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Improved sequential convex programming using modified Chebyshev-Picard iteration for ascent trajectory optimization

AEROSPACE SCIENCE AND TECHNOLOGY 2022年第0期120卷 107234-107234页

作者： Ma, Yangyang Pan, Binfeng Hao, Chuanchuan Tang, Shuo Northwestern Polytech Univ Sch Astronaut Xian 710072 Peoples R China Northwestern Polytech Univ Natl Key Lab Aerosp Flight Dynam Xian 710072 Peoples R China Shanghai Inst Aerosp Syst Engn Shanghai 201109 Peoples R China

This paper presents an improved sequential convex programming (SCP) algorithm for ascent trajectory optimization of launch vehicles, by exploiting the state-of-the-art modified Chebyshev-Picard iteration (MCPI) technique. In the proposed algorithm, the MCPI technique is first utilized to transcribe the continuous-time optimization problem into a sequence of finite-dimensional subproblems. The lossless and successive convexification techniques are then employed to deal with the nonconvexity in optimization. The resulting convex subproblems can be reliably and efficiently solved via a primal-dual interior-point method solver. Numerical simulations for a minimum-time ascent trajectory optimization problem are conducted and the results show that the proposed algorithm has significant improvements over the standard SCP (which uses the Euler or trapezoidal rule for discretization), pseudospectral SCP, and GPOPS. (C) 2021 Elsevier Masson SAS. All rights reserved.

关键词： Launch vehicle Trajectory optimization sequential convex programming Modified Chebyshev-Picard iteration

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hp-Adaptive RPD based sequential convex programming for reentry trajectory optimization

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AEROSPACE SCIENCE AND TECHNOLOGY 2022年第0期130卷

作者： Zhang, Tengfei Su, Hua Gong, Chunlin Northwestern Polytech Univ Sch Astronaut Shaanxi Aerosp Flight Vehicle Design Key Lab Xian 710072 Peoples R China

sequential convex programming (SCP) methods have been developed to solve reentry trajectory optimization problems. Due to the oversimplified discretization and iteration, the accuracy and efficiency of the existing SCP methods can be further improved. In this paper, a SCP algorithm based on the hpadaptive Radau pseudospectral discretization (RPD) is proposed. In the proposed algorithm, the iteration process is divided into three stages depending on the characteristics of subproblems. The constraint relaxation technique is applied in the first stage to ensure that the iteration is stable. During the second stage, the number and position of discretized points will be updated adaptively according to the discretization error and the curvature of state. In the last stage, the linearization error is reduced by several iterations without updating mesh, and the regularization technique is utilized to improve the convergence rate of this process. The proposed algorithm is validated and examined by a typical reentry example. With comparable or even higher results accuracy, the CPU time reduced by 40%-70% when compared to other SCP methods, and is only twentieth of that of GPOPS-II. (c) 2022 Elsevier Masson SAS. All rights reserved.

关键词： Reentry Trajectory optimization sequential convex programming hp -adaptive Radau pseudospectral

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Weight-adaptive augmented Lagrange multiplier sequential convex programming for nonlinear trajectory optimization

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AEROSPACE SCIENCE AND TECHNOLOGY 2024年 155卷

作者： Dong, Cheng-Long Xie, Lei He, Rui-Zhi Zhou, Xiang Zhang, Hong-Bo Natl Univ Def Technol Coll Aerosp Sci & Engn Changsha 410073 Peoples R China

