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This is an early access version, the complete PDF, HTML, and XML versions will be available soon.
Article

MIPLP: A Mixed-Integer Piecewise-Linear Programming Path-Planning Approach for the Three-Point Reeds–Shepp Problem

by
Xing Zhou
1,*,
Wenxin Zhang
1,*,
Lin Li
2,
Hao Gao
3,
Daqiang Zhang
4,
Zhen Zhang
1,
Zhaoqing Li
1 and
Qijiao Lei
1
1
College of Intelligence Science and Technology, National University of Defense Technology, Changsha 410073, China
2
School of Intelligent Manufacturing, Hunan First Normal University, Changsha 410073, China
3
Test Center, National University of Defense Technology, Xi’an 710100, China
4
School of Software Engineering, Tongji University, Shanghai 201805, China
*
Authors to whom correspondence should be addressed.
Drones 2026, 10(6), 408; https://doi.org/10.3390/drones10060408
Submission received: 30 March 2026 / Revised: 15 May 2026 / Accepted: 21 May 2026 / Published: 25 May 2026
(This article belongs to the Special Issue Advanced Cross-Domain Unmanned Platform Command and Security Technology: 2nd Edition)
Versions Notes

Abstract

This paper studies an inspection path-planning task for cross-domain platforms, in which a Reeds–Shepp unmanned surface vehicle (USV) must plan the shortest curvature-constrained path from the starting configuration (e.g., the USV depot) to the intermediate inspection point and then to the terminal configuration (e.g., the technical facility). The problem emerges from cooperative inspection applications and can be formulated as a three-point Reeds–Shepp problem (3PRSP), where the heading at the intermediate point needs to be optimized. To the best of our knowledge, neither closed-form nor optimization-based solutions exist for this problem. We propose an approximation-and-optimization-based approach that approximates the trigonometric constraints arising from the Reeds–Shepp forward–backward motion kinematics using piecewise-linear formulations, enabling the resulting model to be effectively solved by mathematical programming solvers. Extensive simulations and comparisons with the three-point Dubins approach and related methods demonstrate the accuracy and computational efficiency of the proposed method.
Keywords: cooperative inspection; unmanned surface vehicle (USV); path-planning; Reeds–Shepp problem; free-heading; piecewise-linear approximation cooperative inspection; unmanned surface vehicle (USV); path-planning; Reeds–Shepp problem; free-heading; piecewise-linear approximation

Share and Cite

MDPI and ACS Style

Zhou, X.; Zhang, W.; Li, L.; Gao, H.; Zhang, D.; Zhang, Z.; Li, Z.; Lei, Q. MIPLP: A Mixed-Integer Piecewise-Linear Programming Path-Planning Approach for the Three-Point Reeds–Shepp Problem. Drones 2026, 10, 408. https://doi.org/10.3390/drones10060408

AMA Style

Zhou X, Zhang W, Li L, Gao H, Zhang D, Zhang Z, Li Z, Lei Q. MIPLP: A Mixed-Integer Piecewise-Linear Programming Path-Planning Approach for the Three-Point Reeds–Shepp Problem. Drones. 2026; 10(6):408. https://doi.org/10.3390/drones10060408

Chicago/Turabian Style

Zhou, Xing, Wenxin Zhang, Lin Li, Hao Gao, Daqiang Zhang, Zhen Zhang, Zhaoqing Li, and Qijiao Lei. 2026. "MIPLP: A Mixed-Integer Piecewise-Linear Programming Path-Planning Approach for the Three-Point Reeds–Shepp Problem" Drones 10, no. 6: 408. https://doi.org/10.3390/drones10060408

APA Style

Zhou, X., Zhang, W., Li, L., Gao, H., Zhang, D., Zhang, Z., Li, Z., & Lei, Q. (2026). MIPLP: A Mixed-Integer Piecewise-Linear Programming Path-Planning Approach for the Three-Point Reeds–Shepp Problem. Drones, 10(6), 408. https://doi.org/10.3390/drones10060408

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