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

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.

💡 Research Summary

The paper addresses the problem of achieving finite‑time (FT) convergence in bilateral teleoperation of fully actuated nonlinear Euler‑Lagrange (EL) robots. Traditional proportional‑plus‑damping (P + d) schemes guarantee only asymptotic stability, which means the synchronization error vanishes only as time approaches infinity. Recent FT controllers based on sliding‑mode or neural‑network techniques provide faster convergence but suffer from chattering, require differentiable control signals, or rely on variable‑gain strategies that only guarantee convergence to a neighborhood of the origin.

To overcome these limitations, the authors propose a family of continuous‑time, nonlinear P + d controllers derived from an energy‑shaping framework. Each robot is modeled by the standard EL dynamics

 M_i(q_i) ¨q_i + C_i(q_i, ˙q_i) ˙q_i + ∇_{q_i}U_i(q_i) = τ_i + f_i,

where f_i represents passive human or environment forces (Assumption A1). The key idea is to reshape the potential energy of the robots by introducing a virtual controller state θ_i and a desired potential function dU(q, θ). The total stored energy of the combined robot‑controller system is defined as

 H = dU(q, θ) + ∑_i K_i(q_i, ˙q_i) + E_i(t),

where K_i is kinetic energy and E_i(t) accounts for the passive work done by the human/environment. By differentiating H and selecting the control torque

 τ_i = −∇{q_i}cU(q, θ) − ∇{˙q_i}sF_i(˙q_i),

the energy balance reduces to a sum of strictly dissipative terms. When velocity measurements are unavailable, the second term disappears, yielding a purely potential‑shaping controller τ_i = −∇_{q_i}cU(q, θ).

The controller dynamics for the virtual states are given by

 ˙θ_i = −(1/D_{ci})