Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Limiting Kinetic Energy through Control Barrier Functions: Analysis and Experimental Validation

Federico Califano, Daniel Logmans, Wesley Roozing

Abstract

In the context of safety-critical control, we propose and analyse the use of Control Barrier Functions (CBFs) to limit the kinetic energy of torque-controlled robots. The proposed scheme is able to modify a nominal control action in a minimally invasive manner to achieve the desired kinetic energy limit. We show how this safety condition is achieved by appropriately injecting damping in the underlying robot dynamics independently of the nominal controller structure. We present an extensive experimental validation of the approach on a 7-Degree of Freedom (DoF) Franka Emika Panda robot. The results demonstrate that this approach provides an effective, minimally invasive safety layer that is straightforward to implement and is robust in real experiments.

Limiting Kinetic Energy through Control Barrier Functions: Analysis and Experimental Validation

Abstract

In the context of safety-critical control, we propose and analyse the use of Control Barrier Functions (CBFs) to limit the kinetic energy of torque-controlled robots. The proposed scheme is able to modify a nominal control action in a minimally invasive manner to achieve the desired kinetic energy limit. We show how this safety condition is achieved by appropriately injecting damping in the underlying robot dynamics independently of the nominal controller structure. We present an extensive experimental validation of the approach on a 7-Degree of Freedom (DoF) Franka Emika Panda robot. The results demonstrate that this approach provides an effective, minimally invasive safety layer that is straightforward to implement and is robust in real experiments.

Paper Structure

This paper contains 15 sections, 3 theorems, 27 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Methods
  3. Background
  4. Control Barrier Functions
  5. Robots and their energetic analysis
  6. Bounding kinetic energy with CBFs
  7. External interaction forces
  8. Experimental results
  9. Experimental Setup
  10. Experiment 1: Step response
  11. Experiment 2: Contact loss
  12. Experiment 3: External interaction
  13. Experiment 4: Kinetic energy error validation
  14. Discussion
  15. Conclusions and future work

Key Result

Theorem 1

Let $h(\boldsymbol{x})$ be a CBF on $\mathcal{D}$ for eq:affinecontrolsystem. Any locally Lipschitz controller $\boldsymbol{u}=\boldsymbol{k}(\boldsymbol{x})$ such that $\dot{h}(\boldsymbol{x},\boldsymbol{u}) \geq -\alpha (h(\boldsymbol{x}))$ provides forward invariance of the safe set $\mathcal{S}$

Figures (13)

  • Figure 1: CBF-based safety filter.
  • Figure 2: Control architecture of the experimental setup.
  • Figure 3: Experiment 1 (Step response): End-effector y-position.
  • Figure 4: Experiment 1 (Step response): Total kinetic energy.
  • Figure 5: Experiment 1 (Step response): Safety filter power injection.
  • ...and 8 more figures

Theorems & Definitions (8)

  • Theorem 1: Ames2017
  • Theorem 2
  • proof
  • Remark 1: Relation to energy-based CBFs in Singletary2021
  • Remark 2: Passivity/Stability preservation property of (\ref{['eq:ECBF']})
  • Theorem 3
  • proof
  • Remark 3