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- In order to run this script you must ensure to have the "functions" folder in your working directory
MPC Control of a differential drive unicycle
This is a live script which implements a MPC controller for a differential drive unicycle. There are various topic covered here:
- Implementation of multiple shooting to solve an optimal control problem
- Solve a trajectory optimization and apply the optimal actions in open loop
- Close the loop by implementing a MPC algorithm for the point to point motion problem
- Implement a trajectory tracking MPC
T = 3; % Time horizon of the optimal control problem
N = round(T/dt,0); % Number of timesteps
Tk = 0.1; % Time at which a "kick" occurs
Nk = round(Tk/dt, 0); % Time step of the kick event
x_start = [0; 0; 0]; % Starting position
x_target = [1 ; 1; pi]; % Arrival
d = 0.1; % Distance of the wheels 10 cm
r = 0.05; % wheel radius 5 cm
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OCP solution
Here we solve an optimal control problem for the differential drive unicycle. We have to find the control action (velocities) that drive the system from the starting to the arrival configuration
x_des = repmat(x_target, [1, N+1]);
[x_opt, u_opt] = solve_ocp(r, d, x_start, x_des, dt, N, w_x, w_u); % Check the function for details
Here we integrate the control action. Why this is needed?
This function is kind of a "simulator". First of all usually when solving an OCP the timestep is quite large with respect to the one of a simulator. This function allows you to set a dt of the simulator smaller in order to have more accurate results. You may also want to use a different integration scheme and compare the results with the one you are using inside the ocp formulation.
The main point in this example though, is to show where the robot would be when it gets kicked. In the ocp formulation there is no kick, and the prediction of the state will be wrong in presence of disturbances.
x_int = integrate_unicycle(r, d, x_start, u_opt, dt, N, 0);
% Plot the optimal trajectory
plot(x_int(1,:), x_int(2, :))
plot(x_opt(1, :), x_opt(2, :), ['--', 'r'])
scatter(x_target(1), x_target(2), 'filled')
lgd = legend("Real", "Predicted", "Target");
lgd.Location = 'northwest';
title("Trajectories without disturbances")
Let's see an animation of the system
draw_unicycle(x_opt, x_des, rob_diam)
Now show the control actions
legend("omega_l", "omega_r")
Problem of Open loop trajectory tracking
With the last parameter set as 1 we are "kicking" the robot at a certain instant so we can see how the robot behaves
x_int = integrate_unicycle(r, d, x_start, u_opt, dt, N, Nk);
plot(x_int(1,:), x_int(2, :))
plot(x_opt(1, :), x_opt(2, :), '--r')
scatter(x_target(1), x_target(2), 'filled')
title("Trajectories with disturbances")
lgd = legend("Real", "Predicted", "Target");
lgd.Location = 'northwest';
MPC
This run really slow. It can be improved A LOT, but for didactic purposes it's easier to understand
T_mpc = 3; % For how long we want to control the robot (in seconds)
N_mpc = round(T_mpc/dt,0);
disp(strcat("Solving... iteration: ", int2str(i), " / ", int2str(N_mpc)))
% In a real case here we wold put a sensor reading
if i == Nk % Here we kick the robot
x0 = x0 + [0; 0.25; 0]; % this is the displacement that it gets
% Basically we are iteratively solving OCPs with different initial
[x_s, u_s] = solve_ocp(r,d, x0, x_des, dt, N, w_x, w_u);
end
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Now you can see that the kick is compensated
x_int_mpc = integrate_unicycle(r, d, x_start, u_mpc, dt, N_mpc, Nk);
plot(x_int_mpc(1,:), x_int_mpc(2, :))
plot(x_int(1, :), x_int(2, :), '--r')
scatter(x_target(1), x_target(2), 'filled')
lgd = legend("Closed loop (MPC)", "Open loop", "target");
lgd.Location='northwest';
draw_unicycle(x_int_mpc, x_des, rob_diam)
Trajectory following
It is really the same as before, but in this case the reference is moving
a = 1; b=1; radius_tracking = 0.5;
dtheta_des = 2; % Desired angular velocity
circle_des = circle(a, b, radius_tracking, theta0, dtheta_des, dt, N+1);
traj_d(3, :) = circle_des(3, :) + pi/2;% sum 90 deg to have the tangent to the point
Open loop trajectory tracking
[x_s, u_s] = solve_ocp(r, d, x0, traj_d, dt, N, w_x, w_u);
draw_unicycle(x_s, traj_d, rob_diam)
This has the same problem seen before. So let's close the loop with MPC
disp(strcat("Solving... iteration: ", int2str(i), " / ", int2str(N_mpc)))
% In a real case here we wold put a sensor reading
circle_des = circle(a, b, radius_tracking, circle_des(3, 2), dtheta_des, dt, N); % receding horizon
traj_d(3, :) = circle_des(3, :) + pi/2; % sum 90 deg to have the tangent to the point
[x_s, u_s] = solve_ocp(r, d, x0, traj_d, dt, N, w_x, w_u);
end
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Finally check the solution
x_int_mpc = integrate_unicycle(r, d, x_start, u_mpc, dt, N_mpc, 0);
plot(x_int_mpc(1,:), x_int_mpc(2, :))
title("MPC trajectory tracking")