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A Robust Task-Level Control Architecture for Learned Dynamical Systems

Eshika Pathak, Ahmed Aboudonia, Sandeep Banik, Naira Hovakimyan

TL;DR

This work tackles task-execution mismatch in dynamical-systems–based learning from demonstration by introducing L1-DS, a task-level control architecture that augments nominal learned dynamics with a Control Lyapunov Function (CLF)–based stabilizer and an $\$ adaptive controller. The approach also incorporates a windowed DTW-based target selector to maintain phase-consistent tracking despite temporal misalignments. The key contributions are (i) a robust nominal stabilization layer, (ii) a principled L1 adaptive augmentation to handle matched and unmatched disturbances at the task level, and (iii) a forward-looking DTW-based target selection mechanism that improves phase alignment. Empirical validation on LASA and IROS handwriting datasets demonstrates improved trajectory tracking under various disturbances, highlighting the practical potential of robust task-level control for learned dynamical systems.

Abstract

Dynamical system (DS)-based learning from demonstration (LfD) is a powerful tool for generating motion plans in the operation (`task') space of robotic systems. However, the realization of the generated motion plans is often compromised by a ''task-execution mismatch'', where unmodeled dynamics, persistent disturbances, and system latency cause the robot's actual task-space state to diverge from the desired motion trajectory. We propose a novel task-level robust control architecture, L1-augmented Dynamical Systems (L1-DS), that explicitly handles the task-execution mismatch in tracking a nominal motion plan generated by any DS-based LfD scheme. Our framework augments any DS-based LfD model with a nominal stabilizing controller and an L1 adaptive controller. Furthermore, we introduce a windowed Dynamic Time Warping (DTW)-based target selector, which enables the nominal stabilizing controller to handle temporal misalignment for improved phase-consistent tracking. We demonstrate the efficacy of our architecture on the LASA and IROS handwriting datasets.

A Robust Task-Level Control Architecture for Learned Dynamical Systems

TL;DR

This work tackles task-execution mismatch in dynamical-systems–based learning from demonstration by introducing L1-DS, a task-level control architecture that augments nominal learned dynamics with a Control Lyapunov Function (CLF)–based stabilizer and an adaptive controller. The approach also incorporates a windowed DTW-based target selector to maintain phase-consistent tracking despite temporal misalignments. The key contributions are (i) a robust nominal stabilization layer, (ii) a principled L1 adaptive augmentation to handle matched and unmatched disturbances at the task level, and (iii) a forward-looking DTW-based target selection mechanism that improves phase alignment. Empirical validation on LASA and IROS handwriting datasets demonstrates improved trajectory tracking under various disturbances, highlighting the practical potential of robust task-level control for learned dynamical systems.

Abstract

Dynamical system (DS)-based learning from demonstration (LfD) is a powerful tool for generating motion plans in the operation (`task') space of robotic systems. However, the realization of the generated motion plans is often compromised by a ''task-execution mismatch'', where unmodeled dynamics, persistent disturbances, and system latency cause the robot's actual task-space state to diverge from the desired motion trajectory. We propose a novel task-level robust control architecture, L1-augmented Dynamical Systems (L1-DS), that explicitly handles the task-execution mismatch in tracking a nominal motion plan generated by any DS-based LfD scheme. Our framework augments any DS-based LfD model with a nominal stabilizing controller and an L1 adaptive controller. Furthermore, we introduce a windowed Dynamic Time Warping (DTW)-based target selector, which enables the nominal stabilizing controller to handle temporal misalignment for improved phase-consistent tracking. We demonstrate the efficacy of our architecture on the LASA and IROS handwriting datasets.

Paper Structure

This paper contains 31 sections, 1 theorem, 15 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Learning Dynamical Systems from Demonstrations
  4. L1 Adaptive Control
  5. a. State Predictor:
  6. b. Piecewise-Constant Adaptive Law:
  7. c. Low-Pass Filtered Control Law:
  8. Control Lyapunov Function (CLF) Quadratic Programs
  9. Dynamic Time Warping (DTW)
  10. Proposed Control Architecture: L1-DS
  11. Nominal Learned Dynamics
  12. Nominal Stabilizing Control
  13. Target Point Selection via Windowed DTW
  14. L1 Adaptive Control Augmentation
  15. Task-execution mismatch
  16. ...and 16 more sections

Key Result

theorem 1

Consider the dynamical systems in (eq:nom-target-traj) and (eq:closed_loop_l1). Let Assumptions ass:domain--ass:unc and inequalities eq:design hold. Then $z(t)$ is bounded around $z^{*}(t)$, $z(t) \in \mathcal{O}(z^*(t), \rho), \ \text{for all}\ t \ge t_0$. Furthermore, the closed-loop state $z(t)$ where the ultimate bound is defined as

Figures (4)

  • Figure 1: Proposed control architecture. $p_{\text{ref}}$ is the reference low-level state (e.g., desired joint positions), $\tau$ represents the control inputs (e.g., joint torques) applied to the robot dynamics, and $p$ is the actual measured low-level state (e.g., actual joint positions).
  • Figure 2: Windowed DTW-Based Target Selector
  • Figure 3: (a) LASA Angle, perfect command following regime with step disturbance; (b) LASA GShape, imperfect command following regime with unmatched multi-sine disturbance; (c) LASA DoubleBendedLine, imperfect command following regime with matched multi-sine disturbance; (d) IROS RShape, imperfect command following regime with unmatched constant disturbance; (e) IROS IShape, imperfect command following regime with matched multi-sine and unmatched periodic step disturbance.
  • Figure 4: Disturbances used for the LASA dataset experiments. Appropriate magnitude-scaled versions of these were used for the IROS experiments.

Theorems & Definitions (1)

  • theorem 1