An Energy-Based Approach to the Force-Impedance Control Problem for Robot Manipulators

Authors

Haojun Ma, Mauricio Muñoz-Arias, Jacquelien M. A. Scherpen, Alessandro Macchelli

Abstract

This work proposes a new force-impedance controller design method for robot manipulators in the port-Hamiltonian (PH) framework. Compared with former work in the Euler–Lagrange (EL) framework, fewer control parameters and constraints are needed to achieve asymptotic stability. Besides, a clear physical interpretation can be given due to the PH formalism. First, a canonical transformation is adopted to recast the joint space model into a workspace model. We then achieve impedance control by shaping the inertial and stiffness matrices. Additionally, a change of variable strategy allows an integral force action, such that the force error is included in the system’s passive output. Furthermore, a damping injection is applied to obtain a smoother noncontact-to-contact transition. Finally, we conduct simulations and experiments to compare the advantages of our new force-impedance control law with respect to the EL approaches.

Citation

• Journal: IEEE Transactions on Control Systems Technology
• Year: 2026
• Volume: 34
• Issue: 1
• Pages: 123–138
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tcst.2025.3606519

BibTeX

@article{Ma_2026,
  title={{An Energy-Based Approach to the Force-Impedance Control Problem for Robot Manipulators}},
  volume={34},
  ISSN={2374-0159},
  DOI={10.1109/tcst.2025.3606519},
  number={1},
  journal={IEEE Transactions on Control Systems Technology},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Ma, Haojun and Muñoz-Arias, Mauricio and Scherpen, Jacquelien M. A. and Macchelli, Alessandro},
  year={2026},
  pages={123--138}
}

