On the Stability of the Passive Dynamics of Quadrupedal Running with a Bounding Gait

This paper examines the passive dynamics of quadrupedal bounding. First, an unexpected difference between local and global behavior of the forward speed versus touchdown angle in the selfstabilized Spring Loaded Inverted Pendulum (SLIP) model is exposed and discussed. Next, the stability properties of a simplified sagittal plane model of our Scout II quadrupedal robot are investigated. Despite its simplicity, this model captures the targeted steady state behavior of Scout II without dependence on the fine details of the robot structure. Two variations of the bounding gait, which are observed experimentally in Scout II, are considered. Surprisingly, numerical return map studies reveal that passive generation of a large variety of cyclic bounding motion is possible. Most strikingly, local stability analysis shows that the dynamics of the open loop passive system alone can confer stability to the motion! These results can be used in developing a general control methodology for legged robots, resulting from the synthesis of feedforward and feedback models that take advantage of the mechanical sysPortions of this paper have previously appeared in conference publications Poulakakis, Papadopoulos, and Buehler (2003) and Poulakakis, Smith, and Buehler (2005b). The first and third authors were with the Centre for Intelligent Machines at McGill University when this work was performed. Address all correspondence related to this paper to the first author. The International Journal of Robotics Research Vol. 25, No. 7, July 2006, pp. 669-687 DOI: 10.1177/0278364906066768 ©2006 SAGE Publications Figures appear in color online: http://ijr.sagepub.com tem, and might explain the success of simple, open loop bounding controllers on our experimental robot. KEY WORDS—passive dynamics, bounding gait, dynamic running, quadrupedal robot