Direct Solution of Multi-Objective Optimal Control Problems Applied to Spaceplane Mission Design

Ricciardi, Lorenzo A.; Maddock, Christie; Vasile, Massimiliano

doi:10.2514/1.g003839

Cited by 19 publications

(8 citation statements)

References 45 publications

(80 reference statements)

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“…, where x(t − i+1 ) and u(t − i+1 ) refer to the first points of the next leg and x(t + i ) and u(t + i ) refer the last point of the considered leg. The multiple shooting approach can be considered as a compromise between the single shooting method, which has a limited number of variables but also an excessive sensitivity with respect to control variables at the start of the shooting, and the collocation methods, which do not suffer the excess of sensitivity of some variables, but have to deal with a much higher number of variables ( Rao 2009, Becerra 2012, Böhme and Frank 2017and Kelly 2017.…”

Section: Multiple-shootingmentioning

confidence: 99%

Single-stage to orbit ascent trajectory optimisation with reliable evolutionary initial guess

2021

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In this paper, the ascent trajectory optimization of a lifting body Single-Stage To Orbit (SSTO) reusable launch vehicle is investigated. The work is carried out using a Direct Multiple Shooting method to solve the Optimal Control problem. The crucial initialisation of the optimisation process is performed by using a combination of two evolutionary algorithms, namely a Multi-Objective Parzen-based Estimation of Distribution (MOPED) algorithm and a Multi-Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA). Multi-Objective Parzen-based Estimation of Distribution (MOPED) belongs to the class of Estimation of Distribution Algorithms (EDAs) and it is used in the first phase of the initial guess research to explore the search space, then Multi-Population Adaptive Inflationary Differential Evolution Algorithm (MP-AIDEA) is used to refine the obtained results, and better fulfill the imposed constraints. The initial guesses obtained with this evolutionary framework were tested on different multiple shooting configurations. The importance of the continuity properties of the employed mathematical models was also quantitatively addressed.

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Section: Multiple-shootingmentioning

confidence: 99%

Single-stage to orbit ascent trajectory optimisation with reliable evolutionary initial guess

2021

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“…MODHOC, Multi-Objective Direct Hybrid Optimal Control solver [6,7], is based on a Direct Finite Elements Transcription (DFET) of the optimal control problem [8] and a solution of the transcribed problem with a multi-agent, multi-objective optimisation algorithm (MACS) [9]. By combining MACS and DFET, MODHOC has the ability to perform a global exploration of the solution space and to converge locally to optimal solutions.…”

Section: Robust Design Optimisationmentioning

confidence: 99%

Robust Trajectory Optimisation of a TSTO Spaceplane Using Uncertainty-Based Atmospheric Models

Ricciardi¹,

Maddock²,

Vasile³

2020

23rd AIAA International Space Planes and Hypersonic Systems and Technologies Conference

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This paper presents a multi-objective trajectory optimisation under uncertainty for the ascent and descent flight paths for the first stage of a two-stage, semi-reusable space launch system. Using Orbital Access' Orbital 500-R launcher as a test case, within the preliminary design phase, robust multi-disciplinary design optimisation is being used to analyse the tradeoffs with both the vehicle and system design and operation. An area of focus is on the predicted aerodynamic performance, and its impact on the design and planned mission scenarios. The model uncertainties are quantified for the atmospheric model and aerodynamic surrogate models and integrated into the optimal control solver MODHOC extended by the addition of an unscented transformation to handle the uncertainties. A multi-objective optimisation under uncertainty is run, examining the Pareto-optimal sets for the ascent and descent trajectories of the first stage spaceplane.

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“…To solve Multi-Objective Optimal Control problems, the following approach was proposed in [8]: first, the multi-objective optimal control problem (1) is translated into a multi-objective NLP problem by using the DFET transcription scheme, which discretises the dynamics of the problem and converts it the finite dimensional problem (3). An automatic and unsupervised process generates feasible guesses before the main loop of the optimisation starts.…”

Section: Solution Of the Mixed Integer Optimal Control Problemmentioning

confidence: 99%

“…The method can thus seamlessly transition between a global exploration mode that generates evenly spread solutions on the Pareto front, to a local exploration mode able to guarantee the local optimality of all the solutions along the same descent directions in criteria space that were used by the global exploration mode. A more complete description of this approach is described in [8].…”

Section: Description Of the Formulationsmentioning

confidence: 99%

“…The problem is here formulated as a multi-phase multi-objective hybrid optimal control problem where the final conditions of each phase depend on the choice of which target is visited. The solution method adopted in this work closely follows [8], which dealt with general multi-phase multi-objective optimal control problems. The approach is based on a direct transcription of the optimal control problem with Direct Finite Elements in Time (DFET) [9,14] and a solution of the resulting multi-objective nonlinear programming (MONLP) problem with Multi Agent Collaborative Search (MACS) [10,15,18], a population based global memetic multi-objective optimisation algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Solving multi-objective dynamic travelling salesman problems by relaxation

Ricciardi

Vasile

2019

Proceedings of the Genetic and Evolutionary Computation Conference Companion

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This paper describes a method to solve Multi-objective Dynamic Travelling Salesman Problems. The problems are formulated as multi-objective hybrid optimal control problems, where the choice of the target destination for each phase is an integer variable. The resulting problem has thus a combinatorial nature in addition to being a multi-objective optimal control problem. The overall solution approach is based on a combination of the Multi Agent Collaborative Search, a population based memetic multi-objective optimisation algorithm, and the Direct Finite Elements Transcription, a direct method for optimal control problems. A relaxation approach is employed to transform the mixed integer problem into a purely continuous problem, and a set of smooth constraints is added in order to ensure that the relaxed variables of the final solution assume an integer value. A special set of smooth constraints is introduced in order to treat the mutually exclusive choices of the targets for each phase. The method is tested on two problems: the first is a motorised Travelling salesman problem described in the literature, the second is a space application where a satellite has to de-orbit multiple debris. For the first problem, the approach is generating better solutions than those reported in the literature.

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Direct Solution of Multi-Objective Optimal Control Problems Applied to Spaceplane Mission Design

Cited by 19 publications

References 45 publications

Single-stage to orbit ascent trajectory optimisation with reliable evolutionary initial guess

Single-stage to orbit ascent trajectory optimisation with reliable evolutionary initial guess

Robust Trajectory Optimisation of a TSTO Spaceplane Using Uncertainty-Based Atmospheric Models

Solving multi-objective dynamic travelling salesman problems by relaxation

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