A genetic algorithm designed for robot trajectory planning

In this work, we deal with a class of problem 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. This kind of result can be found in many works of trajectory planning. Thus, this result is not complete in the sense that we do not have the complete trajectory and, we do not have any idea about the whole time to move. 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 avoid abrupt movement, we should ensure the smoothness of the trajectory at the position, the velocity and the acceleration levels. Thus, the position function must be at least two times differentiable. We use a genetic algorithm to resolve this problem and we show the efficiency of the proposed technique by simulation.