A potential field model using generalized sigmoid functions

The lack of a potential field model capable of providing accurate representations of objects of arbitrary shapes is considered one major limitation in applying the artificial potential field method in many practical applications. In this correspondence, we propose a potential function based on generalized sigmoid functions. The generalized sigmoid model can be constructed from combinations of implicit primitives or from sampled surface data. The constructed potential field model can achieve an accurate analytic description of objects in two or three dimensions and requires very modest computation at run time. In this correspondence, applications of the generalized sigmoid model in path-planning tasks for mobile robots and in haptic feedback tasks are presented. The validation results in this correspondence show that the model can effectively allow the user or mobile robot to avoid penetrations of obstacles while successfully accomplishing the task.