Manageable Convex Region Iteration Without Half-Plane Optimization for Robot Navigation in 2D Cluttered Scenes

To address path safety and algorithm efficiency challenges in robot navigation within complex environments, this paper proposes an integrated path optimization-following framework with a novel Manageable Convex Region Iteration without Half-Plane Optimization (MCRIwHPO). The path planning problem is modeled as nonlinear optimization to generate a time-independent parameterized path. MCRIwHPO adopts a two-stage design: the first stage generates half-plane constraints via ellipse expansion without additional optimization, and the second stage addresses the seed point inclusion constraint in calculating the maximum-area inscribed ellipse, thus ensuring convex region manageability. This design iteratively increases the ellipse area (the lower bound of convex region area) to enhance the convex region's approximation of free space. For path following, obstacle expansion reserves a safety threshold, and a preset performance controller confines following errors within this threshold to avoid collision caused by external disturbances. MCRIwHPO is compared with existing algorithms in simulations with 5-20 obstacles, where it achieves the optimal convex region area with a stable computation time within 50 ms, satisfying real-time requirements. The integrated framework is further implemented on a four-wheel independent drive vehicle for real-world tests, and experimental results show the vehicle smoothly avoids obstacles with prescribed path following errors and maintains stable velocity during navigation, verifying the framework's effectiveness and practical applicability.