Dynamics and Control of Humanoid Robots: A Geometrical Approach

TL;DR

This paper reviews a geometrical framework for modeling and controlling humanoid robots using Lagrangian and Hamiltonian formalisms, emphasizing autonomous dynamics, neural-like control, and applications to biomechanics with simulation examples.

Contribution

It introduces a comprehensive geometrical approach to humanoid robot dynamics and control, integrating Lagrangian and Hamiltonian formalisms with neural-like hierarchical control.

Findings

Develops a configuration manifold for humanoids based on joint angles.

Formulates autonomous Lagrangian and Hamiltonian dynamics on respective phase spaces.

Provides simulation examples demonstrating the effectiveness of the geometrical control approach.

Abstract

his paper reviews modern geometrical dynamics and control of humanoid robots. This general Lagrangian and Hamiltonian formalism starts with a proper definition of humanoid's configuration manifold, which is a set of all robot's active joint angles. Based on the `covariant force law', the general humanoid's dynamics and control are developed. Autonomous Lagrangian dynamics is formulated on the associated `humanoid velocity phase space', while autonomous Hamiltonian dynamics is formulated on the associated `humanoid momentum phase space'. Neural-like hierarchical humanoid control naturally follows this geometrical prescription. This purely rotational and autonomous dynamics and control is then generalized into the framework of modern non-autonomous biomechanics, defining the Hamiltonian fitness function. The paper concludes with several simulation examples. Keywords: Humanoid robots, Lagrangian and Hamiltonian formalisms, neural-like humanoid control, time-dependent biodynamics