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Descent Property in sequential Second-Order Cone programming for Nonlinear Trajectory Optimization

JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2023年第12期46卷 2346-2361页

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

sequential second-order cone programming (SSOCP) is commonly used in aerospace applications for solving nonlinear trajectory optimization problems. The SSOCP possesses good real-time performance. However, one long-standing challenge is its unguaranteed convergence. In this paper, we theoretically analyze the descent property of the L1 penalty function in the SSOCP. Using Karush-Kuhn-Tucker conditions, we obtain two important theoretical results: 1) the L1 penalty function of the original nonlinear problem always descends along the iteration direction;2) a sufficiently small trust region can decrease the L1 penalty function. Based on these two results, we design an improved trust region shrinking algorithm with theoretically guaranteed convergence. In numerical simulations, we verify the proposed algorithm using a reentry trajectory optimization problem.

关键词： Flight Path Angle Optimization Algorithm Crew Exploration Vehicle sequential convex programming Convergence Analysis

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Voltage/VAR Control in Distribution Networks via Reactive Power Injection Through Distributed Generators

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IEEE TRANSACTIONS ON SMART GRID 2012年第3期3卷 1226-1234页

作者： Deshmukh, Siddharth Natarajan, Balasubramaniam Pahwa, Anil Kansas State Univ Dept Elect & Comp Engn Kansas City KS 66506 USA

This paper demonstrates how reactive power injection from distributed generators can be used to mitigate the voltage/VAR control problem of a distribution network. Firstly, power flow equations are formulated with arbitrarily located distributed generators in the network. Since reactive power injection is limited by economic viability and power electronics interface, we formulate voltage/VAR control as a constrained optimization problem. The formulation aims to minimize the combined reactive power injection by distributed generators, with constraints on: 1) power flow equations;2) voltage regulation;3) phase imbalance correction;and 4) maximum and minimum reactive power injection. The formulation is a nonconvex problem thereby making the search for an optimal solution extremely complex. So, a suboptimal approach is proposed based on methods of sequential convex programming (SCP). Comparing our suboptimal approach with the optimal solution obtained from branch and bound method, we show the trade-off in quality of our solution with runtime. We also validate our approach on the IEEE 123 node test feeder and illustrate the efficacy of using distributed generators as distributed reactive power resource.

关键词： convex optimization distributed generation distribution network sequential convex programming voltage/VAR control

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convex Low-Thrust Trajectory Optimization with No-Thrust Constraints and Moving Target

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JOURNAL OF SPACECRAFT AND ROCKETS 2024年第3期61卷 889-899页

作者： Hofmann, Christian Topputo, Francesco Polytech Univ Milan Dept Aerosp Sci & Technol Via La Masa 34 I-20156 Milan Italy MIT Dept Aeronaut & Astronaut Cambridge MA 02139 USA

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Safe Guidance Scheme for Proximity Operations Forced Motion

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2024年第1期48卷 1-18页

作者： Borelli, Giacomo Gaias, Gabriella Colombo, Camilla Polytech Univ Milan Dept Aerosp Sci & Technol Via La Masa 34 I-20156 Milan Italy

Autonomous spacecraft proximity operations represent a key enabler for future mission architectures such as in-orbit servicing, active debris removal, object inspection, and in-orbit assembly. This work addresses safety concepts for the relative trajectory guidance design applicable to challenging proximity operations in the close-range domain. The relative orbital element framework is used to formulate safety checks that improve the trajectory's robustness in case of chaser's malfunctions or loss of control. Particularly, concepts of passive abort safety and active collision safety are applied to the trajectory design to maintain the chaser outside keep-out zones. These definitions are included within a guidance algorithm that exploits sequential convex programming to efficiently solve the fixed final time safety-constrained close-range rendezvous problem. Test cases of reconfiguration between stable relative orbits and synchronization to a rotating hold point are presented, highlighting the advantages in using these new safety concepts in terms of safety, trajectory insight, and formulation efficiency.

关键词： sequential convex programming Guidance and Navigational Algorithms Spacecraft Guidance and Control Active Debris Removal Optimal Control Problem Satellites Flight Safety Rendezvous Guidance Autonomous Rendezvous and Docking Path-Constrained Rendezvous

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Six-Degree-of-Freedom Rocket Landing Optimization via Augmented convex-Concave Decomposition

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 2024年第1期47卷 20-35页

作者： Sagliano, Marco Seelbinder, David Theil, Stephan Lu, Ping German Aerosp Ctr D-28359 Bremen Germany San Diego State Univ Dept Aerosp Engn San Diego CA 92182 USA

