Safe Robotics Control with Directional Projection Control Barrier Functions Via Differentiable Optimization
Yan Wei, Jiajie Yao, Xinyi Yu, Linlin Ou
AI summary
Problem
Existing control barrier functions rely on conservative Euclidean distance metrics or suffer from the computational complexity and feasibility issues of higher-order formulations, limiting their real-time application for complex robotic geometries.
Approach
The method projects 3D polyhedral robots and obstacles onto a 2D plane along their relative velocity vector, then uses a tunable strictly convex padding function and differentiable optimization to compute collision risk via a minimum scaling factor.
Key results
- A tunable uniform scaling function that strictly pads convex polygons for differentiable optimization
- A first-order directional projection CBF that eliminates higher-order complexity
- Rigorous proof of strict convexity and continuous differentiability for the scaling function
- Successful simulation validation on a 2D mobile robot and a 7-DOF Franka manipulator
Why it matters
Provides a computationally efficient and geometrically accurate safety control framework for complex robots operating in dynamic, obstacle-rich environments.
Abstract
Collision avoidance is essential for robotic systems. This paper presents a method for designing directional projec- tion control barrier functions (CBFs) based on differentiable optimization for second-order robotic systems. The approach reduces high-order CBFs to first-order ones and estimates collision risk by examining the intersection of projections along the relative velocity direction. Under the assumption that both the target and obstacles are convex polyhedra whose projections yield convex polygons, a tunable uniform scaling function, centered at the centroid, is introduced to pad the convex polygon. The strict convexity of this padded region is rigorously proven. Using the minimum scaling factor that leads to intersection between two projected convex polygons, a CBF is constructed and incorporated into a tracking controller to ensure collision avoidance. The effectiveness of the proposed method is validated through simulations with a 2D mobile robot and a 7-DOF Franka manipulator.