Smooth Trajectory Planning for Robot Using Particle Swarm Optimization

In this work, we deal with a class of problems of trajectory planning taking into account the smoothness of the trajectory. We assume that we have a set of positions in which the robot must pass. These positions are not assigned in the time axis. In this work, we propose a formulation of this problem, where the total length of the trajectory and the total time to move from the initial to the final position are minimized simultaneously. In order to ensure effective results and avoid abrupt movement, we should ensure the smoothness of the trajectory not only at the position level but also at the velocity and the acceleration levels. Thus, the position function must be at least two times differentiable. In our case, we use a polynomial function. We formulate this problem as a constraint optimization problem. To resolve it, we adapt the usual particle swarm algorithm to our problem and we show its efficiency by simulation.