Global solution of multi-objective optimal control problems with multi agent collaborative search and direct finite elements transcription

This paper addresses the solution of optimal control problems with multiple and possibly conflicting objective functions. The solution strategy is based on the integration of Direct Finite Elements in Time (DFET) transcription into the Multi Agent Collaborative Search (MACS) framework. Multi Agent Collaborative Search is a memetic algorithm in which a population of agents performs a set of individual and social actions looking for the Pareto front. Direct Finite Elements in Time transcribe an optimal control problem into a constrained Non-linear Programming Problem (NLP) by collocating states and controls on spectral bases. MACS operates directly on the NLP problem and generates nearly-feasible trial solutions which are then submitted to a NLP solver. If the NLP solver converges to a feasible solution, an updated solution for the control parameters is returned to MACS, along with the corresponding value of the objective functions. Both the updated guess and the objective function values will be used by MACS to generate new trial solutions and converge, as uniformly as possible, to the Pareto front. To demonstrate the applicability of this strategy, the paper presents the solution of the multi-objective extensions of two well-known space related optimal control problems: the Goddard Rocket problem, and the maximum energy orbit rise problem

Direct transcription of low-thrust trajectories with finite trajectory elements

This paper presents a novel approach to the design of Low-Thrust trajectories, based on a first order approximated analytical solution of Gauss planetary equations. This analytical solution is shown to have a better accuracy than a second-order explicit numerical integrator and at a lower computational cost. Hence, it can be employed for the fast propagation of perturbed Keplerian motion when moderate accuracy is required. The analytical solution was integrated in a direct transcription method based on a decomposition of the trajectory into direct finite perturbative elements (DFPET). DFPET were applied to the solution of two-point boundary transfer problems. Furthermore the paper presents an example of the use of DFPET for the solution of a multiobjective trajectory optimisation problem in which both the total ∆V and transfer time are minimized with respect to departure and arrival dates. Two transfer problems were used as test cases: a direct transfer from Earth to Mars and a spiral from a low Earth orbit to the International Space Station

A direct memetic approach to the solution of multi-objective optimal control problems

This paper proposes a memetic direct transcription algorithm to solve Multi-Objective Optimal Control Problems (MOOCP). The MOOCP is first transcribed into a Non-linear Programming Problem (NLP) with Direct Finite Elements in Time (DFET) and then solved with a particular formulation of the Multi Agent Collaborative Search (MACS) framework. Multi Agent Collaborative Search is a memetic algorithm in which a population of agents combines local search heuristics, exploring the neighbourhood of each agent, with social actions exchanging information among agents. A collection of all Pareto optimal solutions is maintained in an archive that evolves towards the Pareto set. In the approach proposed in this paper, individualistic actions run a local search, from random points within the neighbourhood of each agent, solving a normalised Pascoletti-Serafini scalarisation of the multi-objective NLP problem. Social actions, instead, solve a bi-level problem in which the lower level handles only the constraint equations while the upper level handles only the objective functions. The proposed approach is tested on the multi-objective extensions of two well-known optimal control problems: the Goddard Rocket problem, and the maximum energy orbit rise problem

Multi-objective optimal control of ascent trajectories for launch vehicles

This paper presents a novel approach to the solution of multi-objective optimal control problems. The proposed solution strategy is based on the integration of the Direct Finite Elements Transcription method, to transcribe dynamics and objectives, with a memetic strategy called Multi Agent Collaborative Search (MACS). The original multi-objective optimal control problem is reformulated as a bi-level nonlinear programming problem. In the outer level, handled by MACS, trial control vectors are generated and passed to the inner level, which enforces the solution feasibility. Solutions are then returned to the outer level to evaluate the feasibility of the corresponding objective functions, adding a penalty value in the case of infeasibility. An optional single level refinement is added to improve the ability of the scheme to converge to the Pareto front. The capabilities of the proposed approach will be demonstrated on the multi-objective optimisation of ascent trajectories of launch vehicles

Optimal options for rendezvous and impact missions to NEOs

In this paper some potentially interesting transfer options for missions to Near Earth Objects have been studied. Due to thehigh number of potential targets and to the large variety of possible missions that can be considered, especially if resorting to low-thrust propulsion, an extensive analysis of transfer options requires a preliminary approach oriented toward an effective global search, and an appropriately simplified trajectory transcription. Low-thrust options have been modeled through a novel shape-based approach and a global optimization method has been used to look for globally optimal transfers. Different targets have been identified and various mission scenarios have been considered: rendezvous, sample return missions both with and without Earth gravity assist and impact missions

