Randomized path planning on vector fields

Given a vector field defined on a robot's configuration space, in which the vector field represents the system drift, e.g. a wind velocity field, water current flow, or gradient field for some potential function, we present a randomized path planning algorithm for reaching a desired goal configuration. Taking the premise that moving against the vector field requires greater control effort, and that minimizing the control effort is both physically meaningful and desirable, we propose an integral functional for control effort, called the upstream criterion, that measures the extent to which a path goes against the given vector field. The integrand of the upstream criterion is then used to construct a rapidly exploring random tree (RRT) in the configuration space, in a way such that random nodes are generated with an a priori specified bias that favors directions indicated by the vector field. The resulting planning algorithm produces better quality paths while preserving many of the desirable features of RRT-based planning, e.g. the Voronoi bias property, computational efficiency, algorithmic simplicity, and straightforward extension to constrained and nonholonomic problems. Extensive numerical experiments demonstrate the advantages of our algorithm vis-a-vis existing optimality criterion-based planning algorithms.