Port-Hamiltonian modeling of vehicle-manipulator systems: An inertially-decoupled formulation on principal bundles

Authors

Ramy Rashad

Abstract

This paper presents a port-Hamiltonian formulation of vehicle-manipulator systems, 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 and is particularly suitable for control design and numerical simulation. The proposed port-Hamiltonian dynamics is in an inertially-decoupled form that leverages the principal bundle structure of the configuration space and is derived from first principles using Hamiltonian reduction theory. 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. The equivalence is also verified numerically through simulations of a planar vehicle-manipulator system.

Keywords

floating-base manipulators, geometric mechanics, mobile manipulators, port-hamiltonian, vehicle-manipulator systems

Citation

• Journal: Applied Mathematical Modelling
• Year: 2027
• Volume: 164
• Issue:
• Pages: 117381
• Publisher: Elsevier BV
• DOI: 10.1016/j.apm.2026.117381

BibTeX

@article{Rashad_2027,
  title={{Port-Hamiltonian modeling of vehicle-manipulator systems: An inertially-decoupled formulation on principal bundles}},
  volume={164},
  ISSN={0307-904X},
  DOI={10.1016/j.apm.2026.117381},
  journal={Applied Mathematical Modelling},
  publisher={Elsevier BV},
  author={Rashad, Ramy},
  year={2027},
  pages={117381}
}

