Optimal-control approach to trajectory planning for a class of mobile robotic manipulations

Abstract

Optimal-control theory is used in the manipulation planning for an ability-limited robot (i.e., a mobile robot with limited maneuverability). The goal of manipulation is to push an object from a given initial configuration to a goal configuration-a common task could be found in the application of mobile robots to manufacturing, in adaptive fixturing for robotic assembly and in robotic gaming. The ability-limited robot is restricted here to perform only two types of motion in a plane. One is pushing the object forward with a constant and fixed velocity, the other one is rotating the object counter-clockwise along a fixed-radius circle with a constant angular velocity. First, the controllability of the proposed manipulation system is proved. Then, the optimal-planning problem is studied within the framework of a switched system. By the aid of optimal-control theory, it is proved that an optimal trajectory involves at most two switchings between these two simple actions. After evaluating the existence and structure of the candidate optimal trajectories, an optimal planner is implemented to find the optimal trajectory. Finally, manipulation examples are provided to demonstrate the proposed manipulation method.