In this paper an augmented convex-concave decomposition (ACCD) method for treating nonlinear equality constraints in an otherwise convex problem is proposed. This augmentation improves greatly the feasibility of the problem when compared to the original convex-concave decomposition approach. The effectiveness of the ACCD is demonstrated by solving a fuel-optimal six-degree-of-freedom rocket landing problem in atmosphere, subject to multiple nonlinear equality constraints. Compared with known approaches such as sequential convex programming, where conventional linearization (with or without slack variables) is employed to treat those nonlinear equality constraints, it is shown that the proposed ACCD leads to more robust convergence of the solution process and a more interpretable behavior of the sequential convex algorithm. The methodology can also be applied effectively in the case where the determination of discrete controls or decision-making variables needs to be made, such as the on-off use of reaction control system thrusters in the rocket landing problem, without the need for a mixed integer solver. Numerical results are shown for a representative, reusable rocket benchmark problem.

关键词： Rockets Reaction Control System Thrusters sequential convex programming Discrete Control Optimal Control Problem Mathematical Optimization Pseudospectral Methods convex Optimization Soft Landing Guidance Powered Descent Guidance

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Refined mode classification and performance analysis method of dual-mode scramjet vehicles for flight trajectory optimization

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AEROSPACE SCIENCE AND TECHNOLOGY 2024年 152卷

作者： Son, Jiwon Ko, Hyosang Choi, Han-Lim Yee, Kwanjung Seoul Natl Univ Seoul 08826 South Korea Korea Adv Inst Sci & Technol Daejeon 34141 South Korea Inst Adv Aerosp Technol Seoul 08826 South Korea

Hypersonic air-breathing vehicles, utilizing ramjet and scramjet propulsion systems, are emerging as a promising option for future hypersonic transportation due to high specific impulse. The performance of hypersonic aircraft is significantly influenced by their flight trajectory, as combustion efficiency and aerodynamic forces vary markedly with altitude. Although numerous studies have focused on optimizing these trajectories, they have not adequately considered the potential for operational failures in the propulsion system, such as unstart and blowout. This study introduces a trajectory optimization approach for hypersonic aircraft that proactively addresses and mitigates these operational failures. This is achieved by establishing an operational classification process for a dual-mode scramjet engine and proposing a failure mode avoidance strategy using a Gaussian process classifier. Optimized ascent trajectories are achieved through the development of a two-stage robust sequential convex programming approach. The results of trajectory optimization indicate that the failure mode avoidance strategy proposed is crucial in obtaining minimal time trajectories, and that the optimal trajectories include drop motion in the initial stage flight in order to increase combustion efficiency.

关键词： Dual-mode scramjet engine Hypersonic vehicle Trajectory optimization Quasi-1D analysis sequential convex programming

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Multitask-constrained reentry trajectory planning for hypersonic gliding vehicle

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AEROSPACE SCIENCE AND TECHNOLOGY 2024年 155卷

作者： Huang, Ang Yu, Jianglong Liu, Yumeng Hua, Yongzhao Dong, Xiwang Ren, Zhang Beihang Univ Inst Artificial Intelligence Beijing 100191 Peoples R China Beihang Univ Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China Chinese Acad Sci Inst Software Beijing 100190 Peoples R China Beihang Univ Inst Unmanned Syst Beijing 100191 Peoples R China

This paper studies the reentry trajectory planning problems for hypersonic gliding vehicle under multiple tasks. Different from the former achievements, this paper takes into account the practical tasks involved in the reentry phase, including penetration of interceptors, evasion of the no-fly zones, and the arrival of the waypoints. Firstly, the constraints during the reentry phase are analyzed in detail, and the original trajectory planning problem is formulated. Secondly, the hp-adaptive pseudospectral discretization method is proposed to effectively reduce the discretization error. Relevant variables are introduced to relax and transform severe intractable constraints of multiple nonconvex forms, thus enhancing the robustness of the planning process. Thirdly, the improved sequential convex programming with decision variables algorithm is proposed to ensure the converged trajectory satisfies complicated tasks. The theoretical analysis is also presented to demonstrate that the converged trajectory is the approximate stationary solution of the discrete form of the original problem. Finally, the effectiveness of the proposed algorithms is validated through numerical simulation.

