Whole-body Dynamic Collision Avoidance with Time-varying Control Barrier Functions

Abstract: Recently, there has been increasing attention in robot research towards the whole-body collision avoidance. In this paper, we propose a safety-critical controller that utilizes time-varying control barrier functions (time varying CBFs) constructed by Robo-centric Euclidean Signed Distance Field (RC-ESDF) to achieve dynamic collision avoidance. The RC-ESDF is constructed in the robot body frame and solely relies on the robot's shape, eliminating the need for real-time updates to save computational resources. Additionally, we design two control Lyapunov functions (CLFs) to ensure that the robot can reach its destination. To enable real-time application, our safety-critical controller which incorporates CLFs and CBFs as constraints is formulated as a quadratic program (QP) optimization problem. We conducted numerical simulations on two different dynamics of an L-shaped robot to verify the effectiveness of our proposed approach.

• The paper introduces a novel quadratic programming framework that integrates time-varying control barrier functions with a robo-centric ESDF to enhance collision avoidance in dynamic environments.
• It addresses computational inefficiency by constructing the ESDF in the robot’s body frame, significantly reducing the need for real-time updates.
• Simulation results confirm real-time applicability with average computation times under 0.02 seconds, demonstrating robust performance in both single integral and unicycle robot models.

Whole-body Dynamic Collision Avoidance with Time-varying Control Barrier Functions: An Expert Overview

The paper "Whole-body Dynamic Collision Avoidance with Time-varying Control Barrier Functions," authored by Jihao Huang, Xuemin Chi, Zhitao Liu, and Hongye Su, introduces an innovative approach to dynamic collision avoidance in robotic systems. The proposed framework leverages time-varying Control Barrier Functions (CBFs), embedded within a quadratic programming (QP) optimization problem, to ensure both safety and operational efficacy in complex, dynamic environments.

Methodology

The central theme of this paper revolves around addressing the computational inefficiency and inherent limitations of existing collision avoidance strategies. The authors propose two primary contributions:

1. Robo-centric Euclidean Signed Distance Field (RC-ESDF): This method constructs the ESDF in the robot's body frame, significantly reducing computational overheads by eliminating real-time updates.
2. Time-varying CBFs: These are integrated into a safety-critical controller to handle dynamic obstacles by accounting for time-varying scenarios, thereby ensuring continuous safety during navigation and control.

Technical Implementation

Control Lyapunov Functions (CLFs)

To navigate the robot to its destination, two CLFs are designed:

• Distance-based CLF (V_d): This function reduces the Euclidean distance between the robot's current position and its goal.
• Orientation-based CLF (V_theta): Specifically for robots with unicycle dynamics, this function aids in adjusting the robot's angular velocity to align with its goal.

These CLFs ensure stability of the robot's trajectory, forming affine constraints in the optimization problem.

Control Barrier Functions (CBFs)

Dynamic and static obstacles are handled by formulating CBFs based on the RC-ESDF values. The CBFs are used to ensure that collision points lie outside the robot's boundaries. The time-varying aspect of CBFs is introduced to accommodate moving obstacles, making the approach robust against real-time environmental changes. The affine constraints formed by these CBFs are combined with those from CLFs in the QP simulation to enforce safety without unnecessary conservatism.

Quadratic Program Formulation

The optimization problem integrates both CLF and CBF constraints:

• Objective: Minimize control input and slack variables to strike a balance between performance and flexibility.
• Constraints: Enforce both stability (CLF-related) and safety (CBF-related) constraints, ensuring real-time control effectiveness.

The problem is efficiently solved using QPOASES, enabling real-time applicability.

Results

The numerical simulations validate the proposed methodology across different dynamic scenarios using two robot models:

• Single Integral Model: The robot navigates a mixed environment with static and dynamic obstacles.
• Unicycle Model: Enhanced navigation and collision avoidance, considering orientation constraints.

Both scenarios demonstrate the system’s ability to navigate towards its destination while avoiding collisions. The computational efficiency, validated by an average computation time well within real-time requirements (0.0116 seconds for the single integral model and 0.018 seconds for the unicycle model), further solidifies the method's practical application.

Implications and Future Work

The research provides significant steps forward in dynamic collision avoidance. The practical implications include:

• Robotic Navigation: Enhanced safety and efficiency in real-time navigation for varying robotic applications.
• Computational Optimization: Reduced computational load by using RC-ESDF without real-time updates.

However, challenges remain. The method's efficacy is dependent on the density of collision point sampling. Sparse sampling can lead to occasional detection failures. Future research should focus on optimizing the collision point heuristic and extending the approach to multi-robot systems, further enhancing the method's robustness and scalability.

In summary, the proposed safety-critical controller incorporating time-varying CBFs and RC-ESDF in a QP optimization framework offers a compelling solution for whole-body dynamic collision avoidance in robotics. The demonstrated balance between safety and computational efficiency paves the way for its use in increasingly complex and dynamic environments.