A Homotopy-Based Method for Optimization of Hybrid High-Low Thrust Trajectories

Space missions require increasingly more efficient trajectories to provide payload transport and mission goals by means of lowest fuel consumption, a strategic mission design key-point. Recent works demonstrated that the combined (or hybrid) use of chemical and electrical propulsion can give important advantages in terms of fuel consumption, without losing the ability to reach other mission objectives: as an example the Hohmann Spiral Transfer, applied in the case of a transfer to GEO orbit, demonstrated a fuel mass saving between 5-10% of the spacecraft wet mass, whilst satisfying a pre-set boundary constraint for the time of flight. Nevertheless, methods specifically developed for optimizing space trajectories considering the use of hybrid high-low thrust propulsion systems have not been extensively developed, basically because of the intrinsic complexity in the solution of optimal problem equations with existent numerical methods. The study undertaken and presented in this paper develops a numerical strategy for the optimization of hybrid high-low thrust space trajectories. An indirect optimization method has been developed, which makes use of a homotopic approach for numerical convergence improvement. The adoption of a homotopic approach provides a relaxation to the optimal problem, transforming it into a simplest problem to solve in which the optimal problem presents smoother equations and the shooting function acquires an increased convergence radius: the original optimal problem is then reached through a homotopy parameter continuation. Moreover, the use of homotopy can make possible to include a high thrust impulse (treated as velocity discontinuity) to the low thrust optimal control obtained from the indirect method. The impulse magnitude, location and direction are obtained following from a numerical continuation in order to minimize the problem cost function. The initial study carried out in this paper is finally correlated with particular test cases, in order to validate the work developed and to start investigating in which cases the effectiveness of hybrid-thrust propulsion subsists

Orbital Dynamics of an Oscillating Sail in the Earth-Moon System

The oscillating sail is a novel solar sail configuration where a triangular sail is released at a deflected angle with respect to the Sun-direction. As a result, the sail will conduct an undamped oscillating motion around the Sun-line due to the offset between the centre-of-pressure and centre-of-mass. In this paper, the resulting oscillatory motion of the acceleration vector is exploited to design new families of periodic orbits in the Earth-Moon circular restricted three-body system. In particular, the effect of adding an oscillating sail to the family of Lyapunov orbits at the L1- and L2-points as well as the family of distant retrograde orbits (DROs) is investigated. Because the solar sail Earth-Moon system is non-autonomous (due to the apparent orbital motion of the Sun), the sail’s oscillating period, the orbital period and the period of the Sun around the Earth-Moon system all need to be commensurable in order for the orbits to be repeatable over time. Using a differential correction technique, orbits that satisfy these constraints can be obtained and the results comprise new families of periodic orbits that are parameterised by the required sail performance. In addition to exploiting the oscillating sail for generating new orbit families, this paper also investigates its potential for orbital transfers. By combining a systematic search method with a local optimiser, oscillating sail parameters and orbital parameters can be obtained that enable transfers between classical Lyapunov orbits at the L1-point, connections between classical Lyapunov orbits at different Lagrange points as well as transfers between orbits within the family of classical DROs

Hybrid solar sail and SEP propulsion for novel Earth observation missions

In this paper we propose a pole-sitter spacecraft hybridising solar electric propulsion (SEP) and solar sailing. The intriguing concept of a hybrid propulsion spacecraft is attractive: by combining the two forms of propulsion, the drawbacks of the two systems cancel each other, potentially enabling propellant mass saving, increased reliability, versatility and lifetime over the two independent systems. This almost completely unexplored concept will be applied to the continuous monitoring of the Earth’s polar regions through a pole-sitter, i.e. a spacecraft that is stationary above one pole of the Earth. The continuous, hemispherical, real-time view of the pole will enable a wide range of new applications for Earth observation and telecommunications. In this paper, families of 1-year-periodic, minimum-propellant orbits are found, for different values of the sail lightness number and distance from the pole. The optimal control problem is solved using a pseudo-spectral method. The process gives a reference control to maintain these orbits. In addition, for stability issues, a feedback control is designed to guarantee station-keeping in the presence of injection errors, sail degradation and temporary SEP failure. Results show that propellant mass can be saved by using a medium-sized solar sail. Finally, it is shown that the feedback control is able to maintain the spacecraft on-track with only minimal additional effort from the SEP thruster

Optimization of intersatellite routing for real-time data download

The objective of this study is to develop a strategy to maximise the available bandwidth to Earth of a satellite constellation through inter-satellite links. Optimal signal routing is achieved by mimicking the way in which ant colonies locate food sources, where the 'ants' are explorative data packets aiming to find a near-optimal route to Earth. Demonstrating the method on a case-study of a space weather monitoring constellation; we show the real-time downloadable rate to Earth

Design of ballistic three-body trajectories for continuous polar earth observation in the earth-moon system

