We consider the problem of coordinating a collection of robots at an intersection area taking into account dynamical constraints due to actuator limitations. We adopt the coordination space approach, which is standard in multiple robot motion planning. Assuming the priorities between robots are assigned in advance and the existence of a collision-free trajectory respecting those priorities, we propose a provably safe trajectory planner satisfying kinodynamic constraints. The algorithm is shown to run in real time and to return safe (collision-free) trajectories. Simulation results on synthetic data illustrate the benefits of the approach.
We consider the problem of cooperative intersection management. It arises in automated transportation systems for people or goods but also in multi-robots environment. Therefore many solutions have been proposed to avoid collisions. The main problem is to determine collision-free but also deadlock-free and optimal algorithms. Even with a simple definition of optimality, finding a global optimum is a problem of high complexity, especially for open systems involving a large and varying number of vehicles. This paper advocates the use of a mathematical framework based on a decomposition of the problem into a continuous optimization part and a scheduling problem. The paper emphasizes connections between the usual notion of vehicle priority and an abstract formulation of the scheduling problem in the coordination space. A constructive locally optimal algorithm is proposed. More generally, this work opens up for new computationally efficient cooperative motion planning algorithms. This work makes two contributions to geometric motion planning for multiple robots: i) motion plans can be determined that simultaneously optimize an independent performance criterion for each robot; ii) a general spectrum is defined between decoupled and centralized planning. By considering independent performance criteria, we introduce a form of optimality that is consistent with concepts from multi-objective optimization and game theory research. Previous multiple-robot motion planning approaches that consider optimality combine individual criteria into a single criterion. As a result, these methods can fail to find many potentially useful motion plans. We present implemented, multi-robot motion planning algorithms that are derived from the principle of optimality, for three problem classes along the spectrum between centralized and decoupled planning: i) coordination along fixed, independent paths; ii) coordination along independent roadmaps; iii) general, unconstrained motion planning. Several computed examples are presented for all three problem classes that illustrate the concepts and algorithms.  This paper presents a geometric based approach for multiple mobile robot motion coordination. All the robot paths being computed independently, we address the problem of coordinating the motion of the robots along their own path in such a way they do not collide each other. The proposed algorithm is based on a bounding box representation of the obstacles in the so-called coordination diagram. The algorithm is resolution-complete. Its efficiency is illustrated by examples involving more than 100 robots. 1 Introduction and Overview.- 2 Configuration Space of a Rigid Object.- 3 Obstacles in Configuration Space.- 4 Roadmap Methods.- 5 Exact Cell Decomposition.- 6 Approximate Cell Decomposition.- 7 Potential Field Methods.- 8 Multiple Moving Objects.- 9 Kinematic Constraints.- 10 Dealing with Uncertainty.- 11 Movable Objects.- Prospects.- Appendix A Basic Mathematics.- Appendix B Computational Complexity.- Appendix C Graph Searching.- Appendix D Sweep-Line Algorithm.- References. 