关键词： Reentry trajectory planning Multitask sequential convex programming

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Direct-Indirect Hybrid Strategy for Optimal Powered Descent and Landing

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JOURNAL OF SPACECRAFT AND ROCKETS 2023年第6期60卷 1787-1804页

作者： Spada, Fabio Sagliano, Marco Topputo, Francesco Polytech Univ Milan Piazza Leonardo Vinci 32 I-20133 Milan Italy German Aerosp Ctr Nav & Control Dept DLR Robert Hooke Str 7 D-28359 Bremen Germany Polytech Univ Milan Dept Aerosp Sci & Technol Via La Masa 34 I-20156 Milan Italy

A hybrid algorithm to solve optimal control problems is discussed in the present paper and applied to the powered descent guidance (PDG) problem. A reference solution is first obtained via a convex direct solver and is then used as guess for the primal-dual boundary-value problem associated with the initial problem. In this context, a covector mapping theorem is used to map the multipliers of the direct solution to the corresponding discrete costates of the indirect method. Collocation based on hp pseudospectral scheme is employed for the convex direct step, while single shooting is used for the indirect step. A switching-detection technique further equips the shooting. As opposed to the hybrid convex-indirect algorithm, a state-of-the-art purely indirect algorithm is outlined;such approach merges the same single shooting approach with a homotopic continuation. The proposed methods are applied to the pinpoint landing formulation of the PDG, framed in a three-dimensional environment. The results are finally outlined, comparing the proposed hybrid strategy to the purely indirect approach. The outcome highlights the gain in computational times for the hybrid optimization technique over the fully homotopic scheme, demonstrating the validity of the former for landing trajectory optimization purposes.

关键词： Powered Descent Guidance Hybrid Optimization Covector Mapping Principle sequential convex programming Indirect Shooting Homotopic Continuation

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Mesh-Based Two-Step convex Optimization for Spacecraft Landing Trajectory Planning on Irregular Asteroid

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JOURNAL OF SPACECRAFT AND ROCKETS 2024年第1期61卷 72-87页

作者： Zhao, Zichen Shang, Haibin Liu, Chengliang Xiao, Shuchen Beijing Inst Technol Sch Aerosp Engn Beijing 100081 Peoples R China Aviat Univ Air Force Sch Guidance Nav & Control Changchun 130022 Peoples R China Aviat Univ Air Force Sch Aviat Serv Changchun 130022 Peoples R China

The problem investigated in this paper is how to rapidly optimize a landing trajectory on an arbitrarily shaped asteroid, subject to practical constraints and a gravitational model suitable for irregular asteroids. The fundamental idea is to convert the nonlinearity involved in the gravitational field into an equivalent convex version and further generate the optimal trajectory using the two-step convex optimization technique to achieve efficient and robust computation. For a given mission area, the positional space is discretized as an exactly sufficient number of small tetrahedron meshes, within which the real gravitations are interpolated as the linear gravitational representation with nonconvexmesh tracking constraints. Asolution space relaxation- penalization technique is proposed to convexify the mesh tracking constraints and keep the feasibility of the resulting convex optimization problem. A series of optimal active meshes are generated by solving this problem and transcribed as corresponding convex active meshing constraints, and further imposing them on the landing trajectory to construct the final convex optimization problem equaling to the original problem. The strength and correctness of this method are demonstrated from both perspectives of theoretical analyses and numerical simulations for landing on 4769 Castalia asteroid, with the comparisons of the state-of-the-art convex-optimization-based methods.

关键词： Mathematical Optimization Asteroids Lagrange Multipliers Spacecraft Landing Mathematical Analysis Optimal Control Problem Propellant sequential convex programming Mesh Generation Precise Soft Landing

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Multi-robot formation control and object transport in dynamic environments via constrained optimization

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INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH 2017年第9期36卷 1000-1021页

作者： Alonso-Mora, Javier Baker, Stuart Rus, Daniela MIT Comp Sci & Artificial Intelligence Lab 77 Massachusetts Ave Cambridge MA 02139 USA Delft Univ Technol Delft Ctr Syst & Control Delft Netherlands

We present a constrained optimization method for multi-robot formation control in dynamic environments, where the robots adjust the parameters of the formation, such as size and three-dimensional orientation, to avoid collisions with static and moving obstacles, and to make progress towards their goal. We describe two variants of the algorithm, one for local motion planning and one for global path planning. The local planner first computes a large obstacle-free convex region in a neighborhood of the robots, embedded in position-time space. Then, the parameters of the formation are optimized therein by solving a constrained optimization, via sequential convex programming. The robots navigate towards the optimized formation with individual controllers that account for their dynamics. The idea is extended to global path planning by sampling convex regions in free position space and connecting them if a transition in formation is possible - computed via the constrained optimization. The path of lowest cost to the goal is then found via graph search. The method applies to ground and aerial vehicles navigating in two- and three-dimensional environments among static and dynamic obstacles, allows for reconfiguration, and is efficient and scalable with the number of robots. In particular, we consider two applications, a team of aerial vehicles navigating in formation, and a small team of mobile manipulators that collaboratively carry an object. The approach is verified in experiments with a team of three mobile manipulators and in simulations with a team of up to sixteen Micro Air Vehicles (quadrotors).

关键词： Multi-robot systems motion planning formation control constrained optimization sequential convex programming team of aerial vehicles micro air vehicles collaborative mobile manipulators collaborative object transport

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