A Modified Homotopy Optimization for Parameter Identification in Dynamic Systems with Backlash Discontinuity

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.