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Safety-Critical Control for Robotic Manipulators using Collision Cone Control Barrier Functions

Lucas Almeida

TL;DR

This work addresses safety-critical control for robotic manipulators operating amidst dynamic obstacles by extending Collision Cone Control Barrier Functions (C3BFs) to manipulators and integrating them with Cartesian impedance control. A real-time QP safety filter minimally perturbs the nominal impedance command to enforce the safety condition $\dot{h}(x) + \alpha(h(x)) \ge 0$, with $\dot{h}$ expressed as $L_f h + L_g h u$. The main contributions include the formulation of a C3BF for manipulators, the derivation and validity of the associated safety constraint, and demonstration via PyBullet simulations under diverse obstacle dynamics, showing robust collision avoidance with limited performance impact. This approach offers a principled, real-time mechanism to ensure safety in manipulation tasks, paving the way for hardware experiments and adaptation to more complex multi-obstacle environments and perceptual inputs.

Abstract

This paper presents a comprehensive approach for the safety-critical control of robotic manipulators operating in dynamic environments. Building upon the framework of Control Barrier Functions (CBFs), we extend the collision cone methodology to formulate Collision Cone Control Barrier Functions (C3BFs) specifically tailored for manipulators. In our approach, safety constraints derived from collision cone geometry are seamlessly integrated with Cartesian impedance control to ensure compliant yet safe end-effector behavior. A Quadratic Program (QP)-based controller is developed to minimally modify the nominal control input to enforce safety. Extensive simulation experiments demonstrate the efficacy of the proposed method in various dynamic scenarios.

Safety-Critical Control for Robotic Manipulators using Collision Cone Control Barrier Functions

TL;DR

This work addresses safety-critical control for robotic manipulators operating amidst dynamic obstacles by extending Collision Cone Control Barrier Functions (C3BFs) to manipulators and integrating them with Cartesian impedance control. A real-time QP safety filter minimally perturbs the nominal impedance command to enforce the safety condition , with expressed as . The main contributions include the formulation of a C3BF for manipulators, the derivation and validity of the associated safety constraint, and demonstration via PyBullet simulations under diverse obstacle dynamics, showing robust collision avoidance with limited performance impact. This approach offers a principled, real-time mechanism to ensure safety in manipulation tasks, paving the way for hardware experiments and adaptation to more complex multi-obstacle environments and perceptual inputs.

Abstract

This paper presents a comprehensive approach for the safety-critical control of robotic manipulators operating in dynamic environments. Building upon the framework of Control Barrier Functions (CBFs), we extend the collision cone methodology to formulate Collision Cone Control Barrier Functions (C3BFs) specifically tailored for manipulators. In our approach, safety constraints derived from collision cone geometry are seamlessly integrated with Cartesian impedance control to ensure compliant yet safe end-effector behavior. A Quadratic Program (QP)-based controller is developed to minimally modify the nominal control input to enforce safety. Extensive simulation experiments demonstrate the efficacy of the proposed method in various dynamic scenarios.

Paper Structure

This paper contains 7 sections, 1 theorem, 20 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Problem Formulation
  4. Methodology
  5. Simulation Experiments
  6. Results and Discussion
  7. Conclusion and Future Work

Key Result

Theorem 1

Consider a manipulator end‐effector whose dynamics are given by where $p_m\in\mathbb{R}^3$ denotes the end‐effector position, $v_m\in\mathbb{R}^3$ its velocity, and $u\in\mathbb{R}^3$ is the control input. Let an obstacle be moving with constant velocity $v_o$ (i.e., $\dot{p}_o=v_o$ and $\dot{v}_o=0$) with known position $p_o$. Define the relative position and v Assume that the safety requirement

Figures (2)

  • Figure 1: PyBullet Simulation of manipulator and obstacle
  • Figure 2: PyBullet Simulation of a Manipulator avoiding the obstacle using distance based CBF

Theorems & Definitions (2)

  • Theorem 1: Validity of the Collision Cone CBF for a Manipulator End-Effector
  • proof