Optimal trajectory planning of a mobile robot with spatial manipulator for obstacle avoidance

Mobile robots consist of a mobile platform with one or many manipulators mounted on it are of great interest in a number of applications. Combination of platform and manipulator causes robot operates in extended work space. The analysis of these systems includes kinematics redundancy that makes more complicated problem. However, it gives more feasibility to robotic systems because of the existence of multiple solutions in a specified workspace. This paper presents a methodology in generating paths and trajectories for both the mobile platform and a 3DOF manipulator mounted on it, in the presence of obstacles. Obstacles add kinematics constraint into optimization problem. The method employs smooth and continuous functions such as polynomials. The proposed method includes obtaining time history of the mobile robot motion. It is supposed that the obstacles can be enclosed in cylinders. The platform has been used in this research is a differentially-driven platform. The core of the method is based on mapping the nonholonomic constraint to a space where it can be satisfied trivially. A suitable criterion can be used to solve an optimization problem to find the optimal solution. In this research, the problem of path planning with simultaneous optimization of kinematics and dynamic indices has been accomplished using genetic algorithm in order to find the global optimum solution. The validity of the methodology is demonstrated by using a differential-drive mobile manipulator system, various simulations of platform with a spatial 3-link manipulator are presented to show the effectiveness of the presented method.