A Geometric Task-Space Port-Hamiltonian Formulation for Redundant Manipulators

TL;DR

This paper introduces a new geometric port-Hamiltonian framework for redundant manipulators that separates task-space and null-space dynamics, enabling improved control and impedance shaping.

Contribution

It presents a novel geometric port-Hamiltonian formulation for redundant manipulators, including a change of coordinates and a split of momentum variables, with application to IDA-PBC control.

Findings

Effective impedance shaping of a 7-DOF robot in simulation

New geometric formulation clarifies task and null-space dynamics

Demonstrates advantages over traditional Hamiltonian models

Abstract

We present a novel geometric port-Hamiltonian formulation of redundant manipulators performing a differential kinematic task $\eta=J(q)\dot{q}$, where $q$ is a point on the configuration manifold, $\eta$ is a velocity-like task space variable, and $J(q)$ is a linear map representing the task, for example the classical analytic or geometric manipulator Jacobian matrix. The proposed model emerges from a change of coordinates from canonical Hamiltonian dynamics, and splits the standard Hamiltonian momentum variable into a task-space momentum variable and a null-space momentum variable. Properties of this model and relation to Lagrangian formulations present in the literature are highlighted. Finally, we apply the proposed model in an \textit{Interconnection and Damping Assignment Passivity-Based Control} (IDA-PBC) design to stabilize and shape the impedance of a 7-DOF Emika Panda robot in simulation.