Optimal trajectory planning for Omni-directional mobile robots using direct solution of optimal control problem

Abstract

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.

Trajectory planning for mechanical systems in the presence of dynamic obstacles

“…, a l ) (14) to be minimized. Then, like it is done in [7], the motion planning problem in question is considered as the constrained nonlinear optimization problem to minimize (14) under the conditions (11) -( 13) which is suggested to be solved numerically. In this note, the conditions which guarantee that the formulated optimization problem has a solution are not analyzed.…”

“…Motion planning problems are of high importance for various robotic systems and the last decades have witnessed a lot of attention paid to this area of research among control theorists and engineers. Meanwhile, typical approaches to reference trajectories construction are based on using time polynomials which proved to be an effective tool, e.g., for differentially flat dynamical systems (see [1,2,3,4,5,6,7,8,9]). Numerical optimization procedures to meet geometrical, velocity and acceleration constraints are discussed in [1,6,7].…”

“…Meanwhile, typical approaches to reference trajectories construction are based on using time polynomials which proved to be an effective tool, e.g., for differentially flat dynamical systems (see [1,2,3,4,5,6,7,8,9]). Numerical optimization procedures to meet geometrical, velocity and acceleration constraints are discussed in [1,6,7]. Some analytical ideas of constrained trajectory planning for mechanical systems can be found e.g., in the monograph [2] and in papers [8,9].…”