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convex Trajectory Optimization Using Thrust Regularization

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2024年第2期47卷 339-346页

作者： Morelli, Andrea Morselli, Alessandro Giordano, Carmine Topputo, Francesco Polytech Univ Milan Dept Aerosp Sci & Technol I-20156 Milan Italy

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Optimization methods for advanced design of aircraft panels: a comparison

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OPTIMIZATION AND ENGINEERING 2010年第4期11卷 583-596页

作者： Colson, Benoit Bruyneel, Michael Grihon, Stephane Raick, Caroline Remouchamps, Alain SAMTECH Sa Liege Belgium AIRBUS France Toulouse France

Advanced nonlinear analyses developed for estimating structural responses for recent applications for the aerospace industry lead to expensive computational times. However optimization procedures are necessary to quickly provide optimal designs. Several possible optimization methods are available in the literature, based on either local or global approximations, which may or may not include sensitivities (gradient computations), and which may or may not be able to resort to parallelism facilities. In this paper sequential convex programming (SCP), Derivative Free Optimization techniques (DFO), Surrogate Based Optimization (SBO) and Genetic Algorithm (GA) approaches are compared in the design of stiffened aircraft panels with respect to local and global instabilities (buckling and collapse). The computations are carried out with software developed for the European aeronautical industry. The specificities of each optimization method, the results obtained, computational time considerations and their adequacy to the studied problems are discussed.

关键词： Structural optimization sequential convex programming Derivative-free optimization Surrogate-based optimization Aeronautical engineering

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Long-Term Fuel-Optimal Collision Avoidance Maneuvers with Station-Keeping Constraints

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2024年第9期47卷 1855-1871页

作者： Pavanello, Zeno Pirovano, Laura Armellin, Roberto Univ Auckland Te Punaha Atea Space Inst Auckland Cent 20 Symonds St Auckland 1010 New Zealand

This work presents a sequential convex program method to compute fuel-optimal collision avoidance maneuvers for long-term encounters. The low-thrust acceleration model is used to account for the control, but the method can compute high-thrust maneuvers by increasing the maximum available acceleration. Dealing with the long-term conjunction poses additional challenges compared to the short-term problem because the encounter is not instantaneous. Thus, under the assumption of Gaussian statistics, the probability of collision is replaced by a simpler metric, the instantaneous probability of collision (IPoC), and a keep-out zone constraint is formulated as a continuous condition to be respected throughout the time frame of interest. The robustness of the solution is improved by introducing a constraint on the sensitivity of IPoC. Furthermore, the collision avoidance problem is coupled with the classical station-keeping requirement for geostationary Earth orbit satellites and with a return to the nominal orbit condition for low Earth orbit satellites. Even though no guarantee is given for the recovery of the global optimum solution, numerical simulations in different orbital regimes show that the proposed approach can yield a local fuel-optimal solution with a run time suitable for autonomous applications.

关键词： sequential convex programming Mathematical Optimization Collision Avoidance Algorithm Satellite Collision Satellite Maneuvers Trajectory Optimization convex Optimization Spacecraft Control Low Thrust Trajectory

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Decentralized Multi-UAV Path Planning Based on Two-Layer Coordinative Framework for Formation Rendezvous

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IEEE ACCESS 2022年 10卷 45695-45708页

作者： Cheng, Zhekun Zhao, Liangyu Shi, Zhongjiao Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China Beijing Inst Technol Sch Mechatron Engn Beijing 100081 Peoples R China

Unmanned aerial vehicle (UAV) formation rendezvous path planning problem is one of the important research topics in multiple UAV (multi-UAV) coordinated path planning. Aiming at solving low computational efficiency and poor scalability of the traditional multi-UAV path planning method, the decentralized multi-UAV path planning method suitable for obstacle environments is proposed. Firstly, the UAV rendezvous path planning problem with constraints such as the kinematics of UAVs and collision-free constraints is modeled as a non-convex optimal control problem. To minimize formation rendezvous time and energy consumption, a two-layer coordinative framework is developed to solve this problem. In the coordination layer, relying only on the information of neighboring UAVs, each UAV in the decentralized communication graph negotiates the desired flight time using a consensus protocol to achieve coordination among UAVs. In the planning layer, the initial non-convex formation rendezvous path planning problem is decoupled into several sub-problems, which can be solved in parallel by path planners distributed on each UAV using sequential convex programming. Finally, numerical simulations are carried out to verify the effectiveness and scalability of the proposed method. The results show that this decentralized multi-UAV path planning method can handle the minimum-time rendezvous path planning problem and optimize the energy consumption in flight, and the computing time does not increase significantly with the enlargement of the UAV swarm. This decentralized framework scales well with the number of UAVs and can be applied for future urban flight and supplies delivery tasks.

