🤖 AI Summary
Real-time trajectory generation for obstacle avoidance in dynamic environments suffers from reliance on explicit obstacle boundary representations, low computational efficiency, and suboptimal trajectories. Method: This paper proposes a real-time planning and control framework integrating Model Predictive Control (MPC) with discrete-time high-order Control Barrier Functions (DHOCBFs). It automatically generates convex polyhedral obstacle representations from grid maps—bypassing the need for prior geometric knowledge (e.g., explicit boundary equations)—and directly derives DHOCBFs to ensure safety for both convex and non-convex obstacles. Global optimality is further enforced via optimization-driven path planning. Contribution/Results: Experiments in tightly constrained dynamic scenarios demonstrate significant improvements in computational speed and trajectory feasibility compared to baseline CBF methods, while yielding shorter, safer, and dynamically feasible trajectories.
📝 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.