Piecewise Virtual Constraints for Trajectory Planning of Underactuated Mechanical Systems

Underactuated mechanical systems are well-known for the challenges they pose to motion planning and control. In particular, the motion planner for these systems must take into account their dynamics, while the controller has to stabilize all degrees of freedom with a fewer number of actuators. One common way to overcome these hurdles is by employing the concept of virtual (holonomic) constraints for planning and transversal stabilization for control. This paper investigates the use of piecewise virtual constraints to improve motion planning for the systems with one degree of underactuation and demonstrates that periodic motions planned with piecewise constraints can be stabilized using existing tools for orbital stabilization. We have conducted extensive experimental evaluation of the algorithm on a practical pendubot robot, and the results suggest that the proposed method yields considerably smaller cost function values than other approaches, while exhibiting faster convergence.