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Finite-Time Teleoperation of Euler-Lagrange Systems via Energy-Shaping

Lazaro F. Torres, Carlos I. Aldana, Emmanuel Nuño, Emmanuel Cruz-Zavala

TL;DR

This work tackles finite-time convergence in bilateral teleoperation of Euler-Lagrange robots under passive human/environment interactions. It adopts an energy-shaping framework with damping injection to cancel undesired potential and create a homogeneous negative-degree approximation, enabling global finite-time stability when external forces vanish. The authors propose a family of continuous P+d controllers, including state-feedback, output-feedback, and bounded versions, validated by simulations and experiments on 6-DoF platforms; the approach avoids chattering and does not require velocity measurements in some designs. The results offer practical, robust finite-time synchronization for teleoperation, with future directions toward delays and uncertainty handling.

Abstract

This paper proposes a family of finite-time controllers for the bilateral teleoperation of fully actuated nonlinear Euler-Lagrange systems. Based on the energy-shaping framework and under the standard assumption of passive interactions with the human and the environment, the controllers ensure that the position error and velocities globally converge to zero in the absence of time delays. In this case, the closed-loop system admits a homogeneous approximation of negative degree, and thus the control objective is achieved in finite-time. The proposed controllers are simple, continuous-time proportional-plus-damping-injection schemes, validated through both simulation and experimental results.

Finite-Time Teleoperation of Euler-Lagrange Systems via Energy-Shaping

TL;DR

This work tackles finite-time convergence in bilateral teleoperation of Euler-Lagrange robots under passive human/environment interactions. It adopts an energy-shaping framework with damping injection to cancel undesired potential and create a homogeneous negative-degree approximation, enabling global finite-time stability when external forces vanish. The authors propose a family of continuous P+d controllers, including state-feedback, output-feedback, and bounded versions, validated by simulations and experiments on 6-DoF platforms; the approach avoids chattering and does not require velocity measurements in some designs. The results offer practical, robust finite-time synchronization for teleoperation, with future directions toward delays and uncertainty handling.

Abstract

This paper proposes a family of finite-time controllers for the bilateral teleoperation of fully actuated nonlinear Euler-Lagrange systems. Based on the energy-shaping framework and under the standard assumption of passive interactions with the human and the environment, the controllers ensure that the position error and velocities globally converge to zero in the absence of time delays. In this case, the closed-loop system admits a homogeneous approximation of negative degree, and thus the control objective is achieved in finite-time. The proposed controllers are simple, continuous-time proportional-plus-damping-injection schemes, validated through both simulation and experimental results.
Paper Structure (13 sections, 4 theorems, 44 equations, 3 figures)

This paper contains 13 sections, 4 theorems, 44 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Finite-Time Stability and Homogeneous Systems
  4. System Dynamics and Controller Design
  5. Achieving Global Finite-Time Convergence
  6. State-Feedback Control
  7. Output-Feedback Control
  8. Bounded Controllers
  9. Additional Remarks
  10. Simulations and Experiments
  11. Simulation Results
  12. Experimental Results
  13. Conclusion

Key Result

Proposition 1

Consider a bilateral teleoperation system (eq:manipulator_model) satisfying A1 and A2. Set the energy-shaping controller (eq:energy_shaping_controller) with ${^d\mathcal{U}}({\bf q},{\boldsymbol \theta})$ and ${^s\mathcal{F}_i}({\bf \dot q}_i)$ as in dPot1 and dis1, respectively. Finally, set the Then $\triangleleft$

Figures (3)

  • Figure 1: Position error and torques of controllers C1 and TSMC.
  • Figure 2: Position error comparison between controller C1-- C4 in their finite-time and asymptotic version.
  • Figure 3: Position tracking of controller C4 under external forces.

Theorems & Definitions (4)

  • Proposition 1
  • Proposition 2
  • Proposition 3
  • Proposition 4