We study the motion-planning problem for pairs and triples of robots operating in a shared workspace containing n obstacles. A standard way to solve such problems is to view the collection of robots as one composite robot, whose number of degrees of freedom is d, the sum of the numbers of degrees of freedom of the individual robots. We show that it is sufficient to consider a constant number of robot systems whose number of degrees of freedom is at most d \\Gamma 1 for pairs of robots, and d \\Gamma 2 for triples. (The result for a pair assumes that the sum of the number of degrees of freedom of the robots constituting the pair reduces by at least one if the robots are required to stay in contact; for triples a similar assumption is made. Moreover, for triples we need to assume that a solution with positive clearance exists.) We use this to obtain an O(n d ) time algorithm to solve the motion-planning problem for a pair of robots; this is one order of magnitude faster than what the st...

A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collision-free configurations and whose edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out to be relatively easy to choose, Increased efficiency can also be achieved by tailoring some components of the method (e.g., the local planner) to the considered robots. In this paper the method is applied to planar articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (/spl ap/150 MIPS), after learning for relatively short periods of time (a few dozen seconds).

Presents a new approach to the multi-robot path planning problem, where a number of robots are to change their positions through feasible motions in the same static environment. The approach is probabilistically complete. That is, any solvable problem is guaranteed to be solved within a finite amount of time. The method, which is an extension of previous work on probabilistic single-robot planners, is very flexible in the sense that it can easily be applied to different robot types. In this paper the authors apply it to non-holonomic car-like robots, and present experimental results which show that the method is powerful and fast.

A tractor-trailer robot consists of a car-like tractor towing a passive trailer. Due to its highly nonholonomic nature, the kinematics of this type of robot are complicated and difficult to compute. We present exact closed-form solutions for the kinematic parameters of a tractor-trailer robot and use them to construct an exact and efficient motion planner in the absence of obstacles. This local planner can be employed in a probabilistic global planner, which allows us to plan motions in the presence of obstacles.