Toward efficient trajectory planning: the path-velocity decomposition
International Journal of Robotics Research
Guided self-scheduling: A practical scheduling scheme for parallel supercomputers
IEEE Transactions on Computers
Bisections and ham-sandwich cuts of convex polygons and polyhedra
Information Processing Letters
Factoring: a method for scheduling parallel loops
Communications of the ACM
A linear algorithm for bisecting a polygon
Information Processing Letters
Safe self-scheduling: a parallel loop scheduling scheme for shared-memory multiprocessors
International Journal of Parallel Programming
Convex Decomposition of Simple Polygons
ACM Transactions on Graphics (TOG)
Fast Triangulation of Simple Polygons
Proceedings of the 1983 International FCT-Conference on Fundamentals of Computation Theory
Multiple path coordination for mobile robots: a geometric algorithm
IJCAI'99 Proceedings of the 16th international joint conference on Artificial intelligence - Volume 2
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We present two problems in multiple-robot motion planning that can be quite naturally solved using techniques from the parallel processing community to dictate how the robots interact with each other and techniques from computational geometry to apply these techniques in the geometric environment in which the robots operate. The first problem we consider is a load-balancing problem in which a pool of work must be divided among a set of processors in order to minimize the amount of time required to complete all the work. We describe a simple polygon partitioning algorithm that allows techniques from parallel processor scheduling to be applied in the multiple-robot setting in order to achieve a good balance of the work. The second problem is that of collision avoidance, where one must avoid that two (or more) processors occupy the same resource at the same time. For this problem, we describe a procedure for robot interaction that is derived from procedures used in shared-memory computers along with a geometric data structure that can efficiently determine when there are potential robot collisions.