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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.00339 |
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| _version_ | 1866929476979392512 |
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| author | Wang, Kun Lu, Fangmin Chen, Zheng Li, Jun |
| author_facet | Wang, Kun Lu, Fangmin Chen, Zheng Li, Jun |
| contents | This work presents a Physics-Informed Indirect Method (PIIM) that propagates the dynamics of both states and co-states backward in time for trajectory optimization problems. In the case of a Time-Optimal Soft Landing Problem (TOSLP), based on the initial co-state vector normalization technique, we show that the initial guess of the mass co-state and the numerical factor can be eliminated from the shooting procedure. As a result, the initial guess of the unknown co-states can be constrained to lie on a unit 3-D hypersphere. Then, using the PIIM allows one to exploit the physical significance of the optimal control law, which further narrows down the solution space to a unit 3-D octant sphere. Meanwhile, the analytical estimations of the fuel consumption and final time are provided. Additionally, a usually overlooked issue that results in an infeasible solution with a negative final time, is fixed by a simple remedy strategy. Consequently, the reduced solution space becomes sufficiently small to ensure fast, robust, and guaranteed convergence for the TOSLP. Then, we extend the PIIM to solve the Fuel-Optimal Soft Landing Problem (FOSLP) with a homotopy approach. The numerical simulations show that compared with the conventional indirect method with a success rate of 89.35%, it takes a shorter time for the proposed method to find the feasible solution to the FOSLP with a success rate of 100%. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_00339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Physics-Informed Indirect Method for Trajectory Optimization Wang, Kun Lu, Fangmin Chen, Zheng Li, Jun Optimization and Control This work presents a Physics-Informed Indirect Method (PIIM) that propagates the dynamics of both states and co-states backward in time for trajectory optimization problems. In the case of a Time-Optimal Soft Landing Problem (TOSLP), based on the initial co-state vector normalization technique, we show that the initial guess of the mass co-state and the numerical factor can be eliminated from the shooting procedure. As a result, the initial guess of the unknown co-states can be constrained to lie on a unit 3-D hypersphere. Then, using the PIIM allows one to exploit the physical significance of the optimal control law, which further narrows down the solution space to a unit 3-D octant sphere. Meanwhile, the analytical estimations of the fuel consumption and final time are provided. Additionally, a usually overlooked issue that results in an infeasible solution with a negative final time, is fixed by a simple remedy strategy. Consequently, the reduced solution space becomes sufficiently small to ensure fast, robust, and guaranteed convergence for the TOSLP. Then, we extend the PIIM to solve the Fuel-Optimal Soft Landing Problem (FOSLP) with a homotopy approach. The numerical simulations show that compared with the conventional indirect method with a success rate of 89.35%, it takes a shorter time for the proposed method to find the feasible solution to the FOSLP with a success rate of 100%. |
| title | A Physics-Informed Indirect Method for Trajectory Optimization |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2402.00339 |