A Gaussian-Biased Heuristic for Stochastic Sampling-Based 2D Trajectory Planning Algorithms

This paper addresses the problem of slow convergence for stochastic sampling-based trajectory planners with applications to Unmanned Aerial Vehicles. Typically, stochastic sampling-based trajectory planners apply a uniform probability distribution to the vehicle's configuration space for random sampling. This results in execution times that make these planners not applicable to many real-time systems. The proposed method obtains first the obstacle-free trajectory according to the trajectory planner's steering function. A minimum area bounding ellipse is then defined for the obstacle-free trajectory and is expanded to satisfy a given maximum obstacle intersection area. The resulting elliptical surface is then converted to a Gaussian distribution for randomly generating a given percentage of samples in the interior or along the boundary of the elliptical surface. The proposed Gaussian-biased sampling strategy is applied to a minimum time trajectory planning problem and is compared with a uniformly distributed sampling strategy as well as two other sampling strategies taken from the literature. Simulations results show that the proposed sampling strategy yields a reduction of the computation time for producing an initial trajectory, of the initial trajectory cost, of the final trajectory cost, and of the algorithm's failure rate. Additionally, the proposed Gaussian-biased sampling strategy naturally inherits the completeness and optimality properties of the trajectory planning algorithm.