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Collision-free trajectory planning for UAVs based on sequential convex programming

AEROSPACE SCIENCE AND TECHNOLOGY 2024年 152卷

作者： Zhang, Peiwang Mei, Yu Wang, Hao Wang, Weijia Liu, Jia Xidian Univ Sch Math & Stat Xian Peoples R China Air Force Engn Univ Fundamentals Dept Xian Peoples R China AVIC Xian Flight Automat Control Res Inst Xian Peoples R China

This paper proposes an optimization-based approach to solve the collision-free trajectory planning problem for unmanned aerial vehicles (UAVs) with nonlinear dynamical systems. The problem is modeled as a non- convex optimization problem, and then iteratively solved by sequential convex programming algorithm which approximates non-convex constraints by convexification methods. We linearize the dynamical equations of the UAV and penalize collision-free constraints with a hinge loss. Furthermore, a variable trust region method is employed to ensure the convergence and stability of the algorithm. We apply the algorithm to three-degree-of- freedom UAV case studies. Numerical results validate that our method can provide collision-free trajectories with a 27.19% reduction in total flight time and a 93.61% reduction in computation time on average compared with the genetic algorithm method.

关键词： Trajectory optimization Collision-free trajectory sequential convex programming Variable trust region Linear approximation

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ADJOINT-BASED PREDICTOR-CORRECTOR sequential convex programming FOR PARAMETRIC NONLINEAR OPTIMIZATION

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SIAM JOURNAL ON OPTIMIZATION 2012年第4期22卷 1258-1284页

作者： Quoc Tran Dinh Savorgnan, Carlo Diehl, Moritz Katholieke Univ Leuven Dept Elect Engn ESAT SCD B-3001 Heverlee Belgium Katholieke Univ Leuven Optimizat Engn Ctr OPTEC B-3001 Heverlee Belgium Vietnam Natl Univ Dept Math Mech Informat Hanoi Vietnam

This paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint-based predictor-corrector sequential convex programming. After presenting the algorithm, we prove a contraction estimate that guarantees the tracking performance of the algorithm. Two variants of this algorithm are investigated. The first can be used to treat online parametric nonlinear programming problems when the exact Jacobian matrix is available, while the second variant is used to solve nonlinear programming problems. The local convergence of these variants is proved. An application to a large-scale benchmark problem that originates from nonlinear model predictive control of a hydro power plant is implemented to examine the performance of the algorithms.

关键词： predictor-corrector path-following sequential convex programming adjoint-based optimization parametric nonlinear programming online optimization

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Indirect sequential convex programming for mars entry terminal altitude maximization

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ACTA ASTRONAUTICA 2023年第1期211卷 909-919页

作者： Liu, Xu Li, Shuang Xin, Ming Nanjing Univ Aeronaut & Astronaut Dept Aerosp Control Engn Nanjing 211106 Peoples R China Nanchang Univ Sch Informat Engn Nanchang 330031 Peoples R China Univ Missouri Dept Mech & Aerosp Engn Columbia MO 65211 USA

The uniform trigonometrization method (UTM) faces two difficulties in solving the Mars entry problem with maximum terminal altitude. One is that two possible solutions need to be evaluated by Pontryagin's minimum principle (PMP). The other one is that using numerical continuation logic to solve the Hamiltonian two-point boundary value problem (TPBVP) involves a significant amount of computation. To overcome these two chal-lenges, indirect sequential convex programming (ISCP), which combines the UTM and sequential convex pro-gramming (SCP), is developed in this article. The proposed method first modifies the two control options into a single solution, which eliminates the requirement for PMP evaluation. The nonlinear TPBVP resulted from the improved UTM is then relaxed into a convex programming problem that is established by introducing the virtual control and buffer. Subsequently, the SCP process generates a numerical solution to the Mars entry problem within a short time. Compared to the general pseudospectral method and UTM, simulations demonstrate the effectiveness and efficiency of the ISCP method for longitudinal Mars entry missions with or without path constraints.

关键词： Mars entry terminal altitude maximization Uniform trigonometrization method sequential convex programming Indirect method Two-point boundary value problem

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Mid-Course Trajectory Optimization for Short-Range Head-On Engagement via sequential convex programming

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IEEE ACCESS 2024年 12卷 172046-172060页

作者： Kwon, Hyuck-Hoon Park, Jang-Seong Kim, Jeong-Hun Han, Yong-Su LIG Nex1 Global PGM Syst Design Ctr Seongnam Si 16911 South Korea

If an aerial defense missile with a limited strapdown field-of-view (FOV) is launched with a restricted launch angle against an incoming target at high altitude, there are significant difficulties in establishing an appropriate collision course for head-on engagement. Owing to the time-varying characteristics of the initial phase with several linear and nonlinear constraints, the analytical approach is unsuitable for obtaining the optimal solution. In this paper, a mid-course trajectory for short-range head-on engagement was generated using a convex programming approach. The time-varying characteristics of mass and velocity were considered based on the thrust profile, and the maximum flight path angle was limited as an additional constraint to prevent excessive trajectory shaping. The original nonlinear optimization problem was converted into a convex optimization problem with state augmentation, linearization, and lossless convexification. For lossless convexification, a modified optimization problem with a regularization term is suggested, and it is proved based on the maximum principal of optimal control theory. The numerical results of the modified optimization problem show that the proposed approach is effective for head-on engagement, ensuring lossless convexification. Finally, the results of the convex programming approach were compared with those of state-of-the-art nonlinear programming for verification.

