Abstract
We describe a collections of algorithm to compute smooth trajectories between obstacles, with the objective that the obtained trajectories should be smooth. In particular, we use a vertical cell decomposition algorithm to avoid the obstacles, a best first search algorithm to obtain trajectory sketches and Bézier curves to implement smoothness. We also provide some insights into the correctness arguments for these algorithms. These correctness arguments are intended for use in a formal proof. While we have running implementations of the full program, the formal proofs of correctness are still incomplete.
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Acknowledgments
The initial work on the vertical cell decomposition algorithms was done by Thomas Portet. Studies of potential collisions between Bézier curves and straight line segments were done by Quentin Vermande. Laurent Théry added the possibility to visualize the results on a web page.
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Bertot, Y. (2024). Safe Smooth Paths Between Straight Line Obstacles. In: Capretta, V., Krebbers, R., Wiedijk, F. (eds) Logics and Type Systems in Theory and Practice. Lecture Notes in Computer Science, vol 14560. Springer, Cham. https://doi.org/10.1007/978-3-031-61716-4_3
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