sequential convex programming has become a prominent research focus in aerospace trajectory optimization due to its high computational efficiency. One critical challenge in sequential convex programming is the infeasibility of subproblems, which significantly impacts its stability. To address this issue, certain constraints must be relaxed using relaxation variables, which are then incorporated into the objective function as a penalty term. However, the choice of penalty weight greatly influences the optimality and convergence of sequential convex programming. Therefore, this paper proposes a weight-adaptive augmented Lagrange multiplier sequential convex programming algorithm to tackle the challenge. First, this paper analyzes the difficulty of determining an appropriate penalty weight from the perspective of its penalty effect. Based on this analysis, an augmented penalty term is introduced, and the update rule for the augmented Lagrange multiplier is formulated using the Karush-Kuhn-Tucker conditions. Subsequently, a method with adaptive weight adjustment is designed based on the change in the penalty term to further improve the algorithm's solving speed. Finally, the proposed method is validated through numerical simulations in a Mars-powered landing problem and a small glide vehicle reentry problem. The results show that the proposed method is 20.59 % and 25.16 % faster compared to the general sequential convex programming algorithm, respectively. Furthermore, the proposed method is demonstrated to be robust to the initial choice of penalty weight.

关键词： sequential convex programming Trajectory optimization Penalty weight

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A sequential convex SEMIDEFINITE programming ALGORITHM WITH AN APPLICATION TO MULTIPLE-LOAD FREE MATERIAL OPTIMIZATION

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SIAM JOURNAL ON OPTIMIZATION 2009年第1期20卷 130-155页

作者： Stingl, M. Kocvara, M. Leugering, G. Univ Erlangen Nurnberg Inst Appl Math D-91058 Erlangen Germany Acad Sci Czech Republ Inst Informat Theory & Automat CR-18208 Prague 8 Czech Republic Univ Birmingham Sch Math Birmingham B15 2TT W Midlands England

A new method for the efficient solution of a class of convex semidefinite programming (SDP) problems is introduced. The method extends the sequential convex programming (SCP) concept to optimization problems with matrix variables. The basic idea of the new method is to approximate the original optimization problem by a sequence of subproblems, in which nonlinear functions (defined in matrix variables) are approximated by block separable convex functions. The subproblems are semidefinite programs with a favorable structure which can be efficiently solved by existing SDP software. The new method is shown to be globally convergent. The article is concluded by a series of numerical experiments with free material optimization problems demonstrating the effectiveness of the generalized SCP approach.

关键词： structural optimization material optimization semidefinite programming sequential convex programming

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Nonlinear robust optimization via sequential convex bilevel programming

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MATHEMATICAL programming 2013年第1-2期142卷 539-577页

作者： Houska, Boris Diehl, Moritz Katholieke Univ Leuven Optimizat Engn Ctr OPTEC B-3001 Louvain Belgium

In this paper, we present a novel sequential convex bilevel programming algorithm for the numerical solution of structured nonlinear min-max problems which arise in the context of semi-infinite programming. Here, our main motivation are nonlinear inequality constrained robust optimization problems. In the first part of the paper, we propose a conservative approximation strategy for such nonlinear and non-convex robust optimization problems: under the assumption that an upper bound for the curvature of the inequality constraints with respect to the uncertainty is given, we show how to formulate a lower-level concave min-max problem which approximates the robust counterpart in a conservative way. This approximation turns out to be exact in some relevant special cases and can be proven to be less conservative than existing approximation techniques that are based on linearization with respect to the uncertainties. In the second part of the paper, we review existing theory on optimality conditions for nonlinear lower-level concave min-max problems which arise in the context of semi-infinite programming. Regarding the optimality conditions for the concave lower level maximization problems as a constraint of the upper level minimization problem, we end up with a structured mathematical program with complementarity constraints (MPCC). The special hierarchical structure of this MPCC can be exploited in a novel sequential convex bilevel programming algorithm. We discuss the surprisingly strong global and locally quadratic convergence properties of this method, which can in this form neither be obtained with existing SQP methods nor with interior point relaxation techniques for general MPCCs. Finally, we discuss the application fields and implementation details of the new method and demonstrate the performance with a numerical example.

