Model-based control considers system dynamics to solve challenging control problems; recently, the amount of activity in developing model-based controllers is growing, specifically in rehabilitation robotics. The performance of this controller depends on how accurate the system dynamics has been modeled. Dynamic parameter identification (DPI) of the systems is required for optimal performance of the model-based controller. Current DPI methods are more suitable for systems with continuous dynamics. If any type of discontinuity (e.g., backlash) is present in the system, the DPI may have numerical problems for convergence. In this work, we propose a modified homotopy optimization to identify parameters of a system with mechanical discontinuity (i.e., backlash). The performance of the proposed method was first evaluated through a computer simulation on a system with sandwiched backlash. Results of the DPI showed that the proposed homotopy optimization can identify the discontinuous system parameters with a good accuracy. It was found that ignoring the backlash in the system dynamics imposes large errors in the system DPI. After verifying the proposed method using computer simulations, the DPI was implemented to identify the parameters of a rehabilitation robot with actuator backlash. The proposed method provided a better estimate of the system parameters compared to the no-backlash DPI of the experimental robot. Despite the noise in velocity and acceleration due to the numerical differentiation of the sampled angle measurements, the forward dynamics results are quite accurate for all of the tested configurations with the discontinuous backlash model.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
Brown, P., McPhee, J.: A continuous velocity-based friction model for dynamics and control with physically meaningful parameters. J. Comput. Nonlinear Dyn. 11(5), 054502 (2016). https://doi.org/10.1115/1.4033658
Chen, S., Billings, S.A., Grant, P.M.: Non-linear system identification using neural networks. Int. J. Control 51(6), 1191–1214 (1990). https://doi.org/10.1080/00207179008934126
Ding, M., Hirasawa, K., Kurita, Y., Takemura, H., Takamatsu, J., Mizoguchi, H., Ogasawara, T.: Pinpointed muscle force control in consideration of human motion and external force. In: 2010 IEEE International Conference on Robotics and Biomimetics (ROBIO), pp. 739–744. IEEE (2010). https://doi.org/10.1109/ROBIO.2010.5723418
Enikov, E., Stepan, G.: Microchaotic motion of digitally controlled machines. J. Vib. Control 4(4), 427–443 (1998). https://doi.org/10.1177/107754639800400405
Ghannadi, B., Mehrabi, N., Sharif Razavian, R., McPhee, J., Razavian, R.S., McPhee, J.: Nonlinear model predictive control of an upper extremity rehabilitation robot using a two-dimensional human-robot interaction model. In: IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 502–507. IEEE, Vancouver, British Columbia, Canada (2017). https://doi.org/10.1109/IROS.2017.8202200
Jiang, Z.H., Ishida, T., Sunawada, M.: Neural network aided dynamic parameter identification of robot manipulators. In: 2006 IEEE International Conference on Systems, Man and Cybernetics, pp. 3298–3303. IEEE (2006). https://doi.org/10.1109/ICSMC.2006.384627
Ljung, L.: System Identification: Theory for User, 2nd edn. PTR Prentice Hall Information and System Sciences Series (1987). https://doi.org/10.1016/0005-1098(89)90019-8
Maciejasz, P., Eschweiler, J., Gerlach-Hahn, K., Jansen-Troy, A., Leonhardt, S.: A survey on robotic devices for upper limb rehabilitation. Journal of NeuroEngineering and Rehabilitation 11(3) (2014). https://doi.org/10.1186/1743-0003-11-3
Nordin, M., Gutman, P.O.: Controlling mechanical systems with backlash–a survey. Automatica 38(10), 1633–1649 (2002). https://doi.org/10.1016/S0005-1098(02)00047-X
Nyarko, E.K., Scitovski, R.: Solving the parameter identification problem of mathematical models using genetic algorithms. Appl. Math. Comput. 153(3), 651–658 (2004). https://doi.org/10.1016/S0096-3003(03)00661-1
