A Lévy Flight Based Probabilistic Motion Planning for UAVs in Constricted Environments

Aerial Inspection robotics often demands navigating through complex environments with constricted regions. Such narrow passage scenarios appear, for example, as an unmanned aerial vehicle (UAV) tries to navigate through windows or tunnels, or navigating through a maze. Such UAV motion planning scenario demands 6-DOF motion planning manoeuvres and often suffers computational complexity is-sues. Aerial manipulators exhibit even higher dimensionality. Sampling based probabilistic roadmap planners (PRM) have been successful in motion planning of robots with higher degrees of freedom, but may fail to capture the connectivity of the configuration space in scenarios with a critical narrow passage. This remains as a central drawback for sampling based motion planning algorithms. The primary reason for failure is generally associated with the problem of very low probability of generating candidate sampling configurations within a narrow region. The low Lebesgue volume measure of the narrow passage region acts as adversary to obtain critical sample points inside the region of manoeuvre and thus affects the connectivity of the random graph structure. Several heuristic based sampling strategies can remove this difficulty to a great extent, but a satisfactory answer remains elusive. In this paper, we show a novel technique based on Levy Flights to generate key samples in the narrow regions of the configuration space of UAV motion planning. The technique is based on Random Walk to surface approach for sample generation, it however extends the concept with the support of a heavy tail distribution. The paper shows a complete integration of the proposed sampling scheme into a PRM like planner and shows the UAV motion trajectories for various complex scenarios. The technique substantially improves sample quality at the expense of a minimal additional computation when compared with pure random walk based methods. However, it still outperforms state of the art random bridge building method, in terms of number of collision calls, computational overhead and sample quality. The method is robust to the changes in the parameters related to the structure of the narrow passage, thus giving an additional generality. A number of 2D & 3D motion planning simulations are presented which shows the effectiveness of the method and are compared with the state of the art results.