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LCQPow: a solver for linear complementarity quadratic programs

MATHEMATICAL programming COMPUTATION 2025年第1期17卷 81-109页

作者： Hall, Jonas Nurkanovic, Armin Messerer, Florian Diehl, Moritz Boston Univ Div Syst Engn Boston MA 02215 USA Univ Freiburg Dept Microsyst Engn IMTEK Freiburg Germany

In this paper we introduce an open-source software package written in C++ for efficiently finding solutions to quadratic programming problems with linear complementarity constraints. These problems arise in a wide range of applications in engineering and economics, and they are challenging to solve due to their structural violation of standard constraint qualifications, and highly nonconvex, nonsmooth feasible sets. This work extends a previously presented algorithm based on a sequential convex programming approach applied to a standard penalty reformulation. We examine the behavior of local convergence and introduce new algorithmic features. Competitive performance profiles are presented in comparison to state-of-the-art solvers and solution variants in both existing and new benchmarks.

关键词： Optimization Complementarity constraints sequential convex programming Hybrid 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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Delta-V-optimal centralized guidance strategy for under-actuated N-satellite formations

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ACTA ASTRONAUTICA 2025年 228卷 69-87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 La 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 paper addresses the computation of Delta-V-optimal, safe, relative orbit reconfigurations for satellite formations in a centralized fashion. The formations under consideration comprise an uncontrolled chief spacecraft flying with an arbitrary number, N , of deputy satellites, where each deputy is equipped with a single electric thruster. Indeed, this represents a technological solution that is becoming widely employed by the producers of small-satellite platforms. While adopting a single electric thruster does reduce the required power, weight, and size of the orbit control system, it comes at the cost of rendering the satellite under- actuated. In this setting, the satellite can provide a desired thrust vector only after an attitude maneuver is carried out to redirect the thruster nozzle opposite to the desired thrust direction. In order to further extend the applicability range of such under-actuated platforms, guidance strategies are developed to support different reconfiguration scenarios for N-satellite formations. This paper starts from a classical non-convex quadratically constrained trajectory optimization formulation, which passes through multiple simplifications and approximations to arrive to two novel convex formulations, namely a second-order cone programming formulation, and a linear programming one. Out of five guidance formulations proposed in this article, the most promising three were compared through an extensive benchmark analysis that is applied to fifteen of the most widely-used solvers. This benchmark experiment provides information about the key distinctions between the different problem formulations, and under which conditions each one of them can be recommended.

关键词： Formation flying Relative Orbital Elements Relative trajectory optimization convexification convex optimization sequential convex programming

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Fuel-Optimal Formation Reconfiguration by Means of Unidirectional Low-Thrust Propulsion System

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2025年第2期48卷 404-413页

作者： Mahfouz, Ahmed Gaias, Gabriella Vedova, Florio Dalla Voos, Holger Univ Luxembourg Interdisciplinary Ctr Secur Reliabil & Trust 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 6 Rue Richard Coudenhove Kalergi29 Ave JF Kennedy L-1359 Luxembourg Luxembourg

The use of electric low-thrust propulsion systems for orbit maneuvers is becoming a popular choice among satellite manufacturers due to their inherent merits over their chemical counterparts. Many designers choose to incorporate multiple of such thrusters to insure omnidirectional orbit maneuverability, while others choose to equip their satellite with only one thruster nozzle, aiming to reduce the required power, weight, and size of the orbit control system. This paper proposes guidance and control schemes to address the problem of autonomous optimal relative orbit reconfiguration for a formation of two satellites, one of which utilizes a single low-thrust throttleable nozzle. Such under-actuated orbit control system requires the controlled spacecraft to constantly slew to direct the nozzle to the desired thrust direction. These redirection attitude maneuvers are treated within the guidance layer by accommodating recurrent no-thrust periods during which slew maneuvers take place. The control loop is then closed with an MPC-like scheme. The main motivation of this article is to support the future missions of LuxSpace's flagship satellite, Triton-X. Since the proposed guidance and control schemes are meant to answer realistic market needs, they are designed to have some specific qualities that makes them attractive from the practical point of view. Namely, they require minimal computational loads, besides being able to accommodate operational time constraints, e.g. no thrusting during eclipse or during ground contact, within the guidance layer.