Proietti, T., Crocher, V., Roby-Brami, A., Jarrasse, N.: Upper-limb robotic exoskeletons for neurorehabilitation: a review on control strategies. IEEE Rev. Biomed. Eng. 9, 4–14 (2016). https://doi.org/10.1109/RBME.2016.2552201
Sharifi, M., Behzadipour, S., Vossoughi, G.: Nonlinear model reference adaptive impedance control for human-robot interactions. Control Eng. Pract. 32, 9–27 (2014). https://doi.org/10.1016/j.conengprac.2014.07.001
Soderstrom, T., Stoica, P.G.: System Identification. Prentice-Hall International, Englewood Cliffs (1988)
Sreenivasa, M., Ayusawa, K., Nakamura, Y.: Modeling and identification of a realistic spiking neural network and musculoskeletal model of the human arm, and an application to the stretch reflex. IEEE Trans. Neural Syst. Rehabil. Eng. 24(5), 591–602 (2016). https://doi.org/10.1109/TNSRE.2015.2478858
Su, C.Y., Stepanenko, Y., Svoboda, J., Leung, T.: Robust adaptive control of a class of nonlinear systems with unknown backlash-like hysteresis. IEEE Trans. Autom. Control 45(12), 2427–2432 (2000). https://doi.org/10.1109/9.895588
Tao, G., Kokotovic, P.V.: Adaptive Control of Systems with Actuator and Sensor Nonlinearities. Wiley-Interscience, New York (1996)
Tao, G., Ma, X., Ling, Y.: Optimal and nonlinear decoupling control of systems with sandwiched backlash. Automatica 37(2), 165–176 (2001). https://doi.org/10.1016/S0005-1098(00)00153-9
Taware, A., Tao, G.: Control of Sandwich Nonlinear Systems. Lecture Notes in Control and Information Sciences, vol. 288. Springer, Berlin (2006)
Thanh, T.D., Kotlarski, J., Heimann, B., Ortmaier, T.: Dynamics identification of kinematically redundant parallel robots using the direct search method. Mech. Mach. Theory 52, 277–295 (2012). https://doi.org/10.1016/j.mechmachtheory.2012.02.002
Vyasarayani, C.P., Uchida, T., Carvalho, A., McPhee, J.: Parameter identification in dynamic systems using the homotopy optimization approach. Multibody Syst. Dyn. 26(4), 411–424 (2011). https://doi.org/10.1007/s11044-011-9260-0
Vyasarayani, C.P., Uchida, T., McPhee, J.: Single-shooting homotopy method for parameter identification in dynamical systems. Phys. Rev. 85(3), 036,201 (2012). https://doi.org/10.1103/PhysRevE.85.036201
Wu, J., Wang, J., You, Z.: An overview of dynamic parameter identification of robots. Robot. Comput. Integr. Manuf. 26(5), 414–419 (2010). https://doi.org/10.1016/j.rcim.2010.03.013
Ye, M.: Parameter identification of dynamical systems based on improved particle swarm optimization. In: Intelligent Control and Automation, pp. 351–360. Springer Berlin Heidelberg (2006). https://doi.org/10.1007/978-3-540-37256-1
Zhou, J., Wen, C.: Nonsmooth nonlinearities. In: Adaptive Backstepping Control of Uncertain Systems, Lecture Notes in Control and Information Sciences, vol. 372, pp. 83–96. Springer Berlin Heidelberg, Berlin, Heidelberg (2008). https://doi.org/10.1007/978-3-540-77807-3
We thank the anonymous reviewer who provided very helpful suggestions to improve the paper. This work was funded by the Canada Research Chairs (CRC) program and the Natural Sciences and Engineering Research Council of Canada (NSERC). The authors wish to thank Quanser Inc. for providing the upper extremity rehabilitation robot and Toronto Rehabilitation Institute (TRI) for collaborating.
The DPI of the simulation setup is also done by other conventional optimization methods: Bound Optimization by Quadratic Approximation (BOBYQA) and Pattern Search (PS) in Table 4, and Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) in Table 5. The objective functions for these methods are similar to the SQP method.
About this article
Cite this article
Ghannadi, B., Sharif Razavian, R. & McPhee, J. A modified homotopy optimization for parameter identification in dynamic systems with backlash discontinuity. Nonlinear Dyn 95, 57–72 (2019). https://doi.org/10.1007/s11071-018-4550-1
- Parameter identification
- System dynamics
- Sandwiched backlash
- Homotopy optimization
- Rehabilitation robot