The Port-Hamiltonian Structure of Vehicle Manipulator Systems

TL;DR

This paper introduces a port-Hamiltonian framework for vehicle-manipulator systems, clarifying their energy flow and conservation properties, and providing formulations suitable for control and simulation.

Contribution

It develops a novel port-Hamiltonian formulation for VMS that explicitly reveals energy structure and is compatible with geometric control methods.

Findings

Explicit port-Hamiltonian formulations derived from first principles

Two formulations: standard and inertially-decoupled

Mathematical equivalence with existing equations

Abstract

This paper presents a port-Hamiltonian formulation of vehicle-manipulator systems (VMS), a broad class of robotic systems including aerial manipulators, underwater manipulators, space robots, and omnidirectional mobile manipulators. Unlike existing Lagrangian formulations that obscure the underlying energetic structure, the proposed port-Hamiltonian formulation explicitly reveals the energy flow and conservation properties of these complex mechanical systems. We derive the port-Hamiltonian dynamics from first principles using Hamiltonian reduction theory. Two complementary formulations are presented: a standard form that directly exposes the energy structure, and an inertially-decoupled form that leverages the principal bundle structure of the VMS configuration space and is particularly suitable for control design and numerical simulation. The coordinate-free geometric approach we follow avoids singularities associated with local parameterizations of the base orientation. We rigorously establish the mathematical equivalence between our port-Hamiltonian formulations and existing reduced Euler-Lagrange and Boltzmann-Hamel equations found in the robotics and geometric mechanics literature.