关键词： Robust optimization Mathematical programming with complementarity constraints Bilevel optimization Semi-infinite optimization sequential convex programming

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A method of sequential log-convex programming for engineering design

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OPTIMIZATION AND ENGINEERING 2023年第3期24卷 1719-1745页

作者： Karcher, Cody Haimes, Robert MIT Dept Aeronaut & Astronaut 77 Massachusetts Ave Cambridge MA 02139 USA

A method of sequential Log-convex programming (SLCP) is constructed that exploits the log-convex structure present in many engineering design problems. The mathematical structure of Geometric programming (GP) is combined with the ability of sequential Quadratic Program (SQP) to accommodate a wide range of objective and constraint functions, resulting in a practical algorithm that can be adopted with little to no modification of existing design practices. Three test problems are considered to demonstrate the SLCP algorithm, comparing it with SQP and the modified Logspace sequential Quadratic programming (LSQP). In these cases, SLCP shows up to a 77% reduction in number of iterations compared to SQP, and an 11% reduction compared to LSQP. The airfoil analysis code XFOIL is integrated into one of the case studies to show how SLCP can be used to evolve the fidelity of design problems that have initially been modeled as GP compatible. Finally, a methodology for design based on GP and SLCP is briefly discussed.

关键词： Geometric programming Log-convexity Non-linear programming sequential quadratic programming sequential convex programming

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Online Reentry Trajectory Optimization for Hypersonic Vehicles Using Radau Pseudospectral sequential convex programming

Online Reentry Trajectory Optimization for Hypersonic Vehicl...

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第43届中国控制会议

作者： Zhifei Song Junjie Liu Yuehui Ji Haobo Zhang Junchi Wang Qiang Gao Tianjin Key Laboratory of Control Theory and Application for Complex Systems Maritime College Tianjin University of Technology

ISBN: (数字)9789887581581

ISBN: (纸本)9798350366907

In this paper,an online trajectory optimization scheme is proposed to address the uncertainties and mission changes in hypersonic vehicle reentry trajectory *** combining Radau pseudospectral method and sequential convex programming(SCP),the discretization accuracy and solution speed of the trajectory optimization algorithm are ***,the downrange angle is used as the independent variable in the equations of motion to implement the free time trajectory optimization *** initial trajectory generation method is proposed,which makes the trajectory's terminal state close to the terminal position and thus reduces the number of algorithm optimization ***,the compensation and regularization terms are used,respectively,to maintain the feasibility of the trajectory optimization problem and to improve the convergence rate of the *** the end,the proper trajectory optimization period is set,and the interior-point method is used to solve the reentry trajectory optimization *** simulations demonstrate the validity of the algorithm and online reentry trajectory optimization scheme proposed in this paper.

关键词： Radau pseudospectral method Hypersonic vehicle sequential convex programming Online reentry trajectory optimization

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Rapid Nonlinear convex Guidance Using a Monomial Method

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2025年第4期48卷 736-756页

作者： Burnett, Ethan R. Topputo, Francesco Polytech Univ Milan Dept Aerosp Sci & Technol Via La Masa 34 I-20156 Milan Italy

This paper addresses the challenge of accommodating nonlinear dynamics and constraints in rapid trajectory optimization with impulsive maneuvers, envisioned for use in the context of onboard guidance. We present a novel framework that uniquely employs overparameterized monomial coordinates and precomputed fundamental solution expansions to facilitate rapid optimization while minimizing real-time computational requirements. The fundamental solution expansions are precomputed about an uncontrolled reference trajectory using differential algebra. Unlike traditional approaches that repeatedly evaluate the nonlinear dynamics and constraints as part of complex shooting or collocation-based schemes, this method replaces the nonlinearity inherent to dynamics and constraint functions entirely with a computationally simpler manifold constraint. With this approach, trajectory optimization is posed efficiently as a path-planning problem on the manifold. This problem is entirely convex except for the manifold constraint, readily lending itself to solution via sequential convex programming. We demonstrate the effectiveness of our approach in computing fast and accurate Delta V optimal solutions for long-range spacecraft rendezvous, including problems with nonlinear state constraints.

