Safety-Critical Stabilization of Force-Controlled Nonholonomic Mobile Robots: A Control Barrier Function Approach using Quadratic Programming

Core Concepts

This research proposes a novel control strategy for force-controlled nonholonomic mobile robots that guarantees both stability and safety by combining control Lyapunov functions (CLFs) and control barrier functions (CBFs) within a quadratic programming framework.

Abstract

• Bibliographic Information: Han, T., & Wang, B. (2024). Safety-Critical Stabilization of Force-Controlled Nonholonomic Mobile Robots. arXiv preprint arXiv:2408.10941v2.

• Research Objective: This research paper aims to address the challenge of designing a controller for force-controlled nonholonomic mobile robots that ensures both asymptotic stability and adherence to predefined safety constraints.

• Methodology: The authors develop a safety-critical controller by combining control Lyapunov functions (CLFs) and control barrier functions (CBFs) within a quadratic programming (QP) framework. They first design a nominal controller in polar coordinates to guarantee global asymptotic stability and local exponential stability for the closed-loop system. A strict Lyapunov function is constructed based on this nominal controller and serves as the CLF. A procedure for constructing reciprocal CBFs for cascaded systems is presented, utilizing the CBF of the kinematic model through integrator backstepping. Finally, a γm-QP problem is formulated to combine the CLF and CBF, ensuring both stability and safety.

• Key Findings: The proposed control law, derived by solving the γm-QP problem, guarantees both safety, by maintaining the robot's trajectory within a predefined safe set, and local asymptotic stability. The controller is time-invariant, continuous along trajectories, and easy to implement.

• Main Conclusions: The research demonstrates the effectiveness of combining CLFs and CBFs using QP for achieving safety-critical stabilization in force-controlled nonholonomic mobile robots. The proposed approach offers a systematic and robust solution for applications like autonomous parking with obstacle avoidance and inter-vehicle collision avoidance.

• Significance: This research contributes to the field of robotics by providing a practical and theoretically sound solution for ensuring safety in the control of nonholonomic mobile robots, which is crucial for their real-world deployment.

• Limitations and Future Research: The paper acknowledges that the γm-QP design might lead to undesirable equilibria due to its prioritization of safety over stabilization in certain situations. Future research directions include addressing input constraints, which are common in robotic systems, and extending the approach to safety formation control for multi-agent systems.

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Safety-Critical Stabilization of Force-Controlled Nonholonomic Mobile Robots

by Tianyu Han, ... at arxiv.org 11-05-2024

https://arxiv.org/pdf/2408.10941.pdf