Multi-objective optimisation of many-revolution, low-thrust orbit raising for Destiny mission

This work will present a Multi-Objective approach to the design of the initial, Low-Thrust orbit raising phase for JAXA’s proposed technology demonstrator mission DESTINY. The proposed approach includes a simplified model for Low Thrust, many-revolution transfers, based on an analytical orbital averaging technique, and a simplified control parameterisation. Eclipses and J2 perturbation are also accounted for. This is combined with a stochastic optimisation algorithm to solve optimisation problems in which conflicting performance figures of DESTINY’s trajectory design are concurrently optimised. It will be shown that the proposed approach provides for a good preliminary investigation of the launch window and helps identifying critical issues to be addressed in future design phases

Multi-objective optimisation under uncertainty with unscented temporal finite elements

This paper presents a novel method for multi-objective optimisation under uncertainty developed to study a range of mission trade-offs, and the impact of uncertainties on the evaluation of launch system mission designs. A memetic multi-objective optimisation algorithm, named MODHOC, which combines the Direct Finite Elements in Time transcription method with Multi Agent Collaborative Search, is extended to account for model uncertainties. An Unscented Transformation is used to capture the first two statistical moments of the quantities of interest. A quantification model of the uncertainty was developed for the atmospheric model parameters. An optimisation under uncertainty was run for the design of descent trajectories for a spaceplane-based two-stage launch system

Direct solution of multi-objective optimal control problems applied to spaceplane mission design

This paper presents a novel approach to the solution of multi-phase multi-objective optimal control problems. The proposed solution strategy is based on the transcription of the optimal control problem with Finite Elements in Time and the solution of the resulting Multi-Objective Non-Linear Programming (MONLP) problem with a memetic strategy that extends the Multi Agent Collaborative Search algorithm. The MONLP problem is reformulated as two non-linear programming problems: a bi-level and a single level problem. The bi-level formulation is used to globally explore the search space and generate a well spread set of non-dominated decision vectors while the single level formulation is used to locally converge to Pareto efficient solutions. Within the bi-level formulation, the outer level selects trial decision vectors that satisfy an improvement condition based on Chebyshev weighted norm, while the inner level restores the feasibility of the trial vectors generated by the outer level. The single level refinement implements a Pascoletti-Serafini scalarisation of the MONLP problem to optimise the objectives while satisfying the constraints. The approach is applied to the solution of three test cases of increasing complexity: an atmospheric re-entry problem, an ascent and abort trajectory scenario and a three-objective system and trajectory optimisation problem for spaceplanes

MODHOC - Multi Objective Direct Hybrid Optimal Control

MODHOC (Multi Objective Direct Hybrid Optimal Control) is a toolbox for the design, optimisation and trade off study of space systems and missions. It solves general nonlinear multi phase optimal control problems, automatically computing a well spread set of optimal trade off solutions. In addition, it is able to handle discrete optimisation parameters. In order to do so, MODHOC combines a direct transcription method based on finite elements, aglobal multi objective optimisation algorithm combining evolutionary heuristics and mathematicalprogramming. MODHOC has been applied to a variety of applications: from the optimisation of launch vehiclesand their ascent, abort and re entry trajectories, to the design of the optimal deployment of constellations of satellites, to the design of multi target missions. In this paper, the main elements of MODHOC are described and the application of the software inspace and non space related sample problems is demonstrated

Multi-objective optimal control of re-entry and abort scenarios

This paper presents a novel approach to the solution of multi-phase multi-objective optimal control problems. The proposed solution strategy is based on the integration of the Direct Finite Elements Transcription (DFET) method, to transcribe dynamics and objectives, with a memetic strategy called Multi Agent Collaborative Search (MACS). The original multi-objective optimal control problem is reformulated as two non-linear programming problems: a bi-level and a single level one. In the bi-level problem the outer level, handled byMACS, generates trial control vectors that are then passed to the inner level, which enforces the feasibility of the solution. Feasible control vectors are then returned to the outer level to evaluate the corresponding objective functions. A single level refinement is then run to improve local convergence to the Pareto front. The paper introduces also a novel parameterisation of the controls, using Bernstein polynomials, in the context of the DFET transcription method. The approach is first tested on a known atmospheric re-entry problem and then applied to the analysis of ascent and abort trajectories for a space plane