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PSO Trajectory Planner Using Kinematic Controllers that Ensure Smooth Differential Robot Velocities

A multi-agent differential robot system requires a definite algorithm to behave as a swarm with goal searching capabilities. The classic Particle Swarm Optimization (PSO) algorithm is designed for particles with no mass or physical dimensions unlike differential robots. Therefore, it cannot be directly used to search for a goal using a robotic swarm. We propose the use of the PSO as a trajectory planner to enable the agents to collectively find the optimal path to a goal. The proposed PSO trajectory planner uses multiple known parameters such as inertia weight, a constriction parameter, two scaling factors and two random weighing factors (for the cognitive and social components of the PSO) optimized for differential robots. The planner takes into account the restrictions derived from the kinematic equations of the robotic agents and the finite dimensions of the search space. For that purpose, it is coupled with the necessary controllers to map particle velocities into smooth and continuous differential robot velocities. Four different controllers were tested, including the Transformed Unicycle Controller (TUC), Transformed Unicycle with LQR (TUC-LQR), Transformed Unicycle with LQI (TUC-QI), and a Lyapunov-stable Pose Controller (LSPC). The TUC-LQI controller outperformed the others in terms of achieving smooth continuous differential robot velocities, while following the paths generated by the PSO trajectory planner.