This paper describes the foundations and algorithms of a new probabilistic roadmap (PRM) planner that is: single-query -- instead of pre-computing a roadmap covering the entire free space, it uses the two input query configurations to explore as little space as possible; bi-directional -- it explores the robot's free space by building a roadmap made of two trees rooted at the query configurations; and lazy in checking collisions -- it delays collision tests along the edges of the roadmap until they are absolutely needed. Several observations motivated this strategy: (1) PRM planners spend a large fraction of their time testing connections for collision; (2) most connections in a roadmap are not on the final path; (3) the collision test for a connection is most expensive when there is no collision; and (4) any short connection between two collision-free configurations has high prior probability of being collision-free. The strengths of single-query and bi-directional sampling techniques, and those of delayed collision checking reinforce each other. Experimental results

The coordination of the motions of the robots is one of the fundamental problems for multi-robot systems. A popular approach to avoid planning in the high-dimensional composite configuration space are prioritized and decoupled techniques. While these methods are very efficient, they have two major drawbacks. First, they are incomplete, i.e. they sometimes fail to find a solution even if one exists, and second, the resulting solutions are often not optimal. They furthermore leave open how to assign the priorities to the individual robots. In this paper we present a method for optimizing priority schemes for such prioritized and decoupled planning techniques. Our approach performs a randomized search with hill-climbing to find solutions and to minimize the overall path lengths. The technique has been implemented and tested on real robots and in extensive simulation runs. The experimental results demonstrate that our method is able to seriously reduce the number of failures and to significantly reduce the overall path length for different prioritized and decoupled path planning techniques and even for large teams of robots. 1

Coordinating the motion of multiple mobile robots is one of the fundamental problems in robotics. The predominant algorithms for coordinating teams of robots are decoupled and prioritized, thereby avoiding combinatorially hard planning problems typically faced by centralized approaches. While these methods are very efficient, they have two major drawbacks. First, they are incomplete, i.e. they sometimes fail to find a solution even if one exists, and second, the resulting solutions are often not optimal. In this paper we present a method for finding and optimizing priority schemes for such prioritized and decoupled planning techniques. Existing approaches apply a single priority scheme which makes them overly prone to failure in cases where valid solutions exist. By searching in the space of priorization schemes, our approach overcomes this limitation. It performs a randomized search with hill-climbing to find solutions and to minimize the overall path length. To focus the search, our algorithm is guided by constraints generated from the task specification. To illustrate the appropriateness of this approach, this paper discusses experimental results obtained with real robots and through systematic robot simulation. The experimental results illustrate the superior performance of our approach, both in terms of efficiency of robot motion and in the ability to find valid plans.

In this paper, we consider path planning for a car-like vehicle.

Abstract — Motion planning research has been successful in developing planning algorithms which are effective for solving problems with complicated geometric and kinematic constraints. Various applications in robotics and in other fields demand additional physical realism. Some progress has been made for non-holonomic systems. However systems with significant drift, underactuation and discrete system changes remain challenging for existing planning techniques particularly as the dimensionality of the state space increases. In this paper, we demonstrate a motion planning technique for the solution of problems with these challenging characteristics. Our approach uses sampling-based motion planning and subdivision methods. The problem that we solve is a game that was chosen to exemplify characteristics of dynamical systems that are difficult for planning. To our knowledge, this is first application of algorithmic motion planning to a problem of this type and complexity. I.

We present an algorithm that computes the complete set of Pareto-optimal coordination strategies for two translating polygonal robots in the plane. A collision-free acyclic roadmap of piecewise-linear paths is given on which the two robots move. The robots have a maximum speed and are capable of instantly switching between any two arbitrary speeds. Each robot would like to minimize its travel time independently. The Pareto-optimal solutions are the ones for which there exist no solutions that are better for both robots. The algorithm computes exact solutions in time O(mn log n), in which m is the number of paths in the roadmap, n is the number of coordination space vertices. An implementation with computed examples is presented.

In this paper we incorporate dipolar potential fields used for nonholonomic navigation into a novel potential function designed for multi -- robot navigation. The derived navigation function is suitable for navigation of multiple nonholonomic vehicles. A properly designed discontinuous feedback control law is applied to steer the nonholonomic vehicles. The derived closed form control scheme provides robust navigation with guaranteed collision avoidance and global convergence properties, as well as fast feedback, rendering the methodology particularly suitable for real time implementation. Collision avoidance and global convergence properties are verified through non - trivial computer simulations. 1

. Coordinating the motion of multiple mobile robots is one of the fundamental problems in robotics. The predominant algorithms for coordinating teams of robots are decoupled and prioritized, thereby avoiding combinatorially hard planning problems typically faced by centralized approaches. In this paper we present a method for finding solvable priority schemes for such prioritized and decoupled planning techniques. Existing approaches apply a single priority scheme which makes them overly prone to failure in cases where valid solutions exist. By searching in the space of priorization schemes, our approach overcomes this limitation. To focus the search, our algorithm is guided by constraints generated from the task specification. To illustrate the appropriateness of this approach, this paper discusses experimental results obtained with real robots and through systematic robot simulation. The experimental results demonstrate that our approach can successfully solve many more coordination problems than previous decoupled and prioritized techniques. 1

This paper focuses on the coordination of multiple robots with kinodynamic constraints along specified paths. The presented approach generates continuous velocity profiles that avoid collisions and minimize the completion time for the robots. The approach identifies collision segments along each robot’s path and then optimizes the motions of the robots along their collision and collision-free segments. For each path segment for each robot, the minimum and maximum possible traversal times that satisfy the dynamics constraints are computed by solving the corresponding twopoint boundary value problems. Then the collision avoidance constraints for pairs of robots can be combined to formulate a mixed integer nonlinear programming (MINLP) problem. Since this nonconvex MINLP model is difficult to solve, we describe two related mixed integer linear programming (MILP) formulations that provide schedules that are lower and upper bounds on the optimum; the upper bound schedule is a continuous velocity schedule. The approach is illustrated with robots modeled as double integrators subject to velocity and acceleration constraints. An implementation that coordinates 12 nonholonomic car-like robots is described. 1

Coordinating the motion of multiple mobile robots is one of the fundamental problems in robotics. The predominant algorithms for coordinating teams of robots are decoupled and prioritized, thereby avoiding combinatorially hard planning problems typically faced by centralized approaches. In this paper we present a method for finding solvable priority schemes for such prioritized and decoupled planning techniques. Existing approaches apply a single priority scheme which makes them overly prone to failure in cases where valid solutions exists. By searching in the space of priorization schemes, our approach overcomes this limitation. To focus the search, our algorithm is guided by constraints generated from the task specification. To illustrate the appropriateness of this approach, this paper discusses experimental results obtained with real robots and through systematic robot simulation. The experimental results demonstrate that our approach successfully solves many more coordination problems than previous decoupled and prioritized techniques.