Motion Planning in Dynamic Environments: Obstacles Moving Along Arbitrary Trajectories

This paper generalizes the concept of velocity obstacles [3] to obstacles moving along arbitrary trajectories. We introduce the non-linear velocity obstacle, which takes into account the shape, velocity and path curvature of the moving obstacle. The non-linear v-obstacle allows selecting a single avoidance maneuver (if one exists) that avoids any number of obstacles moving on any known trajectories. For unknown trajectories, the non-linear v-obstacles can be used to generate local avoidance maneuvers based on the current velocity and path curvature of the moving obstacle. This elevates the planning strategy to a second order method, compared to the first order avoidance using the linear v-obstacle, and zero order avoidance using only position information. Analytic expressions for the non-linear v-obstacle are derived for general trajectories in the plane. The nonlinear v-obstacles are demonstrated in a complex traffic example.