Download the bib file

References

• Nava G, Sable Q, Tognon M, Pucci D, Franchi A (2020) Direct Force Feedback Control and Online Multi-Task Optimization for Aerial Manipulators. IEEE Robot Autom Lett 5(2):331–338. https://doi.org/10.1109/lra.2019.2958473 – 10.1109/lra.2019.2958473
• Simetti E, Campos R, Vito DD, Quintana J, Antonelli G, Garcia R, Turetta A (2021) Sea Mining Exploration With an UVMS: Experimental Validation of the Control and Perception Framework. IEEE/ASME Trans Mechatron 26(3):1635–1645. https://doi.org/10.1109/tmech.2020.3025973 – 10.1109/tmech.2020.3025973
• Giordano AM, Calzolari D, De Stefano M, Mishra H, Ott C, Albu-Schaffer A (2021) Compliant Floating-Base Control of Space Robots. IEEE Robot Autom Lett 6(4):7485–7492. https://doi.org/10.1109/lra.2021.3097496 – 10.1109/lra.2021.3097496
• Kim, Whole-body control of non-holonomic mobile manipulator based on hierarchical quadratic programming and continuous task transition. (2019)
• Korayem MH, Shafei AM (2015) Motion equation of nonholonomic wheeled mobile robotic manipulator with revolute–prismatic joints using recursive Gibbs–Appell formulation. Applied Mathematical Modelling 39(5–6):1701–1716. https://doi.org/10.1016/j.apm.2014.09.030 – 10.1016/j.apm.2014.09.030
• Hamad M, Kurdas A, Mansfeld N, Abdolshah S, Haddadin S (2023) Modularize-and-Conquer: A Generalized Impact Dynamics and Safe Precollision Control Framework for Floating-Base Tree-Like Robots. IEEE Trans Robot 39(4):3200–3221. https://doi.org/10.1109/tro.2023.3257515 – 10.1109/tro.2023.3257515
• Huang H, Tang Q, Li H, Liang L, Li W, Pang Y (2016) Vehicle-manipulator system dynamic modeling and control for underwater autonomous manipulation. Multibody Syst Dyn 41(2):125–147. https://doi.org/10.1007/s11044-016-9538-3 – 10.1007/s11044-016-9538-3
• Featherstone, (2008)
• Garofalo, On the closed form computation of the dynamic matrices and their differentiations. (2013)
• Echeandia, Numerical methods to compute the Coriolis matrix and Christoffel symbols for rigid-body systems. J. Comput. Nonlinear Dyn. (2021)
• Lynch, (2017)
• Murray, (2017)
• Saccon A, Traversaro S, Nori F, Nijmeijer H (2017) On Centroidal Dynamics and Integrability of Average Angular Velocity. IEEE Robot Autom Lett 2(2):943–950. https://doi.org/10.1109/lra.2017.2655560 – 10.1109/lra.2017.2655560
• Hatton RL, Choset H (2015) Nonconservativity and noncommutativity in locomotion. Eur Phys J Spec Top 224(17–18):3141–3174. https://doi.org/10.1140/epjst/e2015-50085-y – 10.1140/epjst/e2015-50085-y
• Chhabra R, Emami MR (2015) Symplectic reduction of holonomic open-chain multi-body systems with constant momentum. Journal of Geometry and Physics 89:82–110. https://doi.org/10.1016/j.geomphys.2014.12.011 – 10.1016/j.geomphys.2014.12.011
• van der Schaft A, Jeltsema D (2014) Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control 1(2–3):173–378. https://doi.org/10.1561/2600000002 – 10.1561/2600000002
• Duindam, (2009)
• Rashad R, Stramigioli S (2025) The Port-Hamiltonian Structure of Continuum Mechanics. J Nonlinear Sci 35(2). https://doi.org/10.1007/s00332-025-10130-1 – 10.1007/s00332-025-10130-1
• Rafee Nekoo S, Rashad R, De Wagter C, Fuller SB, Croon G de, Stramigioli S, Ollero A (2025) A review on flapping-wing robots: Recent progress and challenges. The International Journal of Robotics Research 44(14):2305–2339. https://doi.org/10.1177/02783649251343638 – 10.1177/02783649251343638
• Ponce C, Wu Y, Le Gorrec Y, Ramirez H (2024) A systematic methodology for port-Hamiltonian modeling of multidimensional flexible linear mechanical systems. Applied Mathematical Modelling 134:434–451. https://doi.org/10.1016/j.apm.2024.05.040 – 10.1016/j.apm.2024.05.040
• Warsewa A, Böhm M, Sawodny O, Tarín C (2021) A port-Hamiltonian approach to modeling the structural dynamics of complex systems. Applied Mathematical Modelling 89:1528–1546. https://doi.org/10.1016/j.apm.2020.07.038 – 10.1016/j.apm.2020.07.038
• Ponce C, Wu Y, Le Gorrec Y, Ramirez H (2026) A port-Hamiltonian framework for the modeling and FEM discretization of hyperelastic systems. Applied Mathematical Modelling 150:116403. https://doi.org/10.1016/j.apm.2025.116403 – 10.1016/j.apm.2025.116403
