Underactuated mechanical systems: Whether orbital stabilization is an adequate assignment for a controller design?

Abstract The paper contributes to developing algorithms for motion planning and motion control for mechanical systems with two and more passive degrees of freedom by exploring a challenging example in details. As shown, some of arguments of motion planning methods developed for systems of underactuation degree one can be generalized for novel demanding settings, while corresponding arguments and concepts for controller design should be substantially reconsidered and updated. Rigorous theoretical results are well supported by numerical studies.