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.

Probabilistically safe motion planning to avoid dynamic obstacles with uncertain motion patterns

“…In the event that no probabilistically feasible path can be found, mitigation strategies can be implemented to maximize safety, e.g. Wu and How (2012).…”

On Provably Safe Obstacle Avoidance for Autonomous Robotic Ground Vehicles

“…Since those robots are designed for environments that occupy stationary as well as moving obstacles, motion safety and obstacle avoidance are vital safety features for such robots [3,22,25,27].…”

Collision Prediction Among Rigid and Articulated Obstacles with Unknown Motion

“…Instead of answering whether a given state is an ICS or not, it returns the probability of a state being an ICS. Wu and How [16] extended VO to moving obstacles with constrained dynamics but move unpredictably. To compute the velocity obstacle of an obstacle, it first predicts its reachable region considering all possibly feasible trajectories and then maps this reachable region into velocity space by dividing it by time.…”

“…The main challenge in predicting collision steams from the assumption that obstacle's motion is unknown. Existing methods in collision prediction exploit complex behavior prediction [14,15] or consider dynamic constraints [10,11,13,16]. However, these methods all assume either translational or disc objects, which significantly limit their applicability.…”