Guaranteed infinite horizon avoidance of unpredictable, dynamically constrained obstacles

Abstract

This paper presents a new approach to guaranteeing collision avoidance with respect to moving obstacles that have constrained dynamics but move unpredictably. Velocity Obstacles have been used previously to plan trajectories that avoid collisions with obstacles under the assumption that the trajectories of the objects are either known or can be accurately predicted ahead of time. However, for real systems this predicted trajectory will typically only be accurate over short time-horizons. To achieve safety over longer time periods, this paper instead considers the set of all reachable points by an obstacle assuming that the dynamics fit the unicycle model, which has known constant forward speed and a maximum turn rate (sometimes called the Dubins car model). This paper extends the Velocity Obstacle formulation by using reachability sets in place of a single “known” trajectory to find matching constraints in velocity space, called Velocity Obstacle Sets. The Velocity Obstacle Set for each obstacle is equivalent to the union of all velocity obstacles corresponding to any dynamically feasible future trajectory, given the obstacle’s current state. This region remains bounded as the time horizon is increased to infinity, and by choosing control inputs that lie outside of these Velocity Obstacle Sets, it is guaranteed that the host agent can always actively avoid collisions with the obstacles, even without knowing their exact future trajectories. Furthermore it is proven that, subject to certain initial conditions, an iterative planner under these constraints guarantees safety for all time. Such an iterative planner is implemented and demonstrated in simulation.