Adaptive height controller for an agile hopping robot

Abstract This paper addresses the problem of controlling the hopping height and stride length of a monoped hydraulic robot. Hopping over discontinuous, rough terrain with limited surfaces suitable for foot placement requires a controller capable of adjusting the hop height and landing foot position of the robot on each step. This motivates the need for an agile controller that uses the short window of time while the foot is on the ground (the stance phase) to exert the required action to reach the next landing position. This paper contributes a simple yet effective adaptive controller capable of changing the flight time within a single hop. The controller does not require force feedback and is capable of self-tuning its feedback gain parameters in response to changing ground parameters using the results of previous hops. The main contribution of the paper is the development of an analytical understanding of why the controller is capable of adjusting the height in a single step and how the errors in the achieved height can be used to tune automatically the controller gains. This allows the controller to be successfully implemented even if the conditions or parameters are initially unknown, automatically correcting for errors. The controller is first derived for height control of hopping vertically, with no horizontal motion, from an analytical approximation. This is tested in simulation, using a spring–damper model and a more detailed model with a foot mass and compliant ground. The controller is then applied to a hydraulic spring-loaded hopper monoped. An extension allows the control of running on a treadmill, with constant horizontal speed.