Collaborative Research: Kinematic Reductions of Underactuated Mechanical Systems

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One of the most fundamental capabilities for an autonomous orsemi-autonomous robot system is the ability to quickly plan andreliably execute its own motions. We will study these fundamentalproblems for underactuated mechanical systems -- systems with feweractuators than degrees-of-freedom. Our interest in controlling thisclass of systems stems from two considerations. (1) It allowssoftware control redundancy (as opposed to mechanical or actuationredundancy) when one or more actuators of a fully actuated systemfails. (2) It is possible to design inexpensive mechanical systems byminimizing expensive mechanical elements such as actuators andtransmissions and replacing them with advanced control algorithms.We will explore a novel concept for mechanical control systems calledkinematic reductions. A kinematic reduction of a mechanical system isa first-order driftless system whose trajectories can be followed bythe second-order mechanical system. Kinematic reductions allowkinematic constraints (such as obstacles and joint limits) andactuator limits to be handled in a computationally efficient manner,allowing the possibility of real-time trajectory generation forunderactuated systems. Kinematic reductions encode the notion of``preferred'' motion directions for the system, allowing the plannedtrajectories to be followed quickly.To make full use of these properties of mechanical systems forreal-time trajectory generation and control, we will study a number ofopen issues. These include understanding when the kinematic reductionallows for closed-form calculation of motion plans for underactuatedsystems; adapting efficient kinematic motion planners from therobotics literature to kinematically controllable systems; localtrajectory optimization; feedback control to stabilize trajectories ofthe kinematic reductions; and implementation and validation of thecontrol strategies on an experimental vehicle. We also plan toexplore the role kinematic reductions will play in developingreduced-complexity hierarchical hybrid motion models.