Robust Path Planning for Mobile Robot Based on Fractional Attractive Force in 3-Dimension Space

In path planning, potential fields introduce force constraints to ensure curvature continuity of trajectories and thus to facilitate path-tracking design. In previous works, a path planning design by fractional (or non integer or generalized) repulsive potential has been developed to avoid fixed obstacles: danger level of each obstacle was characterized by the fractional order of differentiation, and a fractional road was determined by taking into account danger of each obstacle. If the obstacles are dynamic, the method was extended to obtain trajectories by considering repulsive and attractive potentials taking into account position and velocity of the robot with respect to obstacles. Then, a 2-D space attractive force based on fractional potential was developed. The advantage of the generalized normalized force is the possibility to control its variation. The potential curve is continuously varying and depends only on one parameter, the non-integer order. The obtained path is robust in front of robot parameter variations. This paper presents an extension of these fractional attractive forces in 3-D space for UAV application. This method allows to obtain robust path planning in 3-D space despite UAV mass variations. The robustness of the obtained trajectories is studied. A comparison between a classical method and the proposed approach is presented.