Control algorithms for a vertically-constrained one-legged hopping machine

A physical prototype of a vertically-constrained, one-legged hopping machine is presented. The machine consists of an elevated body supported by a single springy leg and a leg actuator used to manipulate the leg´s length. The body of the machine is a DC motor. The leg and leg actuator are a system of tubes and a mechanical spring that allow smooth and repeatable hopping. Three control algorithms that regulate the machine´s hopping height are presented and tested experimentally. These are: (i) a tabular control scheme that selects the control input on the basis of the desired steady-state hopping height; (ii) a near-inverse controller based on a discrete, hop-to-hop model of the plant dynamics; and (iii) a near-inverse controller with integral error feedback. The machine´s transient and steady-state behavior is evaluated for each controller. The effectiveness of the algorithms is further assessed by subjecting the controlled system to abrupt changes in the body mass. Experimental data indicate that the near-inverse controller with integral height-error feedback gives the best results in compensating for parameter variations