Safety-Critical Planning and Control for Dynamic Obstacle Avoidance Using Control Barrier Functions

TL;DR

This work tackles dynamic obstacle avoidance by integrating an iterative MPC framework with discrete-time high-order control barrier functions (DHOCBFs) derived from convex polytopes in occupancy-grid maps, eliminating the need for explicit obstacle boundary equations. By coupling Jump Point Search (JPS) based dynamic path planning with Safe Convex Polytopes and linearized DHOCBF constraints, the method reformulates safety enforcement into a convex finite-horizon optimization solved iteratively. Across convex and nonconvex dynamic obstacle scenarios, the approach achieves high feasibility and shorter trajectories, with fast per-step computation (sub-50 to ~55 ms) compared to several benchmarks. The framework demonstrates robust real-time performance in densely occupied, mutating environments and offers a scalable path to safety-critical planning in dynamic settings.

Abstract

Dynamic obstacle avoidance is a challenging topic for optimal control and optimization-based trajectory planning problems. Many existing works use Control Barrier Functions (CBFs) to enforce safety constraints for control systems. CBFs are typically formulated based on the distance to obstacles, or integrated with path planning algorithms as a safety enhancement tool. However, these approaches usually require knowledge of the obstacle boundary equations or have very slow computational efficiency. In this paper, we propose a framework based on model predictive control (MPC) with discrete-time high-order CBFs (DHOCBFs) to generate a collision-free trajectory. The DHOCBFs are first obtained from convex polytopes generated through grid mapping, without the need to know the boundary equations of obstacles. Additionally, a path planning algorithm is incorporated into this framework to ensure the global optimality of the generated trajectory. We demonstrate through numerical examples that our framework allows a unicycle robot to safely and efficiently navigate tight, dynamically changing environments with both convex and nonconvex obstacles. By comparing our method to established CBF-based benchmarks, we demonstrate superior computing efficiency, length optimality, and feasibility in trajectory generation and obstacle avoidance.

Figures (6)

• Figure 1: Schematic of the iterative process of solving the convex MPC at time $t$.
• Figure 2: Schematic illustrating how to find the SCP (red). The obstacle detection range is denoted by a blue dashed square centered at $\bar{\mathbf{x}}_{t, k}^{j}$. The obstacles are depicted by green circles, with their boundaries captured by partially occupied cells, and the centers of the cells are marked by black points.
• Figure 3: Finding the open-loop trajectory (black points) based on SCP in grid maps starting at $t$. Polytopes of each color are generated based on the points of the corresponding color, and points in the next iteration $(\bar{\mathbf{x}}_{t,k}^{j+1})$ are confined and generated within the polytopes $h_{\text{scp}}(\mathbf{x}_{t, k}^{j},\bar{\mathbf{x}}_{t, k}^{j})$ created at the current iteration. The point $(\mathbf{x}_{t,1}^{*})$ is selected as the starting point for solving the CFTOC starting at $t+1$.
• Figure 4: Snapshots of the desired path (blue) and SCP (red polygons) at one-second intervals for avoiding 5 convex dynamic obstacles (colorful squares) with a controlled robot (small red circle), with horizon $N=30$. The robot safely reaches the goal location.
• Figure 5: Snapshots of desired path (blue) and SCP (red polygons) at one-second intervals for avoiding 5 nonconvex-shaped dynamic obstacles (colorful fans) with a controlled robot (small red circle), horizon $N=30$. The robot can safely reach the goal location.

Theorems & Definitions (6)

• Definition 1: Free Cell
• Definition 2: Occupied Cell
• Definition 3: Relative degree sun2003initial
• Definition 4: DHOCBF xiong2022discrete
• Theorem 1: Safety Guarantee xiong2022discrete
• Remark 1