One of the most fundamental capabilities for an autonomous or semi-autonomous robot system is the ability to quickly plan and reliably execute its own motions. We will study these fundamental problems for underactuated mechanical systems -- systems with fewer actuators than degrees-of-freedom. Our interest in controlling this class of systems stems from two considerations. (1) It allows software control redundancy (as opposed to mechanical or actuation redundancy) when one or more actuators of a fully actuated system fails. (2) It is possible to design inexpensive mechanical systems by minimizing expensive mechanical elements such as actuators and transmissions and replacing them with advanced control algorithms.
We will explore a novel concept for mechanical control systems called kinematic reductions. A kinematic reduction of a mechanical system is a first-order driftless system whose trajectories can be followed by the second-order mechanical system. Kinematic reductions allow kinematic constraints (such as obstacles and joint limits) and actuator limits to be handled in a computationally efficient manner, allowing the possibility of real-time trajectory generation for underactuated systems. Kinematic reductions encode the notion of ``preferred'' motion directions for the system, allowing the planned trajectories to be followed quickly.
To make full use of these properties of mechanical systems for real-time trajectory generation and control, we will study a number of open issues. These include understanding when the kinematic reduction allows for closed-form calculation of motion plans for underactuated systems; adapting efficient kinematic motion planners from the robotics literature to kinematically controllable systems; local trajectory optimization; feedback control to stabilize trajectories of the kinematic reductions; and implementation and validation of the control strategies on an experimental vehicle. We also plan to explore the role kinematic reductions will play in developing reduced-complexity hierarchical hybrid motion models.
