state.copter.motors.moment_pitch]);sum([state.copter.motors.moment_yaw])] - rotational_drag; |
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state = update_dynamics(state,force,moments); |
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end |
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% integrate the acceleration resulting from the forces and moments to get the |
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% new state |
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function state = update_dynamics(state,force,moments) |
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rot_accel = (moments' / state.copter.inertia)'; |
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state.gyro = state.gyro + rot_accel * state.delta_t; |
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% Constrain to 2000 deg per second, this is what typical sensors max out at |
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state.gyro = max(state.gyro,deg2rad(-2000)); |
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state.gyro = min(state.gyro,deg2rad(2000)); |
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% update the dcm and attitude |
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[state.dcm, state.attitude] = rotate_dcm(state.dcm,state.gyro * state.delta_t); |
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% body frame accelerations |
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state.accel = force / state.copter.mass; |
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% earth frame accelerations (NED) |
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accel_ef = state.dcm * state.accel; |
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accel_ef(3) = accel_ef(3) + state.gravity_mss; |
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% if we're on the ground, then our vertical acceleration is limited |
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% to zero. This effectively adds the force of the ground on the aircraft |
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if state.position(3) >= 0 && accel_ef(3) > 0 |
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accel_ef(3) = 0; |
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end |
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% work out acceleration as seen by the accelerometers. It sees the kinematic |
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% acceleration (ie. real movement), plus gravity |
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state.accel = state.dcm' * (accel_ef + [0; 0; -state.gravity_mss]); |
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state.velocity = state.velocity + accel_ef * state.delta_t; |
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state.position = state.position + state.velocity * state.delta_t; |
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% make sure we can't go underground (NED so underground is positive) |
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if state.position(3) >= 0 |
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state.position(3) = 0; |
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state.velocity = [0;0;0]; |
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state.gyro = [0;0;0]; |
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end |
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% calculate the body frame velocity for drag calculation |
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state.bf_velo = state.dcm' * state.velocity; |
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end |
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function [dcm, euler] = rotate_dcm(dcm, ang) |
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% rotate |
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delta = [dcm(1,2) * ang(3) - dcm(1,3) * ang(2), dcm(1,3) * ang(1) - dcm(1,1) * ang(3), dcm(1,1) * ang(2) - dcm(1,2) * ang(1); |
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dcm(2,2) * ang(3) - dcm(2,3) * ang(2), dcm(2,3) * ang(1) - dcm(2,1) * ang(3), dcm(2,1) * ang(2) - dcm(2,2) * ang(1); |
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dcm(3,2) * ang(3) - dcm(3,3) * ang(2), dcm(3,3) * ang(1) - dcm(3,1) * ang(3), dcm(3,1) * ang(2) - dcm(3,2) * ang(1)]; |
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dcm = dcm + delta; |
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% normalise |
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a = dcm(1,:); |
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b = dcm(2,:); |
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error = a * b'; |
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t0 = a - (b *(0.5 * error)); |
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t1 = b - (a *(0.5 * error)); |
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t2 = cross(t0,t1); |
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dcm(1,:) = t0 * (1/norm(t0)); |
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dcm(2,:) = t1 * (1/norm(t1)); |
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dcm(3,:) = t2 * (1/norm(t2)); |
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% calculate euler angles |
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euler = [atan2(dcm(3,2),dcm(3,3)); -asin(dcm(3,1)); atan2(dcm(2,1),dcm(1,1))]; |
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end |
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