关键词： Path planning Autonomous aerial vehicles Planning Kinematics Task analysis programming Mathematical models Unmanned aerial vehicle path planning decentralized coordination sequential convex programming collision-free

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Robust sparse array design for adaptive beamforming against DOA mismatch

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SIGNAL PROCESSING 2018年 146卷 41-49页

作者： Wang, Xiangrong Amin, Moeness Wang, Xianghua Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China Villanova Univ Ctr Adv Commun Villanova PA 19085 USA Shandong Univ Sci & Technol Coll Elect Engn & Automat Qingdao 266590 Peoples R China

The performance of an adaptive beamformer is significantly influenced by its array configuration. The problem of optimum array configuration for minimum variance distortionless response (MVDR) beam formers has been recently investigated under the assumption of accurate estimate or prior exact knowledge of the source direction of arrival (DOA). Inaccuracies in DOA can lead to significant performance degradation. Improving the robustness of MVDR beamformers has commonly been achieved by adding appropriate constraints in the determination of beamforming weights, such as the linearly constrained minimum variance (LCMV) beamformer. This work examines the sensitivity of different sparse array configurations towards uncertainty in the source DOA. It proposes enhancing system robustness through optimizing array configurations. The sparse array design problem is formulated in terms of maximizing the output signal-to-interference-plus-noise ratio (SINR) of the MVDR and LCMV beamformers. The constrained maximization problem is expressed as the fraction of matrix determinants, and a sequential convex programming algorithm is adopted for the solution of the corresponding non-convex problem. Numerical examples are presented to validate the robustness of configured sparse array MVDR and LCMV beamformers for small errors in source directional angles. (C) 2017 Elsevier B.V. All rights reserved.

关键词： MVDR Beamforming LCMV Beamforming Robust sparse array Angle uncertainty sequential convex programming

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Uncertain trajectory planning integrating polynomial chaos and convex programming

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART G-JOURNAL OF AEROSPACE ENGINEERING 2022年第12期236卷 2544-2564页

作者： Tan, Yiting Jing, Wuxing Gao, Changsheng Harbin Inst Technol Sch Astronaut Harbin 150001 Peoples R China

The present work explores the robust trajectory optimization scheme considering both the initial state disturbance and multiple constraints. An uncertain multi-constraint optimization model has been first established. Due to the existence of the stochastic disturbance, standard numerical trajectory planning algorithms cannot be directly applied to address the considered issue. Hence, based on the intrusive polynomial chaos expansion, we present a deterministic quantification for the stochastic state and constraints, so that the transformed optimization model becomes solvable for standard numerical optimization methods. To obtain the enhanced computational performance, an hp pseudo-spectral sequential convex programming procedure combined with a penalty function and backtracking search is proposed. This is achieved by discretizing and convexifying the nonlinear dynamics/constraints using hp quadrature collocation and successive linearization, respectively, and by adjusting the confidence region manually in the iteration. The simulation of a three-dimensional interception with the specific impact angle is conducted to verify the effectiveness. The simulation results show that the initial solutions are insensitive to the convex optimization, and the control commands generated by the proposed algorithm are effective against the initial state disturbance.

关键词： Initial state disturbance uncertainness quantification generalized polynomial chaos expansion sequential convex programming HP pseudo-spectral collocation penalty function technique

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Topology optimisation of crankshaft for weight reduction possibility in farming tractor

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INTERNATIONAL JOURNAL OF MATERIALS & PRODUCT TECHNOLOGY 2021年第3期63卷 212-227页

作者： Giridharadhayalan, M. Ramkumar, T. Selvakumar, M. Dr Mahalingam Coll Engn & Technol Dept Mechatron Engn Pollachi 642003 India Dr Mahalingam Coll Engn & Technol Dept Mech Engn Pollachi 642003 India Dr Mahalingam Coll Engn & Technol Dept Automobile Engn Pollachi 642003 India

The crankshaft is one of the heaviest parts of farm tractor which contributes around 11% total weight of vehicle. This research aims to optimise the lightweight model of internal combustion diesel engine crankshaft for better fuel economy of the farm tractor. Lightweight design of the crankshaft is carried out by sequential convex programming (SCP)-based topology optimisation. This optimisation is performed using minimum compliance as objective function and percentage of volume from 50% to 90% as response constraints. Analysis is carried out for optimisation results through ANSYS Workbench finite element analysis software. Optimised crankshaft model with feasible design and possible manufacturability is subjected for design validation to ensure strength. Von-Misses stress and total deformation of the volume fraction 90% optimised model are slightly higher compared to the benchmark model, but ensures good structural rigidity and factor of safety. Optimised crankshaft model results about 8% weight reduction in the existing crankshaft model by considering all factors influencing design and manufacturing.

