Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models

This two-part paper discusses the analysis and control of legged locomotion in terms of N -step capturability: the ability of a legged system to come to a stop without falling by taking N or fewer steps. We consider this ability to be crucial to legged locomotion and a useful, yet not overly restrictive criterion for stability. Part 1 introduces a theoretical framework for assessing N -step capturability. This framework is used to analyze three simple models of legged locomotion. All three models are based on the 3D Linear Inverted Pendulum Model. The first model relies solely on a point foot step location to maintain balance, the second model adds a finite-sized foot, and the third model enables the use of centroidal angular momentum by adding a reaction mass. We analyze how these mechanisms influence N -step capturability, for any N > 0. Part 2 will show that these results can be used to control a humanoid robot. ∗T. Koolen and T. de Boer are with the Delft University of Technology, the Netherlands †J. Pratt and T. Koolen are with the Institute for Human and Machine Cognition, Florida ‡J. Rebula is with the University of Michigan, Ann Arbor §A. Goswami is with the Honda Research Institute, California ¶This work was funded through the Army Tank and Automotive Research and Development Command (W56HZV04-C-0072), the Defense Advanced Research Projects Agency (FA8650-05-C-7265), the Office of Naval Research (N00014-091-0913-01), NASA (NNX10AG54A), and the Honda Research Institute.