An algorithm for planning collision-free paths among polyhedral obstacles
Communications of the ACM
Introduction to algorithms
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Planning Algorithms
Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms
Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms
Least squares quantization in PCM
IEEE Transactions on Information Theory
Voronoi-like partition of lattice in cellular automata
Mathematical and Computer Modelling: An International Journal
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Multi-robot coverage and exploration are fundamental problems in robotics. A widely used, efficient and distributable algorithm for achieving coverage of a convex environment with Euclidean metrics is that proposed by Cortes which is based on the discrete-time Lloyd's algorithm. This algorithm is not directly applicable to general Riemannian manifolds with boundaries that are non-convex and are intrinsically non-Euclidean. In this paper we generalize the control law based on minimization of the coverage functional to such non-Euclidean spaces punctured by obstacles. We also propose a practical discrete implementation based on standard graph search-based algorithms. We demonstrate the applicability of the proposed algorithm by solving efficient coverage problems on a sphere and a torus with obstacles, and exploration problems in non-convex indoor environments.