关键词： Small Satellites Model Predictive Control Trajectory Optimization convex Optimization sequential convex programming Autonomous Guidance and Control Formation Flying Low Thrust Propulsion

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Efficient optimization method for variable-specific-impulse low-thrust trajectories with shutdown constraint

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Science China(Technological Sciences) 2022年第3期65卷 581-594页

作者： JIA FeiDa QIAO Dong HAN HongWei LI XiangYu School of Aerospace Engineering Beijing Institute of TechnologyBeijing 100081China Key Laboratory of Autonomous Navigation and Control for Deep Space Exploration Ministry of Industry and Information TechnologyBeijing 100081China

This paper develops a sequential convex programming(SCP)-based method to solve the minimum-fuel variable-specific-impulse low-thrust transfer problem considering shutdown constraint,with emphasize on improving the computational *** variable parameter engine is more applicable for many low-thrust scenarios,therefore,both a continuously variable model and a ladder variable model are ***,the original problem is convexified by processing the constraint feasible domain,which is composed of the nonlinear dynamic equations and second-order equality constraint,into convex ***,the approximation is generated to close the optimal solution of the low-thrust problem by iteratively solving the convexified ***,the switching self-detection and adaptive node refinement methods are presented,which can improve the accuracy of the solution and accelerate the convergence during the approximation process and is especially necessary and effective in the scenarios with shutdown *** numerical simulations,the comparison with the homotopic approach shows that the proposed method only needs 4%computational time as that of the homotopic approach,and two variable-specificimpulse examples further demonstrate the effectiveness and efficiency of the proposed method.

关键词： low-thrust trajectory variable-specific-impulse shutdown constraint sequential convex programming switching self-detection and adaptive node refinement

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An efficient method for collision-free and jerk-constrained trajectory generation with sparse desired way-points for a flying robot

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Science China(Technological Sciences) 2021年第8期64卷 1719-1731页

作者： CHEN YongXue DONG Wei DING Ye State Key Laboratory of Mechanical System and Vibration Shanghai Jiao Tong UniversityShanghai200240China

In this paper,an efficient approach is developed to plan jerk-constrained smooth trajectories passing through desired way-points with allowable accuracy for an autonomous ***,based on the B-spline model,we introduce the sequential convex programming(SCP)into the flexible path planning method to satisfy the way-points *** approximating the quadrotor and obstacles as spheres and directed planes,the length-optimal and collision-free path planning problem is formulated as a nonconvex optimization problem and solved by *** initial C^(3) continuous path curve for optimization is constructed efficiently based on a proposed strategy of generating new way-points near the obstacles without the need to calculate the embedding distance between the curve and the *** this basis,the time-optimal speed planning problem is addressed in two *** the first step,the forward-backward approach is introduced to solve the problem under the chord error,velocity,and acceleration constraints by changing the variables and deforming the *** by relaxing the constraints appropriately,the problem under jerk constraints is formulated into a linear programming(LP)*** feasibility of the proposed approach is verified through simulations and an indoor navigation *** proposed approach can generate a C^(3) continuous collision-free trajectory that passes through the sparse desired way-points with allowable accuracy while guaranteeing the chord error,velocity,acceleration,and jerk *** the number of sample points is 3000,the proposed speed planning method reduces the calculation time by 40%compared to an existing method.

关键词： collision avoidance speed optimization motion planning sequential convex programming quadrotor

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A convex programming-Based Approach to Trajectory Optimization for Survivability Enhancement of Homing Missiles

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INTERNATIONAL JOURNAL OF AERONAUTICAL AND SPACE SCIENCES 2022年第5期23卷 992-1008页

作者： Cho, Sung-Bong Choi, Han-Lim Korea Adv Inst Sci & Technol Dept Aerosp Engn Daejeon South Korea

This paper addresses trajectory optimization of a homing missile to simultaneously consider the homing performance and evasive maneuver against a defending interceptor. An optimal control problem that maximizes the miss distance from the interceptor while ensuring zero homing error is presented;the adjoint method is applied to efficiently compute the miss distance objective. Then, a sequential convex program (SCP) methodology that computes the optimized trajectory by solving a sequence of convex subproblems is adopted to obtain the optimized trajectory. Numerical examples on a homing scenario of an air-to-surface missile toward a stationary target demonstrate the validity and efficacy of the proposed convex program-based method compared to traditional nonlinear program approaches.

