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

2025-12-16

AI Summary

This paper addresses the challenges of dynamic modeling and energy shaping in task-space control of redundant manipulators. Methodologically, it introduces a novel task-space geometric port-Hamiltonian (G-PHS) model grounded in differential geometry: it defines an orthogonal momentum decomposition on the task manifold, explicitly separating standard generalized momentum into task-space and null-space components with rigorous correspondence to the Lagrangian framework; it further unifies analytical and geometric Jacobians to naturally embed kinematic constraints. The key contributions are: (i) the first formulation of a task-space G-PHS structure, enabling IDA-PBC-based energy shaping; and (ii) high-fidelity impedance shaping and stable control demonstrated in simulation on a 7-DOF Panda robot, validating the model’s energy consistency, geometric structure preservation, and superior control performance.

Technology Category

• Intelligent Robots: Manipulation
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

We present a novel geometric port-Hamiltonian formulation of redundant manipulators performing a differential kinematic task $η=J(q)dot{q}$, where $q$ is a point on the configuration manifold, $η$ 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 extit{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.

Problem

• Develops a geometric port-Hamiltonian model for redundant manipulators performing kinematic tasks.
• Splits Hamiltonian momentum into task-space and null-space components via coordinate transformation.
• Applies the model in IDA-PBC control to stabilize and shape impedance for a 7-DOF robot.

Innovation

• Geometric port-Hamiltonian formulation for redundant manipulators
• Splits momentum into task-space and null-space variables
• Applies IDA-PBC control for impedance shaping in simulation