  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.
