Discrete Mechanics and Optimal Control for Passive Walking with Foot Slippage

TL;DR

This paper develops a geometric mechanics-based model and numerical integrators for a passive walker with foot slip, and proposes a method to generate optimal control policies for such hybrid systems.

Contribution

It introduces a novel modeling approach for passive walkers with foot slip and a discrete mechanics-based method for optimal control policy generation.

Findings

Effective variational integrators for foot slip dynamics

Successful trajectory tracking with optimal control policies

Enhanced numerical stability in simulations

Abstract

Forced variational integrators are given by the discretization of the Lagrange-d'Alembert principle for systems subject to external forces, and have proved useful for numerical simulation studies of complex dynamical systems. In this paper we model a passive walker with foot slip by using techniques of geometric mechanics, and we construct forced variational integrators for the system. Moreover, we present a methodology for generating (locally) optimal control policies for simple hybrid holonomically constrained forced Lagrangian systems, based on discrete mechanics, applied to a controlled walker with foot slip in a trajectory tracking problem.