Optimal Geodesic Curvature Constrained Dubins' Path on Sphere with Free Terminal Orientation
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916396637618176 |
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| author | Kumar, Deepak Prakash Darbha, Swaroop Manyam, Satyanarayana Gupta Tran, Dzung Casbeer, David W. |
| author_facet | Kumar, Deepak Prakash Darbha, Swaroop Manyam, Satyanarayana Gupta Tran, Dzung Casbeer, David W. |
| contents | In this paper, motion planning for a vehicle moving on a unit sphere with unit speed is considered, wherein the desired terminal location is fixed, but the terminal orientation is free. The motion of the vehicle is modeled to be constrained by a maximum geodesic curvature $U_{max},$ which controls the rate of change of heading of the vehicle such that the maximum heading change occurs when the vehicle travels on a tight circular arc of radius $r = \frac{1}{\sqrt{1 + U_{max}^2}}$. Using Pontryagin's Minimum Principle, the main result of this paper shows that for $r \leq \frac{1}{2}$, the optimal path connecting a given initial configuration and a final location on the sphere belongs to a set of at most seven paths. The candidate paths are of type $CG, CC,$ and degenerate paths of the same, where $C \in \{L, R\}$ denotes a tight left or right turn, respectively, and $G$ denotes a great circular arc. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_10363 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Geodesic Curvature Constrained Dubins' Path on Sphere with Free Terminal Orientation Kumar, Deepak Prakash Darbha, Swaroop Manyam, Satyanarayana Gupta Tran, Dzung Casbeer, David W. Optimization and Control In this paper, motion planning for a vehicle moving on a unit sphere with unit speed is considered, wherein the desired terminal location is fixed, but the terminal orientation is free. The motion of the vehicle is modeled to be constrained by a maximum geodesic curvature $U_{max},$ which controls the rate of change of heading of the vehicle such that the maximum heading change occurs when the vehicle travels on a tight circular arc of radius $r = \frac{1}{\sqrt{1 + U_{max}^2}}$. Using Pontryagin's Minimum Principle, the main result of this paper shows that for $r \leq \frac{1}{2}$, the optimal path connecting a given initial configuration and a final location on the sphere belongs to a set of at most seven paths. The candidate paths are of type $CG, CC,$ and degenerate paths of the same, where $C \in \{L, R\}$ denotes a tight left or right turn, respectively, and $G$ denotes a great circular arc. |
| title | Optimal Geodesic Curvature Constrained Dubins' Path on Sphere with Free Terminal Orientation |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2409.10363 |