Code developed for the work published in "C. Tiriolo, W. Lucia - A Set-Theoretic Control Approach to the Trajectory Tracking Problem for Input-Output Linearized Wheeled Mobile Robots - CDC - LCSS 2023" Full paper at: https://doi.org/10.1109/LCSYS.2023.3286774 The code validates the strategy developed in the above paper by means of both simulations and experiments.

Consider the input-constrained differential-drive robot and a bounded and smooth trajectory $q_r(k)=\left[x_r(k),y_r(k),\theta_r(k)\right]^T$ Design a trajectory tracking control law $[\omega_{R}(k),\omega_{L}(k)]^T=\phi(k,q(k),q_r(k))\in\mathcal{U}_d$ such that the tracking error $\tilde{q}(k)=q(k)-q_r(k)$ remains bounded $\forall k\geq 0$.

The code was tested on Matlab 2022a environment. It requires the Ellipsoidal Toolbox ET (https://www.mathworks.com/matlabcentral/fileexchange/21936-ellipsoidal-toolbox-et). To reproduce the experiments discussed in the paper, see Khepera_IV_TCP folder, a Khepera IV robot is required. The script implements a Bluetooth client that sends velocity commands to the robot in order to make it track a desired trajectory (eight-shaped and circular tractories are currently available). For further details refer to the paper.

• ST_FL_Trajectory_Tracking_Differential_Drive_CDC23.m: It's the main script that simulates the Trajectory tracking Set-Theoretic strategy.
• one_step_ellipsoidal_reachable_set.m: It's a Matlab function used to implement the offline phase of the algorithm. It computes the one-step reachable set starting from a given ellipsoidal set whose shaping matrix is given (see the full paper for further details).
• online_phase_CDC.m: It's a Matlab function that implements the online phase optimization (see Eqs (25a)-(25b) in the full paper for further details).
• online_terminal_optim.m: It implements optimization (27) (see full paper for further details)
• DiffDrive.m: It's a Matlab function that implements the unicycle kinematics. It's used by the method ode45 to solve the differential equations describing the mobile robot's motion in the plane.

• Khepera_IV_TCP/Khepera_iv_ST_disturbance_traj_track.m: It's the main script used to perform the experiment described in the paper.
• Khepera_IV_TCP/Khepera4.m: It represents the core of the application. It is a Matlab class that implements the main communication functionalities between the tracking controller running on Matlab and the server running on Khepera IV
• Khepera_IV_TCP/STTT_control_parameters.m: It's a Matlab class defining the parameters needed by the proposed tracking controller.
• Khepera_IV_TCP/"eight_traj_generation.m" implements the reference eight-shaped trajectory.

• Run "ST_FL_Trajectory_Tracking_Differential_Drive_CDC23.m"

• Connect KheperaIV to the host machine through Bluetooth and set the right port on the script "Khepera_IV_TCP/Khepera_iv_ST_disturbance_traj_track.m".
• Run the Bluetooth server on the KheperaIV side and then, run the script "Khepera_IV_TCP/Khepera_iv_ST_disturbance_traj_track.m".

• https://www.youtube.com/watch?v=A0Tlbgr08tY&ab_channel=PreCySeGroup