# A Non-Smooth Numerical Optimization Approach to the Three-Point Dubins Problem (3 PDP)
## 6 Algorithms
### Pattern Search with Root Finder
[[https://doi.org/10.3390/a17050184](https://doi.org/10.3390/a17050184)]([https://doi.org/10.3390/a17050184](https://doi.org/10.3390/a17050184)). * [PERSON] and [PERSON] (2023) [PERSON] [PERSON]; [PERSON] [PERSON] On the Intersection of Computational Geometry Algorithms with Mobile Robot Path Planning. _Algorithms_**2023**, _16_, 498. [[https://doi.org/10.3390/a16110498](https://doi.org/10.3390/a16110498)]([https://doi.org/10.3390/a16110498](https://doi.org/10.3390/a16110498)). * [PERSON] et al. (2024) [PERSON]; [PERSON] [PERSON]; [PERSON]; [PERSON] MPTREE: A Sampling-based Vehicle Motion Planner for Real-time Obstacle Avoidance. _IFAC-PapersOnLine_**2024**, _58_, 146-153. [[https://doi.org/10.1016/j.ifacol.2024.07.332](https://doi.org/10.1016/j.ifacol.2024.07.332)]([https://doi.org/10.1016/j.ifacol.2024.07.332](https://doi.org/10.1016/j.ifacol.2024.07.332)). * [PERSON] and [PERSON] (2007) [PERSON]; [PERSON] Time-optimal paths for a Dubins airplane. In Proceedings of the 2007 46 th IEEE Conference on Decision and Control, New Orleans, LA, USA, 12-14 December 2007; pp. 2379-2384. [[https://doi.org/10.1109/CDC.2007.4434966](https://doi.org/10.1109/CDC.2007.4434966)]([https://doi.org/10.1109/CDC.2007.4434966](https://doi.org/10.1109/CDC.2007.4434966)). * (6) [PERSON] [PERSON]; [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON] Online 3-Dimensional Path Planning with Kinematic Constraints in Unknown Environments Using Hybrid A* with Tree Pruning. _Sensors_**2021**, _21_, 1152. [[https://doi.org/10.3390/s21041152](https://doi.org/10.3390/s21041152)]([https://doi.org/10.3390/s21041152](https://doi.org/10.3390/s21041152)). * (7) [PERSON] Some examples of the solution of a special kind of problem on greatest and least quantities. _Soobshch. Karkovsk. Mat. Obshch. N887_, \(1\), 250-276. * (8) [PERSON] Markov-Dubins path via optimal control theory. _Comput. Optim. Appl._**2017**, _68_, 719-747. [[https://doi.org/10.1007/s10589-017-9923-8](https://doi.org/10.1007/s10589-017-9923-8)]([https://doi.org/10.1007/s10589-017-9923-8](https://doi.org/10.1007/s10589-017-9923-8)). * (9) [PERSON] On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents. _[PERSON]. [PERSON]_**1957**, _79_, 497-516. * (10) [PERSON] Three-Dimensional Dubins-Path-Guided Continuous Curvature Path Smoothing. _Appl. Sci._**2022**, _12_, 11336. [[https://doi.org/10.3390/app122211336](https://doi.org/10.3390/app122211336)]([https://doi.org/10.3390/app122211336](https://doi.org/10.3390/app122211336)). * (11) [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] A new Markov-Dubins hybrid solver with learned decision trees. _Eng. Appl. Artif. Intell._**2023**, _122_, 106166. * (12) [PERSON]; [PERSON]; [PERSON] [PERSON]; [PERSON] [PERSON]; [PERSON] An Iterative Dynamic Programming Approach to the Multipoint Markov-Dubins Problem. _IEEE Robot. Autom. Lett._**2020**, \(5\), 2483-2490. * (13) [PERSON] Markov-Dubins interpolating curves. _Comput. Optim. Appl._**2019**, _73_, 647-677. [[https://doi.org/10.1007/s10589-019-0](https://doi.org/10.1007/s10589-019-0)]([https://doi.org/10.1007/s10589-019-0](https://doi.org/10.1007/s10589-019-0)) 0076-y. * (14) [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Robot motion planning: Can GPUs be a game changer? In Proceedings of the 2021 IEEE 45 th Annual Computers, Software, and Applications Conference (COMPSAC), Virtual, 12-16 July 2021; pp. 21-30. * (15) [PERSON]; [PERSON] [PERSON] Traveling Salesman Problem with Neighborhoods: A Graph-Based Approach. _Algorithms_**2013**, \(6\), 84-99. [[https://doi.org/10.3390/a6010084](https://doi.org/10.3390/a6010084)]([https://doi.org/10.3390/a6010084](https://doi.org/10.3390/a6010084)). * (16) [PERSON]; [PERSON] Heuristics and Learning Models for Dubins MinMax Traveling Salesman Problem. _Sensors_**2023**, _23_, 6432. [[https://doi.org/10.3390/s23146432](https://doi.org/10.3390/s23146432)]([https://doi.org/10.3390/s23146432](https://doi.org/10.3390/s23146432)).