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 vobstacle 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 vobstacle are derived for general trajectories in the plane. The non-linear v-obstacles are demonstrated in a complex traffic example.

Vehicle navigation in dynamic environments is a challenging task, especially when the motion of the obstacles populating the environment is unknown beforehand and is updated at runtime. Traditional motion planning approaches are too slow to be applied in real-time to this problem, whereas reactive navigation methods have generally a too short look-ahead horizon. Recently, iterative planning has emerged as a promising approach, however, it does not explicitly take into account the movements of the obstacles.This paper presents a real-time motion planning approach, based on the concept of the Non-Linear V-Obstacle (NLVO) (Shiller et al., 2001). Given a predicted environment, the NLVO models the set of velocities which lead to collisions with static and moving obstacles, and an estimation of the times-to-collision. At each controller iteration, an iterative A* motion planner evaluates the potential moves of the robot, based on the computed NLVO and the traveling time. Previous search results are reused to both minimize computation and maintain the global coherence of the solutions.We first review the concept of the NLVO, and then present the iterative planner. The planner is then applied to vehicle navigation and demonstrated in a complex traffic scenario.

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