On discretization methods for approximating optimal paths in regions with direction-dependent costs
Information Processing Letters
Approximate shortest paths in anisotropic regions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Shortest Gently Descending Paths
WALCOM '09 Proceedings of the 3rd International Workshop on Algorithms and Computation
On discretization methods for approximating optimal paths in regions with direction-dependent costs
Information Processing Letters
Power consumption modeling of skid-steer tracked mobile robots on rigid terrain
IEEE Transactions on Robotics
Approximation algorithms for shortest descending paths in terrains
Journal of Discrete Algorithms
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We discuss the problem of computing optimal paths on terrains for a mobile robot, where the cost of a path is defined to be the energy expended due to both friction and gravity. The physical model used by this problem allows for ranges of impermissible traversal directions caused by overturn danger or power limitations. The model is interesting and challenging, as it incorporates constraints found in realistic situations, and these constraints affect the computation of optimal paths. We give some upper- and lower-bound results on the combinatorial size of optimal paths on terrains under this model. With some additional assumptions, we present an efficient approximation algorithm that computes for two given points a path whose cost is within a user-defined relative error ratio. Compared with previous results using the same approach, this algorithm improves the time complexity by using 1) a discretization with reduced size, and 2) an improved discrete algorithm for finding optimal paths in the discretization. We present some experimental results to demonstrate the efficiency of our algorithm. We also provide a similar discretization for a more difficult variant of the problem due to less restricted assumptions.