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We present a new approach to the multi-robot path planning problem, where a numberof robots are to change their positions through feasible motions in the same static environment. Rather than the usual decoupled planning, we use a coordinated approach. As a result we can show that the method is probabilistically complete, that is, any solvable problem will be solved within a nite amount of time. A data-structure storing multi-robot motions is built in two steps. First, a roadmap is constructed for just one robot. For this we use the Probabilistic Path Planner, which guarantees that the approach can be easily applied to di erent robot types. In the second step, a number of these simple roadmaps are combined into a roadmap for the composite robot. This data-structure can be used for retrieving multi-robot paths. We have applied the method to car-like robots, and simulation results are presented which show that problems involving up to 5 car-like robots in complex environments are solved successfully in computation times in the order of seconds, after a preprocessing step the construction of the data structure that consumes, at most, a few minutes. Such a preprocessing step however needs to be performed just once, for a given static environment.

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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.

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