Nonlinear Dynamics

, Volume 95, Issue 1, pp 57–72 | Cite as

A modified homotopy optimization for parameter identification in dynamic systems with backlash discontinuity

  • Borna GhannadiEmail author
  • Reza Sharif Razavian
  • John McPhee
Original Paper


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.


Parameter identification System dynamics Sandwiched backlash Homotopy optimization Rehabilitation robot 



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.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Systems Design EngineeringUniversity of WaterlooWaterlooCanada

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