Height Control for a One-Legged Hopping Robot using a One-Dimensional Model

The hopping machine considered in this paper is like a pogo-stick; it has a small foot and a leg spring. Unlike a pogo-stick which uses a mechanical spring, the spring for the hopper is pneumatic. The controller is based on Raibert’s three-part control system [1]. Raibert controlled hopping height by delivering a specified thrust value during stance. This paper describes a model-based height controller that allows a wide range of apex heights to be selected and achieved. As shown in Figure 1, a hopping cycle consists of four phases. There are two flight phases, ascent and descent, and two stance phases, compression and extension. The height can be changed by setting the leg to an appropriate length during descent. Changing the leg length effectively changes the air spring constant. In this way, energy can be added to or removed from the system to change the apex height. Proportional control has been used to regulate hopping height in simulation [2]. For the Monopod II robot, an adaptive energy feedback controller was used to control the apex energy and thus the apex height [3]. A discrete closed form trajectory model was used to control a bow leg hopper [4]. Model parameters were experimentally determined with a least squares fit to a set of recorded trajectories. A simulation of a vertical hopping machine was controlled using a near-inverse discrete-time model [5]. Time-varying or unknown parameters were estimated with a recursive least-squares parameter estimator. Because the model was able to update itself in this way, the controller was much less sensitive to modeling errors and even abrupt changes in physical parameters.