No abstract

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.

We present a new and complete multi-level approach for solving path planning problems for nonholonomic robots. At the rst level a path is found that disrespects some of the nonholonomic constraints. At each next level a new path is generated, by transformation of the path generated at the previous level. The transformation is such that more nonholonomic constraints are respected than at the previous level. At the nal level all nonholonomic constraints are respected.We present t wo techniques for these transformations. The rst, which w e call the Pick and Link technique, repeatedly picks pieces from the given path, and tries to replace these by more feasible ones. The second technique restricts the free con guration space to a tube" around the given path, and a roadmap, capturing the free space connectivity within this tube, is constructed by the Probabilistic Path Planner. F rom this roadmap we retrieve a new, more feasible, path.In the intermediate levels we plan paths for what we refer to as semi-holonomic subsystems. Such a system is obtained by taking the real physical system, and removing some of its nonholonomic constraints.In this paper, we apply the scheme to car-like robots pulling trailers, that is, tractor-trailer robots. In this case, the real system is the tractor-trailer robot, and the ignored constraints in the semi-holonomic subsystems are the kinematic ones on the trailers. These are the constraints of rolling without slipping, on the trailers wheels.Experimental results are given that illustrate the time-e ciency of the resulting planner. In particular, we show that using the multi-level scheme leads to signi cantly better performance in computation time and path shape than direct transformations to feasible paths.