Computational geometry: an introduction
Computational geometry: an introduction
The NURBS book
The complexity of the two dimensional curvature-constrained shortest-path problem
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Robot Motion Planning
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Randomized single-query motion planning in expansive spaces
Randomized single-query motion planning in expansive spaces
Planning Algorithms
Spatial Planning: A Configuration Space Approach
IEEE Transactions on Computers
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In this paper, a geometrical approach is developed to generate simultaneously optimal (or near-optimal) smooth paths for a set of non-holonomic robots, moving only forward in a 2D environment cluttered with static and moving obstacles. The robots environment is represented by a 3D geometric entity called Bump-Surface, which is embedded in a 4D Euclidean space. The multi-motion planning problem (MMPP) is resolved by simultaneously finding the paths for the set of robots represented by monoparametric smooth C2 curves onto the Bump-Surface, such that their inverse images onto the initial 2D workspace satisfy the optimization motion-planning criteria and constraints. The MMPP is expressed as an optimization problem, which is solved on the Bump-Surface using a genetic algorithm. The performance of the proposed approach is tested through a considerable number of simulated 2D dynamic environments with car-like robots.