Richard Epenoy

Centre National d’Etudes Spatiales | CNES · DTN/DV/IFL

This paper investigates the numerical computation of minimum-fuel low-thrust trajectories subject to bound constraints on the duration of thrust and coast arcs. First, an optimal control problem is formulated. The constraints on thrust and coast periods are written as a single discontinuous bound constraint on the control norm depending on time and...

This paper investigates the numerical computation of minimum-fuel low-thrust trajectories subject to bound constraints on the duration of thrust and coast arcs. First, these constraints are written as a single nonsmooth bound constraint on the control norm depending on time and on a set of free parameters considered as additional state variables. T...

Quasi-satellite orbits (QSOs) are considered by JAXA’s MMX mission, in which CNES is involved, for the scientific observation of the Martian moon Phobos prior to landing and sample return operations. These periodic orbits, originally defined in the Mars-Phobos circular restricted three-body problem, generically lose periodicity once the eccentricit...

Quasi-Satellite Orbits (QSOs) are considered by JAXA’s MMX mission, in which CNES is involved, for the scientific observation of the Martian moon Phobos prior to landing and sample return operations. These periodic orbits, originally defined in the Mars-Phobos Circular Restricted Three-Body Problem, generically lose periodicity once the eccentricit...

This paper proposes a novel approach to the solution of optimal control problems under uncertainty (OCPUUs). OCPUUs are first cast in a general formulation that allows the treatment of uncertainties of different nature, and then solved with a new direct transcription method that combines multiple shooting with generalised polynomial algebra to mode...

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 proce...

This paper investigates the numerical computation of low-fuel low-thrust Earth-Moon transfers in a full ephemeris model incorporating the gravitational influence of the Sun, the Moon and all planets of the solar system plus the solar radiation pressure perturbation based on a sample spacecraft area and mass. First, an initial velocity increment to...

This paper proposes an approach to the solution of optimal control problems under uncertainty, that extends the classical direct multiple shooting transcription to account for random variables defined on extended sets. The proposed approach employs a Generalised Intrusive Polynomial Expansion to model and propagate uncertainty. The development of a...

The problem of designing low-energy transfers between the Earth and the Moon has attracted recently a major interest from the scientific community. In this paper, an indirect optimal control approach is used to determine minimum-fuel low-thrust transfers between a low Earth orbit and a Lunar orbit in the Sun–Earth–Moon Bicircular Restricted Four-Bo...

In this paper, we investigate the numerical computation of minimum-energy low-thrust transfers between Libration point orbits in the Circular Restricted Three-Body Problem. We develop a three-step methodology based on optimal control theory, indirect shooting methods and variational equations without using information from invariant manifolds. Nume...

The objective of this book is to present recent advances in celestial and space mechanics written by contributors from both academic institutions and space agencies. It is organized in seven complementary articles, two devoted to celestial mechanics and five dedicated to orbital mechanics. One main motivation and central line of the work presented...

The paper presents a novel algorithm for the automatic planning and scheduling of multi-gravity assist trajectories (MGA). The algorithm translates the design of a MGA transfer into a planning and scheduling process in which each planetary encounter is seen as a scheduled task. All possible transfers form a directional graph that is incrementally b...

The paper presents a novel algorithm for the automatic planning and scheduling of multi-gravity assist trajectories (MGA). The algorithm translates the design of an MGA transfer into a planning and scheduling process in which each planetary encounter is seen as a scheduled task. All possible transfers form a directional graph that is incrementally...

This paper presents the results of a study that has been carried out by Thales Alenia Space (TAS) in cooperation with the French Space Agency (CNES). The aim of this study was to develop a tool to design optimal trajectories for debris removal missions based on the use of a low-thrust propulsion spacecraft. Since the number of possible combinations...

The aim of this paper is to investigate the feasibility of an Earth-to-Mars transfer with reduced transfer time using a high-power electric propulsion system. The study involved a multidisciplinary analysis combining general performance calculations for power-limited systems, an analysis of a nuclear power source that might be available in the futu...

Many-revolution, electric-propulsion trajectories are computationally difficult to optimize. We present several examples of the well-known technique of orbit averaging coupled with indirect optimization methods, and also an example of a direct, unaveraged optimization method. We also present a comparison of these methods to the Q-law, a Lyapunov fe...

