Smooth Path Planning with Subharmonic Artificial Potential Field

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.