Guaranteed Avoidance of Unpredictable, Dynamically Constrained Obstacles Using Velocity Obstacle Sets

Dynamic obstacle avoidance is an important, ubiquitous, and often challenging problem for autonomous mobile robots. This thesis presents a new method to guarantee collision avoidance with respect to moving obstacles that have constrained dynamics but move unpredictably. Velocity Obstacles have been widely used to plan trajectories that avoid collisions with obstacles under the assumption that the path of the objects are either known or can be accurately predicted ahead of time. However, for real systems, this predicted path will typically only be accurate over short time-horizons. To achieve safety over longer time periods, the method introduced here 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 thesis 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 paths. It thus follows that, subject to certain initial conditions, an iterative planner under these constraints guarantees safety for all time. Finally, the an iterative planner is repeatedly tested and analyzed in simulation under various conditions. If the time horizon is set to some finite value, the guaranteed collision avoidance is lost, but the planned trajectories generally become more direct. This effect of varying this time scale also depends on the presence of static obstacles in the environment and on the dynamic limitations of the host robot.