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Passive iFIR filters for data-driven velocity control in robotics

Yi Zhang, Zixing Wang, Fulvio Forni

Abstract

We present a passive, data-driven velocity control method for nonlinear robotic manipulators that achieves better tracking performance than optimized PID with comparable design complexity. Using only three minutes of probing data, a VRFT-based design identifies passive iFIR controllers that (i) preserve closed-loop stability via passivity constraints and (ii) outperform a VRFT-tuned PID baseline on the Franka Research 3 robot in both joint-space and Cartesian-space velocity control, achieving up to a 74.5% reduction in tracking error for the Cartesian velocity tracking experiment with the most demanding reference model. When the robot end-effector dynamics change, the controller can be re-learned from new data, regaining nominal performance. This study bridges learning-based control and stability-guaranteed design: passive iFIR learns from data while retaining passivity-based stability guarantees, unlike many learning-based approaches.

Passive iFIR filters for data-driven velocity control in robotics

Abstract

We present a passive, data-driven velocity control method for nonlinear robotic manipulators that achieves better tracking performance than optimized PID with comparable design complexity. Using only three minutes of probing data, a VRFT-based design identifies passive iFIR controllers that (i) preserve closed-loop stability via passivity constraints and (ii) outperform a VRFT-tuned PID baseline on the Franka Research 3 robot in both joint-space and Cartesian-space velocity control, achieving up to a 74.5% reduction in tracking error for the Cartesian velocity tracking experiment with the most demanding reference model. When the robot end-effector dynamics change, the controller can be re-learned from new data, regaining nominal performance. This study bridges learning-based control and stability-guaranteed design: passive iFIR learns from data while retaining passivity-based stability guarantees, unlike many learning-based approaches.

Paper Structure

This paper contains 15 sections, 1 theorem, 10 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related work
  3. Problem statement
  4. Passive data-driven iFIR control
  5. iFIR controller structure
  6. iFIR controller synthesis
  7. Joint space velocity control
  8. Experimental setting and performance metrics
  9. Nominal tracking
  10. Robust tracking and retraining
  11. Passivity and stability
  12. Cartesian space velocity control
  13. SISO Cartesian velocity control
  14. MIMO Cartesian velocity control
  15. Conclusion and Future Work

Key Result

Theorem 1

Consider a generic iFIR controller $C$ in Definition defi:iFIR. For any real scalars $\rho_{0} \geq 1$, $0 < \rho < 1$, and $M\geq2$, there exists $\epsilon \geq 0$, such that the iFIR controller $C$ obtained by eq:opt with the additional constraints is passive.

Figures (7)

  • Figure 3: Controlled robot velocity feedback loop with model reference in parallel. The output $y$ represents either single joint velocity or end-effector Cartesian velocity.
  • Figure 4: A graphical interpretation of Theorem \ref{['thm:IFIR_tuning']}.
  • Figure 5: Single joint velocity control setting. Flexible wood strips of variable lengths are used to model different dynamic loads. Bode diagrams: reference model dynamics in black and (estimated, linearized) open-loop dynamics in blue.
  • Figure 6: Joint space velocity tracking results. Black: target response and target reference model. Red: closed-loop response and sampled Bode diagram with iFIR controller. Blue: closed-loop response and sampled Bode diagram with PID controller.
  • Figure 7: Closed-loop response to sinusoidal reference (left) and step reference (right). Black: target response. Red: passive iFIR. Blue: PID. Gray: non-passive iFIR. Learning without passivity constraints can cause instability.
  • ...and 2 more figures

Theorems & Definitions (3)

  • Definition 1: iFIR controller
  • Theorem 1
  • proof