Shortest paths for a car-like robot to manifolds in configuration space
International Journal of Robotics Research
Planning Algorithms
IEEE Transactions on Robotics
Nonholonomic distance to polygonal obstacles for a car-like robot of polygonal shape
IEEE Transactions on Robotics
Time-optimal trajectories with bounded curvature in anisotropic media
International Journal of Robotics Research
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In this paper, we characterize the time-optimal trajectories leading a Dubins car in collision with the obstacles in its workspace. Due to the constant velocity constraint characterizing the Dubins car model, these trajectories form a sufficient set of shortest paths between any robot configuration and the obstacles in the environment.Based on these paths, we define and give the algorithm for computing a distance function that takes into account the nonholonomic constraints and captures the nonsymmetric nature of the system. The developments presented here assume that the obstacles and the robot are polygons although the methodology can be applied to different shapes.