A-OctoMap: An Adaptive OctoMap for Online Motion Planning

Traditional robotic motion planning methods often struggle with fixed resolutions in dynamically changing environments. To address these challenges, we introduce the A-OctoMap, an adaptive Octo-Tree structure that enhances spatial representation and facilitates real-time, efficient motion planning. This novel framework allows for dynamic space partitioning and multi-resolution queries, significantly improving computational efficiency and precision. Key innovations include a tree-based data structure for enhanced geometric processing, real-time map updating for accurate trajectory planning, and efficient collision detection. Our extensive testing shows superior navigation safety and efficiency in complex settings compared to conventional methods. A-OctoMap sets a new standard for adaptive spatial mapping in autonomous systems, promising significant advancements in navigating unpredictable environments.

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

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.