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

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

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

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

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

Ecospheric life cycle impacts of annual global space activities

This paper presents a first-order approximation of ecospheric life cycle impacts from annual global space activities across two scenarios using a streamlined Life Cycle Sustainability Assessment (LCSA). The first scenario considers all space missions launched throughout the 2018 calendar year whilst the second is a futuristic scenario where affordable access to space significantly increases the prevalence of space operations. A new space-specific life cycle database and sustainable design tool called the Strathclyde Space Systems Database (SSSD) has been used to compile the inventory of each scenario and generate results across numerous impact categories. The results for each scenario are then compared against normalised values to portray their contribution towards annual worldwide impacts and their severity in terms of planetary boundaries. This allows the relative life cycle sustainability impacts of space activities to be benchmarked for the first time, forming a basis for evaluation and discussion. Overall, the study highlights that despite the relatively small footprint of the space industry at present, this will likely become much more meaningful in the future based on predicted trends. This places an added importance on addressing potential adverse life cycle impacts within the design process of future space technologies and products

On the deflection of asteroids with mirrors

This paper presents an analysis of an asteroid deflection method based on multiple solar concentrators. A model of the deflection through the sublimation of the surface material of an asteroid is presented, with simulation results showing the achievable orbital deflection with, and without, accounting for the effects of mirror contamination due to the ejected debris plume. A second model with simulation results is presented analyzing an enhancement of the Yarkovsky effect, which provides a significant deflection even when the surface temperature is not high enough to sublimate. Finally the dynamical model of solar concentrators in the proximity of an irregular celestial body are discussed, together with a Lyapunov-based controller to maintain the spacecraft concentrators at a required distance from the asteroid

Robust multi-objective optimisation of a descent guidance strategy for a TSTO spaceplane

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, MODHOC, which combines the Direct Finite Elements 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 the Orbital-500R, a commercial semi-reusable, two-stage launch system under development by Orbital Access Lt