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The International Journal of Robotics Research, Vol. 25, No. 7, 669-687 (2006)
DOI: 10.1177/0278364906066768

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

Ioannis Poulakakis

Control Systems Laboratory, Department of Electrical Engineering and Computer Science, The University of Michigan, Ann Arbor, MI 48109, USA, poulakas{at}eecs.umich.edu

Evangelos Papadopoulos

Department of Mechanical Engineering, National Technical University of Athens, Athens, 15780, Greece, egpapado{at}central.ntua.gr

Martin Buehler

Boston Dynamics, Cambridge, MA 02139, USA, buehler{at}BostonDynamics.com

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 self-stabilized 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 system, 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


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