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Combinatorics of a Discrete Trajectory Space for Robot Motion Planning

Felix Wiebe; Shivesh Kumar; Daniel Harnack; Malte Langosz; Hendrik Wöhrle; Frank Kirchner
In: William Holderbaum; J. M. Selig (Hrsg.). 2nd IMA Conference on Mathematics of Robotics. IMA Conference on Mathematics of Robotics (IMA-2022), September 8-10, London, United Kingdom, Springer Proceedings in Advanced Robotics, ISBN 9783030913519, Springer International Publishing, 1/2022.


Motion planning is a difficult problem in robot control. The complexity of the problem is directly related to the dimension of the robot's configuration space. While in many theoretical calculations and practical applications the configuration space is modeled as a continuous space, we present a discrete robot model based on the fundamental hardware specifications of a robot. Using lattice path methods, we provide estimates for the complexity of motion planning by counting the number of possible trajectories in a discrete robot configuration space.


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