# Safety-Critical Control and Planning for Obstacle Avoidance between Polytopes with Control Barrier Functions

arXiv: https://arxiv.org/abs/2109.12313 · HTML: https://mlsanity.com/paper/2109.12313/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2021.

## Built on by (most cited first, 7 of 7)

- [Neural Potential Field for Obstacle-Aware Local Motion Planning](https://mlsanity.com/paper/2310.16362/) (2023)
- [Dynamic High-Order Control Barrier Functions with Diffuser for Safety-Critical Trajectory Planning at Signal-Free Intersections](https://mlsanity.com/paper/2412.00162/) (2024)
- [Learning Maximal Safe Sets Using Hypernetworks for MPC-based Local Trajectory Planning in Unknown Environments](https://mlsanity.com/paper/2410.20267/) (2024)
- [Gaussian Control Barrier Functions : A Non-Parametric Paradigm to Safety](https://mlsanity.com/paper/2203.15474/) (2022)
- [Barrier Certified Safety Learning Control: When Sum-of-Square Programming Meets Reinforcement Learning](https://mlsanity.com/paper/2206.07915/) (2022)
- [Soft Actor-Critic-based Control Barrier Adaptation for Robust Autonomous Navigation in Unknown Environments](https://mlsanity.com/paper/2503.08479/) (2025)
- [Dynamic Neural Potential Field: Online Trajectory Optimization in the Presence of Moving Obstacles](https://mlsanity.com/paper/2410.06819/) (2024)

## Abstract (arXiv)

Obstacle avoidance between polytopes is a challenging topic for optimal control and optimization-based trajectory planning problems. Existing work either solves this problem through mixed-integer optimization, relying on simplification of system dynamics, or through model predictive control with dual variables using distance constraints, requiring long horizons for obstacle avoidance. In either case, the solution can only be applied as an offline planning algorithm. In this paper, we exploit the property that a smaller horizon is sufficient for obstacle avoidance by using discrete-time control barrier function (DCBF) constraints and we propose a novel optimization formulation with dual variables based on DCBFs to generate a collision-free dynamically-feasible trajectory. The proposed optimization formulation has lower computational complexity compared to existing work and can be used as a fast online algorithm for control and planning for general nonlinear dynamical systems. We validate our algorithm on different robot shapes using numerical simulations with a kinematic bicycle model, resulting in successful navigation through maze environments with polytopic obstacles.