Reachability-based control for the active SLIP model

One of the key topics in robotics is legged locomotion, taking inspiration from walking and bouncing gaits of bipeds and quadrupeds. A fundamental tool for analyzing running and hopping is the spring loaded inverted pendulum (SLIP), thanks to its simplicity but also effectiveness in modeling bouncing gaits. Being completely passive, the SLIP model does not have the ability to modify its net energy, which, for example, can be a prohibitive obstacle when traveling on a terrain with varying heights. The actuated version of the SLIP model, the active SLIP, considered in this paper, includes a series actuator that allows energy variations via compressing or extending the spring. In this work, we investigate how different actuator motions can affect the system’s state, and we propose a control strategy, based on graphical and numerical studies of the reachability space, and updated throughout the stance phase, to drive the system to a desired state. We quantify its performance benefits, particularly in serving as an error-recovering method. The objective of our control strategy is not to replace any leg-placement approach proposed by other works, but rather to be paired with any other leg-placement or path planning method. Its main advantage is the ability to reduce the effects of sensing errors and disturbances happening at landing as well as during the stance phase.