In path planning, potential fields introduce force constraints to ensure curvature continuity of trajectories and thus to facilitate path-tracking design. In previous work, a path planning design by fractional (or generalized) repulsive potential has been developed to avoid fixed obstacles. A fractional road was determined by taking into account danger of each obstacle. Danger level of each obstacle is characterized by the fractional order of differentiation. Then a new attractive force based on fractional potential was introduced, with the aim to extend the method to dynamic obstacles characterized by fractional potential fields. In this paper a comparison between each classical attractive force is presented. Then the new attractive force based on fractional potential is introduced. Finally, this attractive force is applied on an example and compare with the Ge and Cui method which is the classical potential fields for motion planning of mobile robots in a dynamic environment.

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