Download the bib file

References

• Chiaverini S, Sciavicco L (1993) The parallel approach to force/position control of robotic manipulators. IEEE Trans Robot Automat 9(4):361–373. https://doi.org/10.1109/70.24604 – 10.1109/70.246048
• Chiaverini S, Siciliano B, Villani L (1994) Force/position regulation of compliant robot manipulators. IEEE Trans Automat Contr 39(3):647–652. https://doi.org/10.1109/9.28078 – 10.1109/9.280780
• Kiguchi K, Fukuda T (2000) Position/force control of robot manipulators for geometrically unknown objects using fuzzy neural networks. IEEE Trans Ind Electron 47(3):641–649. https://doi.org/10.1109/41.84790 – 10.1109/41.847905
• Jung S, Hsia TC, Bonitz RG (2004) Force Tracking Impedance Control of Robot Manipulators Under Unknown Environment. IEEE Trans Contr Syst Technol 12(3):474–483. https://doi.org/10.1109/tcst.2004.82432 – 10.1109/tcst.2004.824320
• Calanca A, Muradore R, Fiorini P (2016) A Review of Algorithms for Compliant Control of Stiff and Fixed-Compliance Robots. IEEE/ASME Trans Mechatron 21(2):613–624. https://doi.org/10.1109/tmech.2015.246584 – 10.1109/tmech.2015.2465849
• Al-Shuka HFN, Leonhardt S, Zhu W-H, Song R, Ding C, Li Y (2018) Active Impedance Control of Bioinspired Motion Robotic Manipulators: An Overview. Applied Bionics and Biomechanics 2018:1–19. https://doi.org/10.1155/2018/820305 – 10.1155/2018/8203054
• Schumacher M, Wojtusch J, Beckerle P, von Stryk O (2019) An introductory review of active compliant control. Robotics and Autonomous Systems 119:185–200. https://doi.org/10.1016/j.robot.2019.06.00 – 10.1016/j.robot.2019.06.009
• Song P, Yu Y, Zhang X (2019) A Tutorial Survey and Comparison of Impedance Control on Robotic Manipulation. Robotica 37(5):801–836. https://doi.org/10.1017/s026357471800133 – 10.1017/s0263574718001339
• Abu-Dakka FJ, Saveriano M (2020) Variable Impedance Control and Learning—A Review. Front Robot AI 7. https://doi.org/10.3389/frobt.2020.59068 – 10.3389/frobt.2020.590681
• Michel Y, Ott C, Lee D (2022) Safety-Aware Hierarchical Passivity-Based Variable Compliance Control for Redundant Manipulators. IEEE Trans Robot 38(6):3899–3916. https://doi.org/10.1109/tro.2022.317447 – 10.1109/tro.2022.3174478
• Lin Y, Chen Z, Yao B (2021) Unified Motion/Force/Impedance Control for Manipulators in Unknown Contact Environments Based on Robust Model-Reaching Approach. IEEE/ASME Trans Mechatron 26(4):1905–1913. https://doi.org/10.1109/tmech.2021.308159 – 10.1109/tmech.2021.3081594
• Burdet E, Osu R, Franklin DW, Milner TE, Kawato M (2001) The central nervous system stabilizes unstable dynamics by learning optimal impedance. Nature 414(6862):446–449. https://doi.org/10.1038/3510656 – 10.1038/35106566
• Howard M, Braun DJ, Vijayakumar S (2013) Transferring Human Impedance Behavior to Heterogeneous Variable Impedance Actuators. IEEE Trans Robot 29(4):847–862. https://doi.org/10.1109/tro.2013.225631 – 10.1109/tro.2013.2256311
• Li Y, Jarrassé N, Burdet E (2017) Versatile Interaction Control and Haptic Identification in Humans and Robots. Springer Tracts in Advanced Robotics 187–20 – 10.1007/978-3-319-51547-2_9
• Yang C, Ganesh G, Haddadin S, Parusel S, Albu-Schaeffer A, Burdet E (2011) Human-Like Adaptation of Force and Impedance in Stable and Unstable Interactions. IEEE Trans Robot 27(5):918–930. https://doi.org/10.1109/tro.2011.215825 – 10.1109/tro.2011.2158251
• Li Y, Ganesh G, Jarrasse N, Haddadin S, Albu-Schaeffer A, Burdet E (2018) Force, Impedance, and Trajectory Learning for Contact Tooling and Haptic Identification. IEEE Trans Robot 34(5):1170–1182. https://doi.org/10.1109/tro.2018.283040 – 10.1109/tro.2018.2830405
• Iskandar M, Ott C, Albu-Schäffer A, Siciliano B, Dietrich A (2023) Hybrid Force-Impedance Control for Fast End-Effector Motions. IEEE Robot Autom Lett 8(7):3931–3938. https://doi.org/10.1109/lra.2023.327003 – 10.1109/lra.2023.3270036
• Ferraguti F, Secchi C, Fantuzzi C (2013) A tank-based approach to impedance control with variable stiffness. 2013 IEEE International Conference on Robotics and Automation 4948–495 – 10.1109/icra.2013.6631284