关键词： Missiles Optimal control convex functions programming Trajectory optimization Navigation Radar tracking Geometry Drones Convergence Head-on trajectory ground-to-air missiles lossless convexification sequential convex programming short-range engagement

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Trajectory optimization with obstacles avoidance via strong duality equivalent and hp-pseudospectral sequential convex programming

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OPTIMAL CONTROL APPLICATIONS & METHODS 2022年第2期43卷 566-587页

作者： Xia, Weibo Wang, Weihong Gao, Chuan Beihang Univ Sch Automat Sci & Elect Engn Beijing Peoples R China China North Ind Grp Corp Nav & Control Res Inst Beijing Peoples R China

A trajectory optimization algorithm is developed in this article to compute a trajectory that avoids obstacles for an unmanned aerial vehicle and minimize the load factor. Quadratic and polyhedron obstacles are both considered in this article. To satisfy the safety distance requirements in engineering practice, a distance-based obstacle avoidance constraint is formulated, which restricts the minimum distance that a vehicle can approach the obstacle. Strong duality equivalent converts the constraints into equivalent forms without introducing binary variables. Subsequently, the trajectory optimization problem is numerically solved via a hp-pseudospectral sequential convex programming method, which iteratively solves a sequence of second-order cone programming subproblems until convergence is attained. Furthermore, a modified trust-region constraint and a customized nominal trajectory update rule are proposed to accelerate the convergence of the algorithm. A group of simulations are performed to demonstrate that the algorithm is computationally efficient and capable of generating a trajectory that satisfies safety distance requirements, preventing conservativeness in the trajectory, reducing the incidence of intersample constraints violation.

关键词： hp-pseudospectral method obstacle avoidance sequential convex programming strong duality trajectory optimization

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Hybrid-order soft trust region-based sequential convex programming for reentry trajectory optimization

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ADVANCES IN SPACE RESEARCH 2024年第6期73卷 3195-3208页

作者： Xie, Lei Zhou, Xiang Zhang, Hong -Bo Tang, Guo-Jian Natl Univ Def Technol Coll Aerosp Sci & Engn Changsha 410073 Hunan Peoples R China Natl Univ Def Technol Hunan Prov Key Lab Aerosp Cross Domain Flight Vehi Changsha 410073 Hunan Peoples R China

Due to the complex aerodynamic effects, the reentry trajectory optimization problem is highly nonlinear. When using sequential convex programming (SCP) methods to solve it, the iteration solution is difficult to converge. To improve this, we propose a hybrid -order soft trust region -based SCP method. We analyze the penalty effect of typical trust regions. Based on the analysis, we develop a hybridorder soft trust region combining a small -weight first -order component and a higher -order components. To solve the subproblem reliably and effectively, we equivalently reformulate it as a second -order cone programming (SOCP) form through the relaxation technique. Combined with the line search method, we further design an SCP algorithm with guaranteed convergence under some assumptions. In the numerical simulations, the effectiveness and robustness of the proposed method have been verified using a nominal case and 200 Monte Carlo cases. (c) 2023 COSPAR. Published by Elsevier B.V. All rights reserved.

关键词： Reentry trajectory sequential convex programming Soft trust region Penalty effect

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Rapid ascent trajectory optimization for guided rockets via sequential convex programming

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2019年第13期233卷 4800-4809页

作者： Zhang, Kai Yang, Shuxing Xiong, Fenfen Beijing Inst Technol Sch Aerosp Engn Beijing Peoples R China Minist Educ Key Lab Dynam & Control Flight Vehicle Beijing 100081 Peoples R China Xian Modern Control & Technol Inst Xian Shaanxi Peoples R China

A sequential convex programming algorithm is proposed to solve the complex ascent trajectory optimization problems for guided rockets in this paper. Due to the nonlinear dynamics and constraints, especially, the nonlinear thrust terms and aerodynamic drag, ascent trajectory optimization problems for guided rockets are always difficult to be solved rapidly. In this paper, first, the complex thrust terms in the dynamic equation are approximately transformed into linear (convex) functions of the angle of attack. Secondly, the nonlinear drag coefficient is transformed into a linear (convex) function of design variables by introducing two new control variables. The relaxation technique is used to relax the constraints between the control variables to avoid non- convexity, and the accuracy of the relaxation is proved using the optimal control theory. Then, nonconvex objective functions and dynamical equations are convexified by first-order Taylor expansions. At last, a sequential convex programming iterative algorithm is proposed to solve the ascent trajectory planning problem accurately and rapidly. The ascent trajectory optimization problem for the terminal velocity maximum is simulated comparing with the general pseudospectral optimal control software method, which demonstrates the effectiveness and rapidity of the proposed method.

