Dynamic obstacle avoidance is a challenging topic for optimal control and optimization-based trajectory planning problems, especially when in a tight environment. Many existing works use control barrier functions (CBFs) to enforce safety constraints within control systems. Inside these works, CBFs are usually formulated under model predictive control (MPC) framework to anticipate future states and make informed decisions, 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 novel framework to the iterative MPC with discrete-time CBFs (DCBFs) to generate a collision-free trajectory. The DCBFs are obtained from convex polyhedra generated in sequential grid maps, 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 enables a unicycle robot to safely and efficiently navigate through tight and dynamically changing environments, tackling both convex and nonconvex obstacles with remarkable computing efficiency and reliability in control and trajectory generation.

翻译：动态障碍规避是运动规划与最优控制领域中的一项挑战性课题，尤其在狭窄环境中更为突出。现有研究多采用控制障碍函数在控制系统中施加安全约束，此类方法常将控制障碍函数融入模型预测控制框架以预测未来状态并做出智能决策，或与路径规划算法结合作为安全增强工具。然而，这些方法通常需要已知障碍物边界方程或存在计算效率低下的问题。本文提出一种融合离散时间控制障碍函数与迭代模型预测控制框架的新颖方法，用于生成无碰撞轨迹。该离散时间控制障碍函数通过序列栅格地图生成的凸多面体构建，无需已知障碍物边界方程。此外，该框架集成路径规划算法以确保生成轨迹的全局最优性。数值算例表明，所提框架可使独轮机器人安全高效地穿越动态变化的狭窄环境，在处理凸与非凸障碍物时展现出显著的计算效率与轨迹生成可靠性。