Quantifying Control Authority in Periodic Motions of Underactuated Mobile Robots

Abstract

The locomotion of legged robots is inherently underactuated, which creates control challenges in terms of rejecting large disturbances. A detailed understanding of how the control authority of a robot evolves over a gait trajectory has the potential to inform the design of controllers that offer superior disturbance rejection capabilities without compromising the efficiency benefits that typically accompany underactuated legged robots. Previous work has shown how the system velocities of an underactuated mechanical system can be decomposed into directions aligned with the inputs, or controlled directions, and directions orthogonal to the inputs, or uncontrolled directions, and applied that decomposition to drive wheeled robots to rest. This decomposition fundamentally provides a measure of the instantaneous control authority of the robot. This paper examines how the same techniques can be applied to inform the control of biped robots walking with periodic gaits. This problem differs from those previously studied in that it necessarily involves ground impacts and non-zero desired velocities. A representative example of a two-link planar biped walking on flat ground shows how a simple open loop controller that implements heuristics identified through the velocity decomposition to make use of the available control authority can improve disturbance rejection when added to a hybrid zero dynamics-based controller.