Modeling and Workspace Characterization of Continuously Compliant Robotic Legs

Abstract

This work introduces a new design paradigm for robotic legs. Our concept extends upon classical series elastic actuation and directly integrates the series compliance into the structure of the leg. This integration reduces the mechanical design complexity and can potentially reduce the overall weight of the leg. In this paper, we introduce a prototype leg with a continuously compliant shank and derive and analyze a non-linear beam model that is used to predict its contact forces. The model is validated in two static experiments: one on the isolated shank and one on the full leg. It shows good agreement with measurements. In our validation, we also studied the influence of the model discretization, showing that about 10 nodes are sufficent. Furthermore, we introduce the concept of a force workspace: the range of forces that can be created by controlling the joint angles of the leg. Due to the coupling of nonlinear deformations and nonlinearities in the kinematics, this workspace is non-trivial. In particular, we demonstrate that it is bounded by a force-singularity in which the force/joint-angle relationship cannot be inverted. The results presented in this work can be applied in the development of state-estimators, set-point filters and controllers, and they can inform the future design of suitable geometries of compliant elements.