Recent advances in electric propulsion technologies such as magnetoplasma rockets gave a new momentum to the study of nuclear electric propulsion concepts for Mars missions. Some recent works have been focused on very short Earth-to-Mars transfers of about 40 days with high-power, variable specific impulse propulsion systems [1]. While the interest...

This paper focuses on the design of a quadratically constrained linear-quadratic regulator for finite-thrust orbital rendezvous. The original linear-quadratic optimal control problem is subject to maximum thrust magnitude and quadratic collision avoidance constraints. Thrust arcs are approximated by impulsive velocity increments and the Yamanaka-An...

This paper investigates the numerical computation of minimum-energy low-thrust transfers between Libration point orbits via optimal control theory and indirect shooting methods. A three-step solution method is built without enforcing prior knowledge about the solution. A feasible control is first determined. Then a sequence of optimal control probl...

This paper focuses on the design of a quadratically-constrained Linear-Quadratic Regulator for finite-thrust orbital rendezvous. The original Linear-Quadratic optimal control problem is subject to maximum thrust magnitude and quadratic collision avoidance constraints. Thrust arcs are approximated by impulsive velocity increments and the Yamanaka-An...

This paper focuses on the issue of minimum-fuel rendezvous between an active chaser satellite with continuous-thrust capability and a passive target satellite. It is first formalized as an optimal control problem subject to a collision-avoidance constraint on the path of the chaser satellite. Then, a new method for dealing with this state constrain...

This paper focuses on the design of a fuel-optimal maneuver strategy for the rendezvous between an active chaser satellite with continuous-thrust capability and a passive target satellite. The problem is formalized as an optimal control problem subject to a collision avoidance constraint on the path of the chaser satellite. Then, a new method for d...

Outline 1 Problem statement -Dynamical equations -Optimal control formulation 2 Solving the path-constrained rendezvous problem -Smoothing the bang-o-bang control -A new approach to deal with the state constraint 3 Numerical results - A rendezvous in Highly Elliptical Orbit -Statement of the test case -Unconstrained rendezvous -Rendezvous under col...

Final workshop of the GTOC3 competition won by the CNES team

This paper focuses on the issue of minimum-fuel deployment for satellite formation flying. We address it as an optimal control problem, the necessary optimality conditions of which are derived from Pontryagin's Maximum Principle. Due to the "bang-off-bang" structure of the control, the shooting function has a singular Jacobian matrix on a large dom...

This paper focuses on the issue of minimum-fuel deployment for satellite formation flying. We address it as an optimal control problem, the necessary optimality conditions of which are derived from Pontryagin's maximum principle. These are numerically enforced by finding the root of a so-called shooting function. However, optimal control laws for m...

This paper presents the solution of the CNES/CS joint team in response to the first ACT competition on global trajectory optimisation. The optimisation tools available at CNES and CS are based on a Lambert's problem formulation associated with a direct optimisation method, or on Pontryagin's maximum principle associated with decomposition–coordinat...

We investigate in this paper the computation of minimum fuel orbital transfers and rendezvous. Each problem is seen as an optimal control problem and is solved by means of shooting methods [1]. This approach corresponds to the use of Pontryagin's Maximum Principle (PMP) [2-4] and leads to the solution of a Two Point Boundary Value Problem (TPBVP)....

In this paper, we investigate the solution of bang-bang optimal control problems by shooting methods. We will show how modifying the performance index by a term depending on a small parameter ε yields more regular controls and shooting functions. A continuation procedure on ε will lead us to a good approximation of the initial solution. Then, a sta...

The aim of this paper is to analyse an alternative scenario for Mars Sample Return Orbiter mission, where electric propulsion is used for Earth-Mars and Mars-Earth heliocentric cruises and for Mars orbit insertion / escape transfers, whereas chemical propulsion is used for final Mars rendezvous. The problem consists in minimizing the initial vehicl...

We are interested in the calculation of the optimal low-thrust transfer of a satellite subjected to solar eclipses. The modeling of this constraint leads to a set of admissible controls U(t,x) discontinuously dependent on the time t and on the state of the system x (the satellite's position). This set of controls does not allow to use the classical...

A unified study of optimal low-thrust transfers is presented, based on the use of averaging techniques. Both minimum-time and fuel-saving strategies using non-constant acceleration are investigated to optimize the trajectory between arbitrary distant orbits. Optimal low-thrust rendezvous could also be treated by the same way. In each case, several...