Rebound, Slip, and Compliance in the Modeling and Analysis of Discrete Impacts in Legged Locomotion

Abstract

An energy-based approach to analysis of the impact problem in three dimensional multi-legged robot locomotion is hereby presented. The goal is to combine rigid and deformable body approaches, which come together naturally in a work-energy framework. The rigid body approach is used to calculate the energy restituted after a foot impacts on the ground, and the ground and the foot are considered rigid bodies throughout the analysis. Then the flexible body approach is used to store the energy restituted to the system through the system’s compliance. The proposed hybrid approach can predict both rebound and non-rebound conditions for an energetic coefficient of restitution greater than zero. Zero tangential velocity (i.e., zero slip) in the impacting end effectors can be also predicted, a condition known as sticking. The article presents a method for determining whether the level of compliance in the system at a given configuration is adequate to insure a no-slip, no-rebound impact, with a focus on leg design.