An optimization-based waypoint generation method for overcoming local minima in artificial potential field navigation

The Artificial Potential Field (APF) method is widely used in robot path planning due to its simplicity and computational efficiency. However, it is well known to suffer from the local minima problem, where the resultant force acting on the robot becomes zero at non-goal configurations, leading to motion stagnation in cluttered environments. This paper proposes an optimization-based waypoint generation framework to address the local minima issue in APF navigation while ensuring explicit collision avoidance. When the direct path between the robot and the target is infeasible due to obstacle interference, intermediate waypoints are generated by solving a constrained optimization problem that guides the robot along a locally defined reference direction while enforcing obstacle clearance constraints for each path segment. Unlike conventional APF modifications that rely on artificial perturbation forces or random escape strategies, the proposed method constructs collision-free intermediate waypoints through finite candidate evaluation and explicit segment-wise collision checking, enabling the robot to avoid obstacles and overcome local-minima while preserving goal-directed motion and ensuring convergence to the target. The effectiveness of the proposed approach is validated through numerical simulations on two robotic platforms, namely a point-mass robot and a wheelchair-type robotic model. The results demonstrate that the method successfully resolves local minima situations, ensures collision-free motion, and consistently guides the robots to their target locations in complex environments. Furthermore, the framework is general and can be applied to different robotic systems.