Nonholonomic Motion Planning for Coupled Planar Rigid Bodies with Passive Revolute Joints

Abstract

Motion planning for coupled rigid bodies in a horizontal plane is investigated. The rigid bodies are serially connected by passive revolute joints. The dynamic constraints on the system are second-order nonholonomic constraints. We attempted to control those n coupled rigid bodies by the translational acceleration inputs at the first joint. If each rigid body is hinged at the center of percussion, it is possible to compose a positioning trajectory by connecting rotational and translational trajectories. Each rigid body can be rotated about its center of percussion by turns. When all rigid bodies are aligned on a straight line, they can be translated. The algorithm for positioning is presented. Simulation shows that the coupled planar rigid bodies can reach the desired configuration by the constructed inputs.