SEMINAR - Anton Shiriaev (NTNU): Trajectory planning for mechanical systems with two and more passive degrees of freedom
Underactuation represents dynamic equality constraints that should be somehow accommodated in process of searching of feasible motions of a mechanical system with passive degrees of freedom and in developing a feedback controller for stabilization. Both tasks of motion planning and motion control can be quite challenging in applications. However, there are conceptual differences in complexity of solutions for such tasks. In particular, a controller design assignment is relatively simple and admits analytical procedures for ensuring an orbital stabilization or an orbital contraction irrespective of a level of underactuation. Similarly, motion planning assignment for systems with one passive degree of freedom often can be solved analytically. Meanwhile, the complexity of motion planning for mechanical system with several passive degrees of freedom (two and more) is indeed an obstacle for planning agile behaviors in the most of application. The talk is aimed at illustrating the point and at exploring several case studies of systems having two passive degrees of freedom, for which solutions are available/derived. The second part of the talk is focused on analytical arguments for performing non-prehensile manipulations for the Butterfly robot. Modeling, motion planning and motion control steps are complemented by the full scale experiment on the educational set-up.