Stability and Control for a Class of Dynamic Legged Climbers

We are interested in the stability and control of dynamic legged climbing. Motivated by the success of the lateral leg spring (LLS) and spring-loaded inverted pendulum (SLIP) templates for transverse and sagittal plane running on horizontal surfaces, our effort is to similarly approximate the analytically intractable dynamics of a full dimensional system through planar models, and develop simple control strategies based on analysis of these approximations. In this report we introduce low-dimensional generalizations of the LLS and SLIP templates capable of ascending and descending by considering configurations of the center of pressure outside of the set of asymptotically stable configurations in the horizontal plane, and allowing a thrust phase to add or remove energy from the hopper. We will provide mathematical analysis of these models where possible, and introduce approximate models and empirical data where analytical analysis is intractable. Stable control strategies developed from these low dimensional templates and approximations are demonstrated through simulation.