When a mobile robot plans its path in an environment with obstacles using Artificial Potential Field (APF) strategy, it may fall into the local minimum point and fail to reach the goal. Also, the derivatives of APF will explode close to obstacles causing poor planning performance. To solve the problems, exponential functions are used to modify potential fields' formulas. The potential functions can be subharmonic when the distance between the robot and obstacles is above a predefined threshold. Subharmonic functions do not have local minimum and the derivatives of exponential functions increase mildly when the robot is close to obstacles, thus eliminate the problems in theory. Circular sampling technique is used to keep the robot outside a danger distance to obstacles and support the construction of subharmonic functions. Through simulations, it is proven that mobile robots can bypass local minimum points and construct a smooth path to reach the goal successfully by the proposed methods.

翻译：在利用人工势场策略规划移动机器人在含障碍物环境中的路径时，机器人可能陷入局部极小点而无法抵达目标。此外，人工势场的导数会在障碍物附近发生发散，导致规划性能不佳。为解决上述问题，采用指数函数对势场公式进行修正。当机器人与障碍物距离超过预设阈值时，势函数可呈现次谐波特性。次谐波函数不存在局部极小值，且指数函数在机器人靠近障碍物时导数增幅平缓，从而从理论上消除了此类问题。采用圆形采样技术使机器人保持与障碍物危险距离之外，并支撑次谐波函数的构建。仿真结果表明，所提方法能使移动机器人有效规避局部极小点，构建平滑路径并成功抵达目标。