Optimal Trajectory planning for Omni-directional Mobile Robots using Direct Solution of Optimal Control Problem

In this paper we address the problem of finding trajectory for Omni-directional mobile robots. The objective of the trajectory planning is moving the robot from its initial position to a final position in the presence of static obstacles while minimizing a quadratic index of performance. Along the trajectory, the robot requires to observe certain velocity and acceleration limitations. This problem can be formulated as a constraint nonlinear optimal control problem. To solve this problem, we employ direct method of numerical solution in which the trajectories are parameterized by parametric polynomial functions. By this transforming, the main optimal control problem converts to a nonlinear programming problem (NLP) by lower computational cost. To solve the NLP and obtaining the trajectories, we utilize a new approach with too small run time. The performance and effectiveness of the proposed method are tested in simulations.