Multi-objective robust trajectory optimisation under epistemic uncertainty and imprecision

Research output: Contribution to conferencePaper

Abstract

This paper presents a novel method to generate robust optimal trajectories for spacecraft equipped with low-thrust propulsion under the effect of epistemic uncertainty. The uncertainties considered for this paper derive from a lack of knowledge on system’s and launcher’s parameters. This is a typical situation in the early stage of the design process when multiple options need to be evaluated and only a partial knowledge of each of them is available. Uncertainties are modelled with probability boxes, or p-boxes, embodying multiple families of distributions. Once the effect of uncertainty is propagated through the system one can calculate the Upper and Lower Expectations on the quantity of interest (for example the mass of propellant). The Lower Expectation defines the worst case effect of the uncertainty when uncertainty is expressed via a p-box. We also propose a method for its calculation, which requires solving an optimization problem. Once the low expectations on the quantities of interest are available, a novel efficient computational scheme is proposed to compute families of control laws that are robust against the effect of uncertainty. Robustness is here considered to be the ability to maximise the desired performance, under uncertainty, with a high probability of satisfying the constraints. The computational scheme proposed in this paper makes use of surrogate models of the Lower Expectations, to radically reduce the computational cost of the robust optimisation problem. This is combined with a dimensionality reduction technique, that allows one to construct surrogate models on low dimensional spaces, and an iterative refinement of the surrogate representation. The training points of the surrogate models are evaluated using FABLE (Fast Analytical Boundary value Low-thrust Estimator), an analytical tool for the fast design and optimisation of low-thrust trajectories. A memetic multi-objective optimisation algorithm, MACS (Multi Agent Collaborative Search), is then used to find the set of Pareto optimal control laws that maximise the Lower Expectation in the achievement of the desired values of objective function and constraints. The proposed approach is then applied to the design of a rendezvous mission to Apophis with a small spacecraft equipped with a low thrust engine.

Conference

Conference70th International Astronautical Congress
Abbreviated titleIAC
CountryUnited States
CityWashington D.C.
Period21/10/1925/10/19
Internet address

Fingerprint

Trajectories
Spacecraft
Uncertainty
Propellants
Multiobjective optimization
Propulsion
Engines
Costs

Keywords

  • epistemic uncertainty
  • resilient satellite
  • robust optimization
  • lower expectation
  • multi-objective optimization

Cite this

Graça Marto, S., Vasile, M., & Epenoy, R. (2019). Multi-objective robust trajectory optimisation under epistemic uncertainty and imprecision. Paper presented at 70th International Astronautical Congress, Washington D.C., United States.
Graça Marto, Simão ; Vasile, Massimiliano ; Epenoy, Richard. / Multi-objective robust trajectory optimisation under epistemic uncertainty and imprecision. Paper presented at 70th International Astronautical Congress, Washington D.C., United States.13 p.
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keywords = "epistemic uncertainty, resilient satellite, robust optimization, lower expectation, multi-objective optimization",
author = "{Gra{\cc}a Marto}, Sim{\~a}o and Massimiliano Vasile and Richard Epenoy",
year = "2019",
month = "10",
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note = "70th International Astronautical Congress, IAC ; Conference date: 21-10-2019 Through 25-10-2019",
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Graça Marto, S, Vasile, M & Epenoy, R 2019, 'Multi-objective robust trajectory optimisation under epistemic uncertainty and imprecision' Paper presented at 70th International Astronautical Congress, Washington D.C., United States, 21/10/19 - 25/10/19, .

Multi-objective robust trajectory optimisation under epistemic uncertainty and imprecision. / Graça Marto, Simão; Vasile, Massimiliano; Epenoy, Richard.

