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Safe Control of Euler-Lagrange Systems with Limited Model Information

Yujie Wang, Xiangru Xu

TL;DR

This work tackles safe control of Euler-Lagrange systems when detailed model information is unavailable and disturbances/measurement uncertainties are present. It introduces a proxy-CBF-BLF architecture that splits the EL dynamics into a proxy subsystem (double integrator with bounded disturbance) and a virtual tracking subsystem (the EL model), using a CBF-based controller for the proxy part and an adaptive BLF-based controller to bound the safe velocity tracking error. Importantly, the approach requires only an upper bound on the inertia norm, avoiding exact knowledge of Coriolis, centrifugal, and gravity terms which are learned online. The authors provide safety guarantees and demonstrate effectiveness through simulations under disturbances and measurement noise.

Abstract

This paper presents a new safe control framework for Euler-Lagrange (EL) systems with limited model information, external disturbances, and measurement uncertainties. The EL system is decomposed into two subsystems called the proxy subsystem and the virtual tracking subsystem. An adaptive safe controller based on barrier Lyapunov functions is designed for the virtual tracking subsystem to ensure the boundedness of the safe velocity tracking error, and a safe controller based on control barrier functions is designed for the proxy subsystem to ensure controlled invariance of the safe set defined either in the joint space or task space. Theorems that guarantee the safety of the proposed controllers are provided. In contrast to existing safe control strategies for EL systems, the proposed method requires much less model information and can ensure safety rather than input-to-state safety. Simulation results are provided to illustrate the effectiveness of the proposed method.

Safe Control of Euler-Lagrange Systems with Limited Model Information

TL;DR

This work tackles safe control of Euler-Lagrange systems when detailed model information is unavailable and disturbances/measurement uncertainties are present. It introduces a proxy-CBF-BLF architecture that splits the EL dynamics into a proxy subsystem (double integrator with bounded disturbance) and a virtual tracking subsystem (the EL model), using a CBF-based controller for the proxy part and an adaptive BLF-based controller to bound the safe velocity tracking error. Importantly, the approach requires only an upper bound on the inertia norm, avoiding exact knowledge of Coriolis, centrifugal, and gravity terms which are learned online. The authors provide safety guarantees and demonstrate effectiveness through simulations under disturbances and measurement noise.

Abstract

This paper presents a new safe control framework for Euler-Lagrange (EL) systems with limited model information, external disturbances, and measurement uncertainties. The EL system is decomposed into two subsystems called the proxy subsystem and the virtual tracking subsystem. An adaptive safe controller based on barrier Lyapunov functions is designed for the virtual tracking subsystem to ensure the boundedness of the safe velocity tracking error, and a safe controller based on control barrier functions is designed for the proxy subsystem to ensure controlled invariance of the safe set defined either in the joint space or task space. Theorems that guarantee the safety of the proposed controllers are provided. In contrast to existing safe control strategies for EL systems, the proposed method requires much less model information and can ensure safety rather than input-to-state safety. Simulation results are provided to illustrate the effectiveness of the proposed method.
Paper Structure (6 sections, 1 figure)

This paper contains 6 sections, 1 figure.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Statement
  3. Control Barrier Functions & Barrier Lyapunov Functions
  4. Control Barrier Functions
  5. Barrier Lyapunov Function
  6. Euler-Lagrange Systems

Figures (1)

  • Figure 1: Illustration of the proposed proxy-CBF-BLF control design scheme for safe control design of EL systems in the joint space. The original EL system is decomposed into the proxy subsystem and the virtual tracking subsystem. The safe velocity for the virtual tracking subsystem is generated by the proxy subsystem. A CBF-QP-based controller is designed for the proxy subsystem to ensure safety, while an adaptive BLF-based control law is proposed for the virtual tracking subsystem to constrain the safe velocity tracking error.