• Dong S, Kuzuno R, Otsuka K, Makihara K (2025) Reduced-order modeling of Hamiltonian formulation in flexible multibody dynamics: Theory and simulations. Applied Mathematical Modelling 144:116055. https://doi.org/10.1016/j.apm.2025.116055 – 10.1016/j.apm.2025.116055
• De Jong S, Brugnoli A, Rashad R, Zhang Y, Stramigioli S (2026) A domain decomposition strategy for natural imposition of mixed boundary conditions in port-Hamiltonian systems. Applied Mathematical Modelling 156:116775. https://doi.org/10.1016/j.apm.2026.116775 – 10.1016/j.apm.2026.116775
• Hogan N (1985) Impedance Control: An Approach to Manipulation: Part I—Theory. Journal of Dynamic Systems, Measurement, and Control 107(1):1–7. https://doi.org/10.1115/1.3140702 – 10.1115/1.3140702
• Ortega, Putting energy back in control. IEEE Control Syst. Mag. (2002)
• Rashad R, Califano F, Stramigioli S (2019) Port-Hamiltonian Passivity-Based Control on SE(3) of a Fully Actuated UAV for Aerial Physical Interaction Near-Hovering. IEEE Robot Autom Lett 4(4):4378–4385. https://doi.org/10.1109/lra.2019.2932864 – 10.1109/lra.2019.2932864
• Yüksel B, Secchi C, Bülthoff HH, Franchi A (2019) Aerial physical interaction via IDA-PBC. The International Journal of Robotics Research 38(4):403–421. https://doi.org/10.1177/0278364919835605 – 10.1177/0278364919835605
• Califano, On the use of energy tanks for robotic systems. (2022)
• Ortega R, van der Schaft A, Castanos F, Astolfi A (2008) Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Trans Automat Contr 53(11):2527–2542. https://doi.org/10.1109/tac.2008.2006930 – 10.1109/tac.2008.2006930
• Duong T, Altawaitan A, Stanley J, Atanasov N (2024) Port-Hamiltonian Neural ODE Networks on Lie Groups for Robot Dynamics Learning and Control. IEEE Trans Robot 40:3695–3715. https://doi.org/10.1109/tro.2024.3428433 – 10.1109/tro.2024.3428433
• Brockett, Robotic manipulators and the product of exponentials formula. (1984)
• Mishra H, Garofalo G, Giordano AM, De Stefano M, Ott C, Kugi A (2023) Reduced Euler-Lagrange Equations of Floating-Base Robots: Computation, Properties, & Applications. IEEE Trans Robot 39(2):1439–1457. https://doi.org/10.1109/tro.2022.3206716 – 10.1109/tro.2022.3206716
• Moghaddam BM, Chhabra R (2024) Singularity-Free Lagrange-Poincaré Equations on Lie Groups for Vehicle-Manipulator Systems. IEEE Trans Robot 40:1393–1409. https://doi.org/10.1109/tro.2023.3347136 – 10.1109/tro.2023.3347136
• Duindam V, Stramigioli S (2008) Singularity-Free Dynamic Equations of Open-Chain Mechanisms With General Holonomic and Nonholonomic Joints. IEEE Trans Robot 24(3):517–526. https://doi.org/10.1109/tro.2008.924250 – 10.1109/tro.2008.924250
• Bullo, (2019)
• Hong Y, Rashad R, Noh S, Lee T, Stramigioli S, Park FC (2021) A geometric formulation of multirotor aerial vehicle dynamics. Nonlinear Dyn 107(1):495–513. https://doi.org/10.1007/s11071-021-07042-6 – 10.1007/s11071-021-07042-6
• Duindam, (2009)
• Chhabra, (2014)
• Van der Schaft, (2000)
• Rashad R, Bicego D, Zult J, Sanchez-Escalonilla S, Jiao R, Franchi A, Stramigioli S (2022) Energy Aware Impedance Control of a Flying End-Effector in the Port-Hamiltonian Framework. IEEE Trans Robot 38(6):3936–3955. https://doi.org/10.1109/tro.2022.3183532 – 10.1109/tro.2022.3183532
• Stramigioli, Energy-aware robotics. (2015)
• Marsden, The reduced Euler-Lagrange equations. (1993)
• Rashad, (2021)
• Müller A (2023) Hamel’s equations and geometric mechanics of constrained and floating multibody and space systems. Proc R Soc A 479(2273). https://doi.org/10.1098/rspa.2022.0732 – 10.1098/rspa.2022.0732
• Cendra, Geometric mechanics, lagrangian reduction, and nonholonomic systems. (2001)
• Bloch, A Author, Brogliato, B Reviewer (2004) Nonholonomic Mechanics and Control. Applied Mechanics Reviews 57(1):B3–B3. https://doi.org/10.1115/1.1641775 – 10.1115/1.1641775
• Wilde M, Kwok Choon S, Grompone A, Romano M (2018) Equations of Motion of Free-Floating Spacecraft-Manipulator Systems: An Engineer’s Tutorial. Front Robot AI 5. https://doi.org/10.3389/frobt.2018.00041 – 10.3389/frobt.2018.00041
• Betsch P, Uhlar S (2007) Energy-momentum conserving integration of multibody dynamics. Multibody Syst Dyn 17(4):243–289. https://doi.org/10.1007/s11044-007-9043-9 – 10.1007/s11044-007-9043-9
• Wang B, Shi D, An Z (2026) Efficient Hamel’s integrator for vehicle-manipulator systems. Applied Mathematical Modelling 154:116708. https://doi.org/10.1016/j.apm.2025.116708 – 10.1016/j.apm.2025.116708