2019. Paper presented at 70th International Astronautical Congress, Washington D.C., United States.

Research output: Contribution to conferencePaper

TY - CONF

T1 - Multi-objective robust trajectory optimisation under epistemic uncertainty and imprecision

AU - Graça Marto, Simão

AU - Vasile, Massimiliano

AU - Epenoy, Richard

PY - 2019/10/25

Y1 - 2019/10/25

N2 - This paper presents a novel method to generate robust optimal trajectories for spacecraft equipped with low-thrust propulsion under the effect of epistemic uncertainty. The uncertainties considered for this paper derive from a lack of knowledge on system’s and launcher’s parameters. This is a typical situation in the early stage of the design process when multiple options need to be evaluated and only a partial knowledge of each of them is available. Uncertainties are modelled with probability boxes, or p-boxes, embodying multiple families of distributions. Once the effect of uncertainty is propagated through the system one can calculate the Upper and Lower Expectations on the quantity of interest (for example the mass of propellant). The Lower Expectation defines the worst case effect of the uncertainty when uncertainty is expressed via a p-box. We also propose a method for its calculation, which requires solving an optimization problem. Once the low expectations on the quantities of interest are available, a novel efficient computational scheme is proposed to compute families of control laws that are robust against the effect of uncertainty. Robustness is here considered to be the ability to maximise the desired performance, under uncertainty, with a high probability of satisfying the constraints. The computational scheme proposed in this paper makes use of surrogate models of the Lower Expectations, to radically reduce the computational cost of the robust optimisation problem. This is combined with a dimensionality reduction technique, that allows one to construct surrogate models on low dimensional spaces, and an iterative refinement of the surrogate representation. The training points of the surrogate models are evaluated using FABLE (Fast Analytical Boundary value Low-thrust Estimator), an analytical tool for the fast design and optimisation of low-thrust trajectories. A memetic multi-objective optimisation algorithm, MACS (Multi Agent Collaborative Search), is then used to find the set of Pareto optimal control laws that maximise the Lower Expectation in the achievement of the desired values of objective function and constraints. The proposed approach is then applied to the design of a rendezvous mission to Apophis with a small spacecraft equipped with a low thrust engine.

AB - This paper presents a novel method to generate robust optimal trajectories for spacecraft equipped with low-thrust propulsion under the effect of epistemic uncertainty. The uncertainties considered for this paper derive from a lack of knowledge on system’s and launcher’s parameters. This is a typical situation in the early stage of the design process when multiple options need to be evaluated and only a partial knowledge of each of them is available. Uncertainties are modelled with probability boxes, or p-boxes, embodying multiple families of distributions. Once the effect of uncertainty is propagated through the system one can calculate the Upper and Lower Expectations on the quantity of interest (for example the mass of propellant). The Lower Expectation defines the worst case effect of the uncertainty when uncertainty is expressed via a p-box. We also propose a method for its calculation, which requires solving an optimization problem. Once the low expectations on the quantities of interest are available, a novel efficient computational scheme is proposed to compute families of control laws that are robust against the effect of uncertainty. Robustness is here considered to be the ability to maximise the desired performance, under uncertainty, with a high probability of satisfying the constraints. The computational scheme proposed in this paper makes use of surrogate models of the Lower Expectations, to radically reduce the computational cost of the robust optimisation problem. This is combined with a dimensionality reduction technique, that allows one to construct surrogate models on low dimensional spaces, and an iterative refinement of the surrogate representation. The training points of the surrogate models are evaluated using FABLE (Fast Analytical Boundary value Low-thrust Estimator), an analytical tool for the fast design and optimisation of low-thrust trajectories. A memetic multi-objective optimisation algorithm, MACS (Multi Agent Collaborative Search), is then used to find the set of Pareto optimal control laws that maximise the Lower Expectation in the achievement of the desired values of objective function and constraints. The proposed approach is then applied to the design of a rendezvous mission to Apophis with a small spacecraft equipped with a low thrust engine.

KW - epistemic uncertainty

KW - resilient satellite

KW - robust optimization

KW - lower expectation

KW - multi-objective optimization

M3 - Paper

ER -

Graça Marto S, Vasile M, Epenoy R. Multi-objective robust trajectory optimisation under epistemic uncertainty and imprecision. 2019. Paper presented at 70th International Astronautical Congress, Washington D.C., United States.