[Paper Review] Identification of Friction Models for MPC-based Control of a PowerCube Serial Robot

Jörg Fehr, Arnim Kargl+1 more|arXiv (Cornell University)|Mar 21, 2022

Advanced Control Systems Optimization4 citations

TL;DR

This paper proposes using the Sparse Identification of Nonlinear Dynamics (SINDy) method to improve friction modeling for model predictive control (MPC) in a Schunk PowerCube serial robot. By comparing SINDy with nonlinear regression on preprocessed and raw data, the study demonstrates that SINDy enables robust, real-time-capable friction identification with minimal preprocessing, significantly enhancing feedforward torque accuracy and reducing model mismatch in a low-cost, laptop-based MPC setup.

ABSTRACT

For model-based control, an accurate and in its complexity suitable representation of the real system is a decisive prerequisite for high and robust control quality. In a structured step-by-step procedure, a model predictive control (MPC) scheme for a Schunk PowerCube robot is derived. Neweul-M$^2$ provides the necessary nonlinear model in symbolical and numerical form. To handle the heavy online computational burden involved with the derived nonlinear model, a linear time-varying MPC scheme is developed based on linearizing the nonlinear system concerning the desired trajectory and the a priori known corresponding feed-forward controller. To improve the identification of the nonlinear friction models of the joints, a nonlinear regression method and the Sparse Identification of Nonlinear Dynamics (SINDy) are compared with each other concerning robustness, online adaptivity, and necessary preprocessing of the input data. Everything is implemented on a slim, low-cost control system with a standard laptop PC.

Motivation & Objective

• Improve model-based control performance of a PowerCube robot by enhancing joint friction modeling using data-driven methods.
• Address model inaccuracies in MPC control caused by imperfect friction representation in assembled robot joints.
• Evaluate whether SINDy outperforms traditional nonlinear regression in identifying friction dynamics under real-world conditions.
• Assess the impact of mechanical assembly and production tolerances on joint friction behavior in a multi-axis robotic system.
• Enable real-time, adaptive friction modeling suitable for low-cost, embedded control systems using sparse regression techniques.

Proposed method

• Derive a nonlinear rigid-body dynamics model of the PowerCube robot using Neweul-M 2 for symbolic and numerical representation.
• Implement a linear time-varying (LTV) MPC scheme by linearizing the nonlinear system around a desired trajectory using a computed torque approach.
• Apply the SINDy method to identify governing friction equations from joint torque and velocity data, using a library of candidate nonlinear terms.
• Compare SINDy with nonlinear regression for friction identification, evaluating robustness to data preprocessing and noise.
• Integrate the identified friction models into the feedforward control path of the LTV-MPC framework to improve torque tracking.
• Validate results using experimental data from joints B and C of the assembled robot, with additional validation on joint A using a LQR framework.

Experimental results

Research questions

• RQ1 Can SINDy identify accurate and robust friction models for robotic joints in an assembled, multi-axis system with minimal data preprocessing?
• RQ2 How does friction behavior in assembled joints differ from isolated joint modules due to mechanical loading and production tolerances?
• RQ3 Does SINDy outperform nonlinear regression in terms of computational efficiency, robustness, and real-time adaptability for friction modeling?
• RQ4 To what extent does the quality of the friction model impact feedforward torque accuracy and overall MPC performance?
• RQ5 Can sparse identification methods like SINDy enable real-time, adaptive friction modeling on low-cost, standard laptop hardware?

Key findings

• SINDy successfully identified joint friction models with high accuracy, even on raw, unprocessed data, demonstrating robustness to data quality and volume.
• The friction characteristics of identical PR90 joint modules differ significantly when assembled in the robot due to additional load on the joint axles, invalidating models derived from isolated modules.
• SINDy achieved performance comparable to nonlinear regression but with significantly lower computational cost, making it more suitable for real-time applications.
• The improved friction models reduced the mismatch between feedforward torque and MPC output torque, particularly evident in motion reversal and zero-crossing trajectories.
• Despite improved feedforward accuracy, trajectory tracking performance did not improve under the current LTV-MPC setup, indicating limitations in the linearizing control approach.
• Future work with a truly nonlinear MPC scheme showed that the improved friction models could significantly enhance tracking performance, confirming the value of accurate friction identification.