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

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 trajectory segments. Each rigid body can be rotated about its center of percussion one after another. When all of the rigid bodies are aligned on a straight line, they can be translated. The algorithm for positioning is presented. Simulations show that the coupled planar rigid bodies can reach the desired configuration by the constructed inputs. KEY WORDS—coupled rigid bodies, passive revolute joints, nonholonomic motion planning, positioning, second-order nonholonomic constraints, underactuated system