Controlling Hopping Height of a Pneumatic

We describe a model-based height controller for a hopping robot with a pneumatically powered leg. The controller explicitly models variation in the leg angle and height. Using an explicit model of the physics of the pneumatic spring and some symmetry assumptions, we derive the desired leg-length setting to regulate apex hopping height using a PD controller. Simulation experiments of hopping in the sagittal plane show reasonable height regulation. For low-speed running, we take advantage of the small variations in the leg angle about the vertical, and demonstrate that the original symmetry assumptions may be relaxed by restricting the leg angle to π/2. Simulations show that the restricted model outperforms the original model by a small but significant amount. I