Bayesian Inference for Path Following Control of Port-Hamiltonian Systems with Training Trajectory Data

Authors

Yuki Okura, Kenji Fujimoto, Ichiro Maruta, Akio Saito, Hidetoshi Ikeda

Abstract

: This paper describes a procedure to design a path following controller of port-Hamiltonian systems based on a training trajectory dataset. The trajectories are generated by human operations, and the training data consist of several trajectories with variations. Hence, we regard the trajectory as a stochastic process model. Then we design a deterministic controller for path following control from the model. In order to obtain reasonable design parameters for a path following controller from the training data, Bayesian inference is adopted in this paper. By using Bayesian inference, we estimate a probability density function of the desired trajectory. Moreover, not only the mean value of the trajectory but also the covariance matrix is acquired. A potential function for path following control is obtained from the probability density function. By incorporating the covariance information into the control system design, it is possible to create a potential function that takes into account uncertainty at each position on the trajectory, and it is expected to construct a control system that generates appropriate assist force for a human operator.

Citation

• Journal: SICE Journal of Control, Measurement, and System Integration
• Year: 2020
• Volume: 13
• Issue: 2
• Pages: 40–46
• Publisher: Informa UK Limited
• DOI: 10.9746/jcmsi.13.40

BibTeX

@article{Okura_2020,
  title={{Bayesian Inference for Path Following Control of Port-Hamiltonian Systems with Training Trajectory Data}},
  volume={13},
  ISSN={1884-9970},
  DOI={10.9746/jcmsi.13.40},
  number={2},
  journal={SICE Journal of Control, Measurement, and System Integration},
  publisher={Informa UK Limited},
  author={Okura, Yuki and Fujimoto, Kenji and Maruta, Ichiro and Saito, Akio and Ikeda, Hidetoshi},
  year={2020},
  pages={40--46}
}

Download the bib file

References

• Slotine, J.-J. E. & Li, W. Composite adaptive control of robot manipulators. Automatica 25, 509–519 (1989) – 10.1016/0005-1098(89)90094-0
• Ortega, R., Loría, A., Nicklasson, P. J. & Sira-Ramírez, H. Passivity-Based Control of Euler-Lagrange Systems. Communications and Control Engineering (Springer London, 1998). doi:10.1007/978-1-4471-3603-3 – 10.1007/978-1-4471-3603-3
• Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory Tracking Control of Nonholonomic Hamiltonian Systems via Generalized Canonical Transformations. European Journal of Control 10, 421–431 (2004) – 10.3166/ejc.10.421-431
• Salisbury, J. Active stiffness control of a manipulator in cartesian coordinates. 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes (1980) doi:10.1109/cdc.1980.272026 – 10.1109/cdc.1980.272026
• Hogan, N. Impedance Control: An Approach to Manipulation. 1984 American Control Conference (1984) doi:10.23919/acc.1984.4788393 – 10.23919/acc.1984.4788393
• Duindam, V. & Stramigioli, S. Port-Based Asymptotic Curve Tracking for Mechanical Systems. European Journal of Control 10, 411–420 (2004) – 10.3166/ejc.10.411-420
• Nielsen, C. & Maggiore, M. Output stabilization and maneuver regulation: A geometric approach. Systems & Control Letters 55, 418–427 (2006) – 10.1016/j.sysconle.2005.09.006
• Akhtar, A., Nielsen, C. & Waslander, S. L. Path Following Using Dynamic Transverse Feedback Linearization for Car-Like Robots. IEEE Trans. Robot. 31, 269–279 (2015) – 10.1109/tro.2015.2395711
• Nakamura, H. Global Nonsmooth Control Lyapunov Function Design for Path-Following Problem via Minimum Projection Method. IFAC-PapersOnLine 49, 600–605 (2016) – 10.1016/j.ifacol.2016.10.231
• Schaft, A. L2-Gain and Passivity Techniques in Nonlinear Control. Lecture Notes in Control and Information Sciences (Springer Berlin Heidelberg, 1996). doi:10.1007/3-540-76074-1 – 10.1007/3-540-76074-1
• Van Der Schaft, A. J. & Maschke, B. M. On the Hamiltonian formulation of nonholonomic mechanical systems. Reports on Mathematical Physics 34, 225–233 (1994) – 10.1016/0034-4877(94)90038-8
• Maschke, B. M., van der Schaft, A. J. & Breedveld, P. C. An intrinsic Hamiltonian formulation of the dynamics of LC-circuits. IEEE Trans. Circuits Syst. I 42, 73–82 (1995) – 10.1109/81.372847
• Fujimoto, K. & Sugie, T. Canonical transformation and stabilization of generalized Hamiltonian systems. Systems & Control Letters 42, 217–227 (2001) – 10.1016/s0167-6911(00)00091-8