Authors

Francesco Cordoni, Luca Di Persio, Riccardo Muradore

Abstract

In this paper we address the problem of implementing a stochastic variable admittance control. Both the variable part of the admittance control and the noise affecting the system may concur to the instability of the system. We propose an energy tank approach, based on the theory of stochastic port–Hamiltonian systems and weak passivity, where the energy dissipated by the stochastic system, if any, is stored into the tank to implement the desired actions. As we consider a non–vanishing noise, we need to consider weaker notion of passivity and convergence. We will show how the notion of weak passivity can be properly defined so that equipping a stochastic system with a suitable energy tank, variable admittance control can be efficiently implemented. We prove that the overall system is weakly passive and it converges toward an invariant measure. Simulation results show the effectiveness of the derived theoretical framework.

Keywords

Variable admittance control; Stochastic port–Hamiltonian systems; Passivity; Ultimately stochastic passive

Citation

  • Journal: IFAC-PapersOnLine
  • Year: 2020
  • Volume: 53
  • Issue: 2
  • Pages: 9986–9991
  • Publisher: Elsevier BV
  • DOI: 10.1016/j.ifacol.2020.12.2716
  • Note: 21st IFAC World Congress- Berlin, Germany, 11–17 July 2020

BibTeX

@article{Cordoni_2020,
  title={{A variable stochastic admittance control framework with energy tank}},
  volume={53},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2020.12.2716},
  number={2},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Cordoni, Francesco and Persio, Luca Di and Muradore, Riccardo},
  year={2020},
  pages={9986--9991}
}

Download the bib file

References

  • Buchli, (2011)
  • Calanca, A., Muradore, R. & Fiorini, P. A Review of Algorithms for Compliant Control of Stiff and Fixed-Compliance Robots. IEEE/ASME Transactions on Mechatronics vol. 21 613–624 (2016) – 10.1109/tmech.2015.2465849
  • Calanca, A., Muradore, R. & Fiorini, P. Impedance control of series elastic actuators: Passivity and acceleration-based control. Mechatronics vol. 47 37–48 (2017) – 10.1016/j.mechatronics.2017.08.010
  • Cosso, A., Fuhrman, M. & Pham, H. Long time asymptotics for fully nonlinear Bellman equations: A backward SDE approach. Stochastic Processes and their Applications vol. 126 1932–1973 (2016) – 10.1016/j.spa.2015.12.009
  • Ferraguti, F. et al. An Energy Tank-Based Interactive Control Architecture for Autonomous and Teleoperated Robotic Surgery. IEEE Transactions on Robotics vol. 31 1073–1088 (2015) – 10.1109/tro.2015.2455791
  • Ferraguti, F., Secchi, C. & Fantuzzi, C. A tank-based approach to impedance control with variable stiffness. 2013 IEEE International Conference on Robotics and Automation 4948–4953 (2013) doi:10.1109/icra.2013.6631284 – 10.1109/icra.2013.6631284
  • Florchinger, P. A Passive System Approach to Feedback Stabilization of Nonlinear Control Stochastic Systems. SIAM Journal on Control and Optimization vol. 37 1848–1864 (1999) – 10.1137/s0363012997317478
  • Franchi, A., Secchi, C., Hyoung Il Son, Bulthoff, H. H. & Giordano, P. R. Bilateral Teleoperation of Groups of Mobile Robots With Time-Varying Topology. IEEE Transactions on Robotics vol. 28 1019–1033 (2012) – 10.1109/tro.2012.2196304
  • Franken, M., Stramigioli, S., Misra, S., Secchi, C. & Macchelli, A. Bilateral Telemanipulation With Time Delays: A Two-Layer Approach Combining Passivity and Transparency. IEEE Transactions on Robotics vol. 27 741–756 (2011) – 10.1109/tro.2011.2142430
  • Hatanaka, T., Chopra, N. & Spong, M. W. Passivity-based control of robots: Historical perspective and contemporary issues. 2015 54th IEEE Conference on Decision and Control (CDC) 2450–2452 (2015) doi:10.1109/cdc.2015.7402575 – 10.1109/cdc.2015.7402575
  • Hogan, N. Impedance Control: An Approach to Manipulation. 1984 American Control Conference (1984) doi:10.23919/acc.1984.4788393 – 10.23919/acc.1984.4788393
  • Khasminskii, (2011)
  • Liberzon, D. & Brockett, R. W. Nonlinear feedback systems perturbed by noise: steady-state probability distributions and optimal control. IEEE Transactions on Automatic Control vol. 45 1116–1130 (2000) – 10.1109/9.863596
  • Satoh, S. & Fujimoto, K. Passivity Based Control of Stochastic Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 58 1139–1153 (2013) – 10.1109/tac.2012.2229791
  • Satoh, S. & Saeki, M. Bounded Stability of Nonlinear Stochastic Systems. SICE Journal of Control, Measurement, and System Integration vol. 8 181–187 (2015) – 10.9746/jcmsi.8.181
  • Tsumugiwa, T., Yokogawa, R. & Hara, K. Variable impedance control based on estimation of human arm stiffness for human-robot cooperative calligraphic task. Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292) vol. 1 644–650 – 10.1109/robot.2002.1013431
  • van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
  • Villani, L. & De Schutter, J. Force Control. Springer Handbook of Robotics 161–185 (2008) doi:10.1007/978-3-540-30301-5_8 – 10.1007/978-3-540-30301-5_8
  • Zhu, W. Q. Nonlinear Stochastic Dynamics and Control in Hamiltonian Formulation. Applied Mechanics Reviews vol. 59 230–248 (2006) – 10.1115/1.2193137