Towards fast running: Open-loop speed and direction control of a single-legged hopper

Traditional 2D single-legged hoppers were able to demonstrate stable bi-directional running in a closed-loop approach. In contrast, we employ an open-loop control to achieve high-speed (≈0.8 m/sec or 1.78 mph) bi-directional dynamic running of the reconfigurable leg length hopper (RLLH). Our hopper has variable linear joint in series with a passive spring that allows changing its effective leg length in realtime. Furthermore by instantaneously changing the leg length at a particular amplitude and frequency. The required “thrust-forces” can be produced. We hypothesize that the direction and the speed of our hopper can be smoothly controlled by only changing the phase of the thrust-forces being applied to the ground, i.e., the change in phase between the leg-reconfiguration and the leg-oscillation. This is experimentally evaluated by varying the phase of leg-reconfiguration up-to the range of 0-2π rad (0-360 deg). Our results show a large region of a symmetric running. Moreover, a novel gait called “in-place running¹” is found, where the speed of running is zero. We demonstrate that by only altering the phase of applying thrust-forces together with a constant leg oscillation can robustly control the speed and transition in the direction of locomotion.