关键词： Orbital Mechanics Structural Kinematics and Dynamics Optimal Control Problem Spacecraft Rendezvous Computing and Informatics sequential convex programming Robot Kinematics Mathematical Optimization Spacecraft Trajectory Optimization Control Theory

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Low-thrust under-actuated satellite formation guidance and control strategies

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ACTA ASTRONAUTICA 2025年 232卷 405-423页

作者： Mahfouz, Ahmed Gaias, Gabriella Dalla Vedova, Florio Voos, Holger Univ Luxembourg SnT 29 Ave JF Kennedy L-1855 Luxembourg Luxembourg Politecn Milan Dept Aerosp Sci & Technol 34 Via Masa I-20156 Milan Italy LuxSpace 9 Rue Pierre Werner L-6832 Betzdorf Luxembourg Univ Luxembourg Fac Sci Technol & Med 2 Pl Univ L-4365 Esch Sur Alzette Luxembourg

This study presents autonomous guidance and control strategies for reconfiguring close-range multi-satellite formations. The formation consists of N under-actuated deputy satellites and an uncontrolled virtual or physical chief spacecraft. Each deputy is equipped with a single throttleable but ungimbaled low-thrust nozzle, requiring a combination of thrust and coast arcs, during the latter attitude adjustments redirect the nozzle to the desired thrust direction. The guidance problem is formulated as a trajectory optimization task incorporating dynamical and physical constraints, along with a minimum acceleration threshold imposed by typical electric thrusters. Two frameworks are considered: centralized and distributed. The centralized approach ensures fuel-optimal solutions but is feasible only for small formations, with all calculations performed on a physical chief satellite. The distributed approach, while sub-optimal, scales better by treating the chief as a virtual point mass and allowing each deputy to handle its own computations. This study focuses on spaceborne closed-loop control implementation, ensuring reliability and automation in solving the optimal control problem. To mitigate infeasibility risks, constraints that pose potential threats are identified and softened. Two Model Predictive Control architectures, shrinking-horizon and fixed-horizon, are implemented and compared in terms of fuel consumption and control accuracy. Their performance is analyzed for typical close-range reconfigurations required in Earth observation missions and benchmarked against existing approaches in the literature.

关键词： Formation flying Relative orbital elements Relative trajectory optimization convexification convex optimization sequential convex programming Model Predictive Control Distributed systems

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Combined Long-Term Collision Avoidance and Stochastic Station-Keeping in Geostationary Earth Orbit

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2025年第4期48卷 840-854页

作者： De Vittori, Andrea Pavanello, Zeno Di Lizia, Pierluigi Mcmahon, Jay Armellin, Roberto Polytech Univ Milan I-20156 Milan Italy Univ Auckland Auckland 1010 New Zealand Univ Colorado Boulder Ann & HJ Smead Aerosp Engn Sci 3775 Discovery Dr Boulder CO 80303 USA Politecn Milan Dept Aerosp Sci & Technol Via Privata Giuseppe La Masa 34 I-20156 Milan Italy Te Punaha Atea Space Inst 20 Symonds St Auckland 1010 New Zealand

To limit the spread of space debris, space situational awareness (SSA) delineates guidelines to preserve current space assets. Developing effective collision avoidance maneuver (CAM) strategies is emerging as a global top priority among the considered countermeasures to debris-generating events. Despite most encounters happening over very short time frames, some conjunctions occur over a longer time window, such as in geostationary Earth orbit (GEO), where the involved objects may have small relative velocities. Besides, external perturbations, particularly the geopotential, lunisolar, and solar radiation pressure ones, exert forces on the spacecraft, causing it to deviate from its designated slot and potentially endanger neighboring satellites. This issue is compounded when considering state uncertainty. The presented work, therefore, introduces convex optimization approaches for long-term CAM and tailored stochastic station-leeping (SK) policy regarding longitude and latitude in this regime. The formulation enables continuous CAM and chance-constrained SK, ensuring satellite adherence to an assigned GEO slot with a given probability. Two kinds of chance constraints are devised: the first one does not consider the correlation between longitude and latitude, but the latter does.

关键词： Active Satellites Space Debris Earth Centered Inertial Orbital Station Keeping Stochastic Optimal Control sequential convex programming Geostationary Orbit Chance Constraint Optimization Long-Term Collision Avoidance

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