Reachability Based and High Order Partial Feedback Linearization Enforced Control Strategies for Realistic Series-Elastic Actuated Hopping Robots

In this work we present hardware and simulation results for control strategies towards series-elastic actuated (SEA) hopping systems. There is an abundance of work regarding the implementation of highly simplified hopper models, the prevalent example being the Spring Loaded Inverted Pendulum (SLIP) model, with the hopes of extracting fundamental control ideas for running and hopping robots. However, real-world compliant legged systems cannot be fully described by such simple models, as real actuators have additional inertia, friction, and potentially SEA coupling dynamics. We seek to provide a control framework capable of precisely regulating footholds that can change arbitrarily on a step-to-step basis, as opposed to simply providing a discrete set of stable limit cycles. We illustrate how high-order partial feedback linearization can be implemented directly on the leg-length state and show how to apply these results so that algorithms designed for the SLIP model already present in the literature can be accurately implemented in more realistic hopping systems. In particular, we use SLIP results which allow for fast analytical computation of the reachable space that can take advantage of parallel processing, thus enabling the ability of on-line motion planning strategies. We present algorithms for selecting both SEA control inputs and touch-down angles by parametrizing the centroid of future reachable spaces, and provide step-length control algorithms that can enforce any foothold chosen randomly from the reachable space of the robot at each step.