Towards precise control of hoppers: Using high order partial feedback linearization to control the hopping robot FRANK

Abstract

In this paper, we describe modeling and control techniques for series-elastic actuated hopping robots. There is an abundance of work regarding the implementation of highly simplified hopper models, the prevalent example being the SLIP model, with the hopes of extracting fundamental control ideas for running and hopping robots. However, real-world systems cannot be fully described by such simple models, as real actuators have their own dynamics including additional inertia and non-linear frictional losses. Therefore, an important step towards demonstrating high controllability and robustness to real-world, uneven terrain is in providing accurate higher-order models of real-world hopper dynamics. Additionally, implementing feedback control for real series-elastic actuators is difficult as the input variable does not instantaneously change the leg length acceleration. In this work we provide both hardware and simulation results that 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 in the SLIP literature can be accurately implemented in more realistic hopping systems to accomplish tasks such as apex state tracking and precise foothold planning.