Deadbeat control with (almost) no sensing in a hybrid model of legged locomotion

Hybrid systems often appear as models of mechatronic devices, and are used to express the discontinuous transition in dynamics that occurs when mechanical contacts are made or broken. Contact state changes can coincide with dramatic shifts in control authority, and become sources of unwanted disturbance when they are exogenously driven. In the natural world, such systems appear in rapid legged locomotion. We present an insight derived from the analysis of running animals -namely that dynamics can be partially or fully controlled through geometric encoding of the desired control law in the feed-forward trajectories of the appendages. The resulting systems use no sensing, or nearly so, yet can exhibit strong (deadbeat) stability. We provide a theoretical proof of a general result, then a simulation study of a simplified model of vertical hopping which rejects ground-height changes without sensing the ground. We thereby show that mechatronic controllers for non-trivial tasks such as manipulation and legged locomotion could be implemented mechanically, with little or no sensing, by encoding the control laws in the open-loop motions chosen. Our results highlight that identification of a control mechanism in an existing animal or machine must take into account that such geometric stabilization may exist without neural or computational feedback.