An Analytical Method for Finding All Dynamically Admissible Paths Around an Obstacle that Maximize Friction Utilization

Path planning through obstacle fields is critically important for advancing the safety and utility of autonomous off-road vehicles. This paper describes the development of an analytical method for modifying point-to-point paths into high-speed paths. The method starts by using, as an input, a point-to-point path plan through an obstacle field such as one generated from an Atype algorithm. This point-to-point method represents the shortest path solution as a series of waypoints that the vehicle must reach in sequence, with each waypoint typically constrained by a nearby obstacle. Because the waypoints produce a C0 continuous but non-differentiable path, the implementation of a waypoint-following method at high speed often requires a vehicle to slow almost completely to a stop, turn, and then speed up at every waypoint. To generate a high-speed path, the point-to-point path must be modified into line segments connected by C1+ smooth curves to maximize vehicle speed while keeping the constraint of avoiding all obstacle collisions. This paper develops such a high-speed path-planning algorithm. The algorithm designs a path consisting of straight line and constant-radius arcs that meet acceleration and speed limits. These line segments and arcs optimize the utilization of available surface friction or, via straightforward transformations, user-defined limits on lateral or longitudinal accelerations including powertrain limits, rollover limits, etc.