Qualitative Study of a Robot Arm as a Hamiltonian System

TL;DR

This paper models a robot arm as a Hamiltonian system using a double pendulum to analyze its stability and phase space behavior under external torques, revealing invariant manifolds and fixed points.

Contribution

It provides a Hamiltonian framework for understanding the stability and phase space structure of a planar robot arm with two links and joints, including effects of external torques.

Findings

Presence of fixed points unaffected by constant torques

Topology of orbits remains stable under certain conditions

Identification of invariant manifolds corresponding to saddle-center fixed points

Abstract

A double pendulum subject to external torques is used as a model to study the stability of a planar manipulator with two links and two rotational driven joints. The hamiltonian equations of motion and the fixed points (stationary solutions) in phase space are determined. Under suitable conditions, the presence of constant torques does not change the number of fixed points, and preserves the topology of orbits in their linear neighborhoods; two equivalent invariant manifolds are observed, each corresponding to a saddle-center fixed point.