关键词： Ascent trajectory optimization guided rockets sequential convex programming complex thrust terms and nonlinear drag optimal control theory

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Receding horizon guidance and control using sequential convex programming for spacecraft 6-DOF close proximity

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AEROSPACE SCIENCE AND TECHNOLOGY 2019年第Apr.期87卷 459-477页

作者： Zhou, Ding Zhang, Yanquan Li, Shunli Harbin Inst Technol Sch Astronaut Harbin 150001 Heilongjiang Peoples R China

This paper presents a receding horizon implementation of sequential convex programming for the spacecraft six-degree-of-freedom close proximity to a non-cooperative target satellite. With linearized relative translational dynamics and newly derived discrete rotational equations in terms of modified Rodrigues parameters, nonlinear system dynamics of the original optimal guidance and control problem for proximity are converted into convex ones for sequentially planning. The nonconvex constraint on field-of-view of the visual sensor pointing with coupled attitude and relative position is then approximately relaxed as a convex standard second-order cone, and concave spherical and ellipsoidal obstacle regions respectively around the target's body and solar arrays are convexified by affine constraints in terms of tangent planes. The original nonlinear optimal guidance and control problem is accordingly transformed into a series of second-order cone programming sub-problems via iteratively successive convexification with the trust region constraints, and sequentially solved using disciplined convex programming method. A close-loop guidance and control using the proposed sequential convex programming scheme is then demonstrated by means of receding horizon to robustly drive the spacecraft maneuvering close to the target. Numerical simulations and results reveal that the proposed method provides rapid and reliable guidance and control performance for six-degree-of-freedom close proximity and shows the potential for on-board implementations in real-time applications. (C) 2019 Elsevier Masson SAS. All rights reserved.

关键词： sequential convex programming 6-DOF close proximity Receding horizon control Spacecraft guidance Modified Rodrigues parameters

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sequential convex programming method using adaptive mesh refinement for entry trajectory planning problem

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AEROSPACE SCIENCE AND TECHNOLOGY 2021年 109卷 106374-106374页

作者： Zhou, Xiang He, Rui-Zhi Zhang, Hong-Bo Tang, Guo-Jian Bao, Wei-Min Natl Univ Def Technol Coll Aerosp Sci & Engn Changsha 410073 Peoples R China China Aerosp Sci & Technol Corp Beijing 100048 Peoples R China

sequential convex programming method is one of the potential approaches to make trajectory generation onboard. However, the contradiction between the solution accuracy and the computational efficiency restricts its application. To overcome the difficulty, a novel sequential convex programming method based on customized adaptive mesh refinement is proposed in this paper. The main contribution includes two aspects. Firstly, a customized adaptive mesh refinement method is developed. The mesh points are adjusted adaptively based on the linearization error after each iteration, and thus the number of mesh points is changed. Secondly, an unconventional convergence condition is proposed, which can make the sequential convex programming method converges to a feasible solution of the original problem with fewer iterations. Taking the entry trajectory planning problem as an example, the simulation results show that the proposed method can decrease the number of mesh points while ensuring the feasibility of converged solution. Due to the fewer iterations, the computational time to solve the original problem is decreased. As a result, a good balance between solution accuracy and computational efficiency is achieved. (C) 2020 Elsevier Masson SAS. All rights reserved.

关键词： Adaptive mesh refinement sequential convex programming Convergence condition Entry trajectory planning

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Trajectory Optimization Using sequential convex programming with Collision Avoidance

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JOURNAL OF CONTROL AUTOMATION AND ELECTRICAL SYSTEMS 2018年第3期29卷 318-327页

作者： Ramalho, Guilherme Matiussi Carvalho, Sidney Roberto Finardi, Erlon Cristian Moreno, Ubirajara Franco Univ Fed Santa Catarina Elect & Elect Engn Dept Florianopolis SC Brazil Univ Fed Santa Catarina Automat & Syst Dept Florianopolis SC Brazil

In multi-robot systems, it is commonly used collaborative approaches to solve complex tasks faster and efficiently. In most of those approaches, the decisions are made centralized or require global information about the objective or the robots, limiting many real implementations. The present work is based on a decentralized solution for the Rendezvous problem, by using only local information about the robots and asymmetrical information about the meeting point. As the primary contribution, we propose a sequential convex programming approach to overcome the non-convexities when physical spaces are taken into account in the optimization problem, which provides the robots with the collision avoidance capability during their movement to the target point. Experiments are also performed to show the effectiveness of the proposed approach.

关键词： Consensus theory Model predictive control Nonlinear programming sequential convex programming Multi-robot systems

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