关键词： Trajectory optimization Evasive maneuver Survivability Homing performance Interception error Adjoint method convexification convex optimization sequential convex programming

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Dynamic Inter-Operator Spectrum Sharing via Lyapunov Optimization

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IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2017年第10期16卷 6365-6381页

作者： Joshi, Satya Krishna Manosha, K. B. Shashika Codreanu, Marian Latva-aho, Matti Univ Oulu Ctr Wireless Commun Oulu 90014 Finland

The problem of spectrum sharing between two operators in a dynamic network is considered. We allow both operators to share (a fraction of) their licensed spectrum band with each other by forming a common spectrum band. The objective is to maximize the gain in profits of both operators by sharing their licensed spectrum bands rather than using them exclusively, while considering the fairness among the operators. This is modeled as a two-person bargaining problem, and cast as a stochastic optimization. To solve this problem, we propose centralized and distributed dynamic control algorithms. At each time slot, the proposed algorithms perform the following tasks: 1) determine spectrum price for the operators;2) make flow control decisions of users data;and 3) jointly allocate spectrum band to the operators and design transmit beamformers, which is known as resource allocation (RA). Since the RA problem is NP-hard, we have to rely on sequential convex programming to approximate its solution. To derive the distributed algorithm, we use alternating direction method of multipliers for solving the RA problem. Numerically, we show that the proposed distributed algorithm achieves almost the same performance as the centralized one. Furthermore, the results show that there is a trade-off between the achieved profits of the operators and the network congestion.

关键词： Co-primary spectrum sharing dynamic control network utility maximization stochastic optimization Lyapunov drift bargaining problem fairness sequential convex programming alternating direction method of multipliers (ADMM) distributed algorithm

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Joint Component Sizing and Energy Management for Fuel Cell Hybrid Electric Trucks

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2022年第5期71卷 4863-4878页

作者： Xun, Qian Murgovski, Nikolce Liu, Yujing Chalmers Univ Technol Dept Elect Engn S-41296 Gothenburg Sweden

This paper proposes a cost-effective way to design and operate fuel cell hybrid electric trucks (FCHETs) where a chance-constrained optimization is formulated. The aim of the introduced problem is to minimize a summation of component cost and operational cost with consideration of fuel cell (FC) degradation and cycle life of energy buffer. We propose to decompose the problem into two sub-problems that are solved by sequential convex programming. The delivered power satisfies a cumulative distribution function of the wheel power demand, while the truck can still traverse driving cycles with a similar speed and travel time without delivering unnecessarily high power. This allows to downsize powertrain components, including electric machine, FC and energy buffer. A case study considering different energy buffer technologies, including supercapacitor (SC), lithium-ion battery (LiB), and lithium-ion capacitor (LiC) is investigated in a set of trucking applications, i.e. urban delivery, regional delivery, construction, and long-haul. Results show that the power rating of the electric machine is drastically reduced when the delivered power is satisfied in a probabilistic sense. Moreover, the configuration with LiB as the energy buffer has the lowest expense but the truck with LiC can carry more payload.

关键词： Energy management Electric machines Wheels Optimization Costs Fuel cells Power demand Chance-constrained energy buffer fuel cell hybrid electric trucks (FCHETs) sequential convex programming wheel power demand

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Reduction of vibration level in rotordynamics by design optimization

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STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION 2007年第2期34卷 139-149页

作者： Strauss, Frank Inagaki, Mizuho Starke, Jens Heidelberg Univ Inst Appl Math D-69120 Heidelberg Germany Toyota Cent Res & Dev Labs Inc Aichi 4801192 Japan

We focus on the reduction of the vibration level of rotors by optimizing the shape of the body. The target is to reduce rotor weight and rotor vibrations leading to higher efficiency and less noise. We consider a finite element discretization of the rotor using a Rayleigh beam model which includes rotary inertia and gyroscopic moments leading to nonself-adjoint systems. We present a general algebraic framework for this case. The mass function is the objective function of the optimization problem and constraints are set on the nonlinear and nonconvex functions of critical speed and unbalanced response. For the numerical solution, algorithms belonging to the class of sequential convex programming are applied for the example of a turbocharger. A remarkable reduction of mass of an initially given prototype could be achieved while significantly reducing the unbalanced response and raising the critical speeds.

关键词： rotating machinery gyroscopic systems vibration level shape optimization sequential convex programming

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