Optimization-Free Smooth Control Barrier Function for Polygonal Collision Avoidance.

Area of Science:

• Robotics and Control Systems
• Computational Geometry
• Optimization Theory

Background:

• Polygonal collision avoidance (PCA) is critical for dynamic systems but challenged by nonsmooth boundaries.
• Existing control barrier function (CBF) methods often rely on optimization and signed distance fields (SDFs), facing computational and boundary issues.

Purpose of the Study:

• To develop an optimization-free, smooth CBF method for efficient and nonconservative polygonal collision avoidance.
• To demonstrate the method's applicability to underactuated nonholonomic vehicles and container crane systems.

Main Methods:

• Representing a lower bound of SDF using nested Boolean logic.
• Applying the log-sum-exp method for smooth approximation of the SDF.
• Developing a CBF-based safety filter for collision avoidance.

Main Results:

• The proposed method achieves computationally efficient and nonconservative collision avoidance.
• Successful extension and simulation of the method for distributed collision avoidance in underactuated nonholonomic vehicles.
• Demonstrated effectiveness in preventing collisions for an underactuated container crane system.

Conclusions:

• The optimization-free smooth CBF method offers a computationally efficient and robust solution for polygonal collision avoidance.
• This approach significantly advances safety and applicability in complex robotic systems, including underactuated vehicles and cranes.