• Ferraguti F, Preda N, Manurung A, Bonfe M, Lambercy O, Gassert R, Muradore R, Fiorini P, Secchi C (2015) An Energy Tank-Based Interactive Control Architecture for Autonomous and Teleoperated Robotic Surgery. IEEE Trans Robot 31(5):1073–1088. https://doi.org/10.1109/tro.2015.245579 – 10.1109/tro.2015.2455791
• Stramigioli, Modeling and IPC Control of Interactive Mechanical Systems—A Coordinate-free Approach (2001)
• 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.2019.293286 – 10.1109/lra.2019.2932864
• 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.2022.318353 – 10.1109/tro.2022.3183532
• van der Schaft A (2017) L2-Gain and Passivity Techniques in Nonlinear Control. Springer International Publishin – 10.1007/978-3-319-49992-5
• Ortega R, van der Schaft A, Maschke B, Escobar G (2002) Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38(4):585–596. https://doi.org/10.1016/s0005-1098(01)00278- – 10.1016/s0005-1098(01)00278-3
• Folkertsma GA, Stramigioli S (2017) Energy in Robotic – 10.1561/9781680833133
• Lozano R, Brogliato B, Egeland O, Maschke B (2000) Dissipative Systems Analysis and Control. Springer Londo – 10.1007/978-1-4471-3668-2
• Ortega R, García-Canseco E (2004) Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control 10(5):432–450. https://doi.org/10.3166/ejc.10.432-45 – 10.3166/ejc.10.432-450
• Fujimoto K, Sakurama K, Sugie T (2003) Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica 39(12):2059–2069. https://doi.org/10.1016/j.automatica.2003.07.00 – 10.1016/j.automatica.2003.07.005
• Donaire A, Junco S (2009) On the addition of integral action to port-controlled Hamiltonian systems. Automatica 45(8):1910–1916. https://doi.org/10.1016/j.automatica.2009.04.00 – 10.1016/j.automatica.2009.04.006
• Dirksz DA, Scherpen JMA (2012) Power-Based Setpoint Control: Experimental Results on a Planar Manipulator. IEEE Trans Contr Syst Technol 20(5):1384–1391. https://doi.org/10.1109/tcst.2011.216351 – 10.1109/tcst.2011.2163514
• Dirksz DA, Scherpen JMA (2012) Power-based control: Canonical coordinate transformations, integral and adaptive control. Automatica 48(6):1045–1056. https://doi.org/10.1016/j.automatica.2012.03.00 – 10.1016/j.automatica.2012.03.003
• Chan-Zheng C, Munoz-Arias M, Scherpen JMA (2023) Tuning Rules for Passivity-Based Integral Control for a Class of Mechanical Systems. IEEE Control Syst Lett 7:37–42. https://doi.org/10.1109/lcsys.2022.318661 – 10.1109/lcsys.2022.3186618
• Ferguson J, Donaire A, Middleton RH (2017) Integral Control of Port-Hamiltonian Systems: Nonpassive Outputs Without Coordinate Transformation. IEEE Trans Automat Contr 62(11):5947–5953. https://doi.org/10.1109/tac.2017.270099 – 10.1109/tac.2017.2700995
• Ferguson J, Donaire A, Ortega R, Middleton RH (2020) Matched Disturbance Rejection for a Class of Nonlinear Systems. IEEE Trans Automat Contr 65(4):1710–1715. https://doi.org/10.1109/tac.2019.293339 – 10.1109/tac.2019.2933398
• Spong, Robot Modeling and Control (2020)
• Fujimoto K, Sugie T (2001) Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters 42(3):217–227. https://doi.org/10.1016/s0167-6911(00)00091- – 10.1016/s0167-6911(00)00091-8
• Wang H, Cheah CC, Ren W, Xie Y (2018) Passive Separation Approach to Adaptive Visual Tracking for Robotic Systems. IEEE Trans Contr Syst Technol 26(6):2232–2241. https://doi.org/10.1109/tcst.2017.274806 – 10.1109/tcst.2017.2748061
• Munoz-Arias M, I. El-Hawwary M, Scherpen JMA (2015) Image-based visual servo control using the port-Hamiltonian approach. IFAC-PapersOnLine 48(13):105–110. https://doi.org/10.1016/j.ifacol.2015.10.22 – 10.1016/j.ifacol.2015.10.222
• Khalil, Nonlinear Systems (2002)
• Donaire A, Perez T (2012) Dynamic positioning of marine craft using a port-Hamiltonian framework. Automatica 48(5):851–856. https://doi.org/10.1016/j.automatica.2012.02.02 – 10.1016/j.automatica.2012.02.022
• Rijs, Philips experimental robot arm: User instructor manual. (2009)
• Bol, Model Generator for Philips Experimental Robotic Arm (2012)
• Han J (2009) From PID to Active Disturbance Rejection Control. IEEE Trans Ind Electron 56(3):900–906. https://doi.org/10.1109/tie.2008.201162 – 10.1109/tie.2008.2011621
• Ma, Force-Impedance Control in the Port-Hamiltonian Framework: Simulation and Experimental Results (2025)