Direct Optimal Motion Planning for Omni-directional Mobile Robots under Limitation on Velocity and Acceleration

This paper describes a low computational direct approach for optimal motion planning and obstacle avoidance of Omni-directional mobile robots within velocity and acceleration constraints on the robot motion. The main purpose of this problem is the minimization of a quadratic cost function while limitations on velocity and acceleration of robot are considered, and collision with any obstacle in the robot workspace is avoided. This problem can be formulated as a constrained nonlinear optimal control problem. To solve this problem, a direct method is utilized which employs polynomials functions for parameterization of trajectories. By this transforming, the main optimal control problem can be rewritten as a nonlinear programming problem (NLP) with lower complexity. To solve the resulted NLP and obtain optimal trajectories, a new approach is used with very small run time. Finally, the performance and effectiveness of the proposed method are tested in simulations and some performance indexes are computed for better assessment. Furthermore, a comparison between the proposed method and another direct method is done to verify the low computational cost and better performance of the proposed method.