This paper investigates orbits and transfer trajectories for continuous polar Earth observation in the Earth-Moon system. The motivation behind this work is to complement the services offered by polar-orbiting spacecraft, which offer high resolution imaging but poor temporal resolution, due to the fact that they can only capture one narrow swath at each polar passage. Conversely, a platform for high-temporal resolution imaging can enable a number of applications, from accurate polar weather forecasting to Aurora study, as well as direct-link telecommunications with high-latitude regions. Such a platform would complement polar orbiters. In this work, we make use of resonant gravity swing-by manoeuvres at the Moon in order to design trajectories that are suitable for quasi-continuous polar observation. In particular, it is shown that the Moon can flip the line of apsides of a highly eccentric, highly inclined orbit from north to south, without the need for thrust. In this way, a spacecraft can alternatively loiter for an extended period of time above the two poles. In addition, at the lunar encounter it is possible to change the period of time spent on each pole. In addition, we also show that the lunar swing-by can be exploited for transfer to a so-called pole-sitter orbit, i.e. a spacecraft that constantly hovers above one of the Earth's poles using continuous thrust. It is shown that, by using the Moon's gravity to change the inclination of the transfer trajectory, the total Δv is less than using a trajectory solely relying on high-thrust or low-thrust, therefore enabling the launchers to inject more mass into the target pole-sitter position

Distributed Spacecraft Path Planning and Collision Avoidance via Reciprocal Velocity Obstacle Approach

This paper presents the development of a combined linear quadratic regulation and reciprocal velocity obstacle (LQR/RVO) control algorithm for multiple satellites during close proximity operations. The linear quadratic regulator (LQR) control effort drives the spacecraft towards their target position while the reciprocal velocity obstacle (RVO) provides collision avoidance capabilities. Each spacecraft maneuvers independently, without explicit communication or knowledge in term of collision avoidance decision making of the other spacecraft in the formation. To assess the performance of this novel controller different test cases are implemented. Numerical results show that this method guarantees safe and collision-free maneuvers for all the satellites in the formation and the control performance is presented in term of Δv and fuel consumption

Hybrid low-thrust transfers to eight-shaped orbits for polar observation

In this paper, transfers from low Earth orbit (LEO) to so-called eight-shaped orbits at the collinear libration points in the circular restricted three-body problem are investigated. The potential of these orbits (both natural and sail displaced) for high-latitude observation and telecommunication has recently been established. The transfer is modelled by distinguishing between a near-Earth phase and an interplanetary phase. The near-Earth phase is first assumed to be executed with the Soyuz Fregat upper-stage, which brings the spacecraft from LEO to a highly elliptic orbit. From there, the interplanetary phase is initiated which uses low-thrust propulsion to inject the spacecraft into one of the eight-shaped orbit’s manifolds. Both solar electric propulsion (SEP), solar sailing and hybridised SEP and solar sailing are considered for this phase. The objective is to maximise the mass delivered to the eight-shaped orbit starting from a realistic Soyuz launch vehicle performance into LEO. Optimal trajectories are obtained by solving the optimal control problem in the interplanetary phase with a direct pseudospectral method. The results show that (over the full range of propulsion techniques) 1564 to 1603 kg can be injected into a natural eight-shaped orbit. Within this relatively small range, hybrid propulsion performs best in terms of mass delivered to the eight-shaped orbit, while SEP enables the fastest transfer times. With the interplanetary phase optimised, the upper-stage near-Earth phase is replaced by a multi-revolution low-thrust spiral. Locally optimal control laws for the SEP thruster and solar sail are derived to minimise the time of flight in the spiral. Both pure SEP and hybrid spiral show a significant reduction in the mass required in LEO to deliver the spacecraft to the eight-shaped orbits. While hybrid propulsion did not stand out for the use of an upper-stage near-Earth phase, it does for the use of a low-thrust spiral as it significantly reduces the spiral time with respect to the pure SEP case

Multiple near-earth asteroid rendezvous mission: solar-sailing options

The scientific interest in near-Earth asteroids (NEAs) and the classification of some of those as potentially hazardous for the Earth stimulated the interest in their exploration. Close-up observations of these objects will drastically increase our knowledge about the overall NEA population. For this reason, a multiple NEA rendezvous mission through solar sailing is investigated, taking advantage of the propellantless nature of this propulsion technology. Considering a spacecraft based on the DLR/ESA Gossamer technology, this work focuses on a method for searching possible sequences of NEA encounters. The effectiveness of the approach is demonstrated through a number of fully-optimised trajectories. The results show that it is possible to visit five NEAs within 10 years with near-term solar-sail technology. Moreover, a study on a reduced NEA database demonstrates the reliability of the approach used, showing that 58% of the sequences found with an approximated trajectory model can be converted into real feasible solar-sail trajectories. Overall, the study shows the effectiveness of the proposed automatic optimisation algorithm, which is able to find solutions for a large number of mission scenarios without any input required from the user

Multiple NEA Rendezvous Mission: Solar Sailing Options

The scientific interest in near-Earth asteroids (NEAs) and the classification of some of those as potentially hazardous asteroid for the Earth stipulated the interest in NEA exploration. Close-up observations of these objects will increase drastically our knowledge about the overall NEA population. For this reason, a multiple NEA rendezvous mission through solar sailing is investigated, taking advantage of the propellantless nature of this groundbreaking propulsion technology. Considering a spacecraft based on the DLR/ESA Gossamer technology, this work focuses on the search of possible sequences of NEA encounters. The effectiveness of this approach is demonstrated through a number of fully-optimized trajectories. The results show that it is possible to visit five NEAs within 10 years with near-term solar-sail technology. Moreover, a study on a reduced NEA database demonstrates the reliability of the approach used, showing that 58% of the sequences found with an approximated trajectory model can be converted into real solar-sail trajectories. Lastly, this second study shows the effectiveness of the proposed automatic optimization algorithm, which is able to find solutions for a large number of mission scenarios without any input required from the user