关键词： crankshaft weight reduction sequential convex programming SCP topology optimisation

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Optimal trajectories and normal load analysis of hypersonic glide vehicles via convex optimization

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AEROSPACE SCIENCE AND TECHNOLOGY 2019年第Apr.期87卷 357-368页

作者： Wang, Zhenbo Univ Tennessee Mech Aerosp & Biomed Engn Dept Knoxville TN 37996 USA

Hypersonic trajectory optimization has been intensively investigated through different approaches;however, the normal-load-optimal entry problems were barely studied and reported in the literature. Finding the optimal trajectories with maximum or minimum peak normal load is essential to evaluate the maneuverability and structural strength of the vehicle. In this paper, both the maximum and minimum peak-normal-load entry trajectories are explored using convex optimization. Based on the previous work, the maximum-peak-normal-load entry problem is firstly addressed by a Big-M method and a line-search approach. Through successive relaxations, the nonconvex discrete-event optimal control problem associated with maximum-peak-normal-load entry is transformed into a sequence of mixed-integer convex optimization problems. Then, a line-search technique is introduced to improve the convergence of the proposed method. Additionally, a sequential convex programming method is designed to solve the minimum-peak-normal-load entry problem to comprehensively analyze the normal load during the entry flight. There are efficient solvers that can solve each relaxed convex subproblem with a global optimum if the feasible set of the subproblem is nonempty. The convergence and accuracy of the proposed methodologies are demonstrated by numerical simulations, and the feasibility of the converged solutions is discussed based on an entry-corridor approach. (C) 2019 Elsevier Masson SAS. All rights reserved.

关键词： Hypersonic vehicles Trajectory optimization convex optimization Mixed-integer programming sequential convex programming

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Stochastic Trajectory Planning for Autonomous Aerobraking Using convex Optimization and Covariance Control

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2024年第8期47卷 1521-1541页

作者： Zhao, Zichen Shang, Haibin Yu, Zhitong Ren, Junjie Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China Lunar Explorat & Space Engineer Ctr Beijing 100190 Peoples R China

Trajectory planning for autonomous aerobraking poses significant technical challenges, primarily due to the complexities associated with ensuring reliable onboard computation, mitigating flying uncertainty, enhancing aerodeceleration efficacy, and guaranteeing sufficient precision. To address this issue, this paper utilizes convex optimization for the first time to synchronously generate an anti-uncertainty trajectory and corresponding closed-loop controller with efficient, robust, and high-precision computational capability. Specifically, a double-loop planning framework is developed. In the inner loop, techniques of covariance control and linear covariance analysis are employed to give rise to a stochastic trajectory planning problem that optimizes the orbiter's capacity to withstand and overcome deviations during flight. Furthermore, for onboard planning considerations, the problem's nonlinearity is equivalently reduced by projecting the time-independent variable into the altitude variable. On this basis, a novel state-complete linearization method is introduced to enable the utilization of sequential convex programming with improved convergence. For the outer loop, the orbiter's motion is decomposed into low-accuracy longitudinal and high-precision dynamics. A differential-correction-based technique is specifically designed to remedy the dynamics in turn. Numerical simulations demonstrate that the proposed method can reduce mission risk by at least 70% while only experiencing an additional cost of velocity impulse amounting to 20%.

关键词： Mathematical Optimization Aerobraking and Aerocapture Model Predictive Control sequential convex programming Numerical Simulation Orbital Eccentricity Flight Path Angle Aerodynamic Coefficients Aerodynamic Performance Planets

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SCPIP - an efficient software tool for the solution of structural optimization problems

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2002年第5期24卷 362-371页

作者： Zillober, C Univ Bayreuth Inst Math D-95440 Bayreuth Germany

This paper describes SCPIP, a FORTRAN77 subroutine that has been proven to be a reliable implementation of convex programming methods in an industrial environment. convex approximation methods like the method of moving asymptotes are used nowadays in many software packages for structural optimization. They are known to be efficient tools for the solution of design problems, in particular if displacement dependent constraints like stresses occur. A major advantage over many but not all classical approaches of mathematical programming is that at an iteration point a local model is formulated. For the solution of such a model no further function and gradient evaluations are necessary besides those at the current iteration point. The first versions of convex approximation methods used all a dual approach to solve the subproblems which is still a very efficient algorithm to solve problems with at most a medium number of constraints. But it is not efficient for problems with many constraints. An alternative is the use of an interior point method for the subproblem solution. This leads to more freedom in the definition of the linear systems where most of the computing time to solve the subproblems is spent. In consequence, large-scale problems can be handled more efficiently.

关键词： convex approximation methods method of moving asymptotes sequential convex programming structural optimization large-scale optimization

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