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Data-Enabled Neighboring Extremal: Case Study on Model-Free Trajectory Tracking for Robotic Arm

Amin Vahidi-Moghaddam, Keyi Zhu, Kaixiang Zhang, Ziyou Song, Zhaojian Li

TL;DR

This work addresses the computational bottleneck of data-enabled predictive control (DeePC) for constrained trajectory tracking by introducing DeeNE, a perturbation-based framework that updates a nominal DeePC solution using second-order variations when initial conditions or reference trajectories change. DeeNE derives linear corrective laws from KKT conditions, yielding a cheap online update to the control action that preserves constraint handling while reducing the need to solve a large optimization at every time step. The approach is extended to handle non-optimal nominal solutions and real-time reference perturbations, and is validated through both simulations and experiments on a 7-DoF robotic arm, achieving substantial speedups with comparable tracking performance and robust constraint satisfaction. The results demonstrate that DeeNE extends the real-time applicability of data-driven DeePC to higher-DoF systems and dynamic environments, with potential for further efficiency gains via dimension reduction.

Abstract

Data-enabled predictive control (DeePC) has recently emerged as a powerful data-driven approach for efficient system controls with constraints handling capabilities. It performs optimal controls by directly harnessing input-output (I/O) data, bypassing the process of explicit model identification that can be costly and time-consuming. However, its high computational complexity, driven by a large-scale optimization problem (typically in a higher dimension than its model-based counterpart--Model Predictive Control), hinders real-time applications. To overcome this limitation, we propose the data-enabled neighboring extremal (DeeNE) framework, which significantly reduces computational cost while preserving control performance. DeeNE leverages first-order optimality perturbation analysis to efficiently update a precomputed nominal DeePC solution in response to changes in initial conditions and reference trajectories. We validate its effectiveness on a 7-DoF KINOVA Gen3 robotic arm, demonstrating substantial computational savings and robust, data-driven control performance.

Data-Enabled Neighboring Extremal: Case Study on Model-Free Trajectory Tracking for Robotic Arm

TL;DR

This work addresses the computational bottleneck of data-enabled predictive control (DeePC) for constrained trajectory tracking by introducing DeeNE, a perturbation-based framework that updates a nominal DeePC solution using second-order variations when initial conditions or reference trajectories change. DeeNE derives linear corrective laws from KKT conditions, yielding a cheap online update to the control action that preserves constraint handling while reducing the need to solve a large optimization at every time step. The approach is extended to handle non-optimal nominal solutions and real-time reference perturbations, and is validated through both simulations and experiments on a 7-DoF robotic arm, achieving substantial speedups with comparable tracking performance and robust constraint satisfaction. The results demonstrate that DeeNE extends the real-time applicability of data-driven DeePC to higher-DoF systems and dynamic environments, with potential for further efficiency gains via dimension reduction.

Abstract

Data-enabled predictive control (DeePC) has recently emerged as a powerful data-driven approach for efficient system controls with constraints handling capabilities. It performs optimal controls by directly harnessing input-output (I/O) data, bypassing the process of explicit model identification that can be costly and time-consuming. However, its high computational complexity, driven by a large-scale optimization problem (typically in a higher dimension than its model-based counterpart--Model Predictive Control), hinders real-time applications. To overcome this limitation, we propose the data-enabled neighboring extremal (DeeNE) framework, which significantly reduces computational cost while preserving control performance. DeeNE leverages first-order optimality perturbation analysis to efficiently update a precomputed nominal DeePC solution in response to changes in initial conditions and reference trajectories. We validate its effectiveness on a 7-DoF KINOVA Gen3 robotic arm, demonstrating substantial computational savings and robust, data-driven control performance.

Paper Structure

This paper contains 13 sections, 2 theorems, 28 equations, 11 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Problem Formulation and Preliminaries
  3. Model-Based Reference Tracking
  4. Data-Enabled Predictive Control (DeePC)
  5. Data-Enabled Neighboring Extremal (DeeNE)
  6. DeeNE with Optimal Nominal Solution
  7. DeeNE with Non-Optimal Nominal Solution
  8. DeeNE Implementation
  9. Case Study on Robotic Arm Motion Control with Constraints
  10. System Specification and DeePC/DeeNE Formulation
  11. Simulation Results
  12. Experimental Results
  13. Conclusion

Key Result

Theorem 1

Consider the optimization problem DeeNE, the augmented cost function DeeNE-aug-cost, and the KKT conditions DeeNE-KKT. If $\bar{J}_{gg} > 0$, the DeeNE policy approximates the perturbed solution for the DeePC DeePC in the presence of initial I/O perturbation $\delta w_{ini}$ and reference perturbation $\delta r$.

Figures (11)

  • Figure 1: Drawing MSU by 7-DoF robotic arm.
  • Figure 2: Control input for 7-DoF Robotic Arm (Simulation).
  • Figure 3: Position tracking for 7-DoF Robotic Arm (Simulation).
  • Figure 4: Orientation tracking for 7-DoF Robotic Arm (Simulation).
  • Figure 5: Control input for 7-DoF Robotic Arm (Experiment).
  • ...and 6 more figures

Theorems & Definitions (7)

  • Theorem 1: Data-Enabled Neighboring Extremal
  • proof
  • Remark 1: Singularity
  • Remark 2
  • Theorem 2: Modified Data-Enabled Neighboring Extremal
  • proof
  • Remark 3: Quadratic Cost