Optimal tuning of adaptive augmenting controller for launch vehicles in atmospheric flight

In this Note, two novel and effective tuning methodologies for an adaptive augmenting control (AAC) system, realized to consistently improve performance and robustness of a standard launch vehicle single-axis attitude controller in atmospheric flight, have been presented. To this end, a methodology for AAC parameter tuning is presented where a robust design optimization (RDO) problem is formulated, and the goal is to maximize a statistical metric that describes FCS performance measured over a set of representative simulations of LV flight. In more detail, adaptive law parameters are tuned with the aim of minimizing attitude error and traversal aerodynamic loads. As major advantages, the occurrence of Loss of vehicle (LOV) events and the issues and burden of the manual trial-and-error procedures currently adopted for the design of the adaption law may be reduced

Indirect Optimization of Satellite Deployment into a Highly Elliptic Orbit

The analysis of the optimal strategies for the deployment of a spacecraft into a highly elliptic orbit is carried out by means of an indirect optimization procedure, which is based on the theory of optimal control. The orbit peculiarities require that several perturbations are taken into account: an 8x8 model of the Earth's potential is adopted and gravitational perturbations from Moon and Sun together with solar radiation pressure are considered. A procedure to guarantee convergence and define the optimal switching structure is outlined. Results concerning mission with up to 4.5 revolutions around the Earth are given and significant features of this kind of deployment are highlighte

Single axis pointing for underactuated spacecraft with a residual angular momentum

The problem of aiming a generic body-fixed axis along an inertially fixed direction is dealt with for an underactuated spacecraft in the presence of a non-zero residual angular momentum, when only two reaction wheels can exchange angular momentum with the spacecraft platform. An analytical condition for the feasibility of the desired pointing is derived first, together with a closed-form solution for the corresponding attitude with zero platform angular rate. A nonlinear controller is then developed in the framework of singular perturbation theory, enforcing a two-timescale response to the system. Convergence to the desired attitude, when the pointing direction falls within admissible limits, is then proved for rest-to-rest maneuvers and randomly generated initial tumbling conditions for a configuration representative of a small-size satellite

Evolutionary optimization of multirendezvous impulsive trajectories

This paper investigates the use of evolutionary algorithms for the optimization of time-constrained impulsive multirendezvous missions. The aim is to find the minimum-ΔV trajectory that allows a chaser spacecraft to perform, in a prescribed mission time, a complete tour of a set of targets, such as space debris or artificial satellites, which move on the same orbital plane at slightly different altitudes. For this purpose, a two-level design approach is pursued. First, an outer-level combinatorial problem is defined, dealing with the simultaneous optimization of the sequence of targets and the rendezvous epochs. The suggested approach is first tested by assuming that all transfer legs last exactly the same amount of time; then, the time domain is discretized over a finer grid, allowing a more appropriate sizing of the time window allocated for each leg. The outer-level problem is solved by an in-house genetic algorithm, which features an effective permutation-preserving solution encoding. A simple, but fairly accurate, heuristic, based on a suboptimal four-impulse analytic solution of the single-target rendezvous problem, is used when solving the combinatorial problem for a fast guess at the transfer cost, given the departure and arrival epochs. The outer-level problem solution is used to define an inner-level NLP problem, concerning the optimization of each body-to-body transfer leg. In this phase, the encounter times are further refined. The inner-level problem is tackled through an in-house multipopulation self-adaptive differential evolution algorithm. Numerical results for case studies including up to 20 targets with different time grids are presented

EOS: A Parallel, Self-Adaptive, Multi-Population Evolutionary Algorithm for Constrained Global Optimization

This paper presents the main characteristics of the evolutionary optimization code named EOS, Evolutionary Optimization at Sapienza, and its successful application to challenging, real-world space trajectory optimization problems. EOS is a global optimization algorithm for constrained and unconstrained problems of real-valued variables. It implements a number of improvements to the well-known Differential Evolution (DE) algorithm, namely, a self-adaptation of the control parameters, an epidemic mechanism, a clustering technique, an arepsilon-constrained method to deal with nonlinear constraints, and a synchronous island-model to handle multiple populations in parallel. The results reported prove that EOS is capable of achieving increased performance compared to state-of-the-art single-population self-adaptive DE algorithms when applied to high-dimensional or highly-constrained space trajectory optimization problems

On the use of A* search for active debris removal mission planning

This paper focuses on the optimal design of an active debris removal mission. A cluster of debris orbiting in sun-synchronous orbit is considered. A numerical score is associated with each debris on the basis of its level of threat. The mission goal is to maximize the cumulative score of the removed debris, while meeting operational constraints on both the total mission ΔV and time. The optimization problem, that is equivalent to a Time-Dependent Orienteering Problem, is formulated in the paper as a search problem on a graph and solved by A*, an optimal tree search algorithm. Three admissible heuristics for enhancing A* performance on the ADR mission design problem are derived in the paper as the exact solutions of relaxed versions of the original combinatorial problem. Their effectiveness is assessed on missions of increasing dimension and complexity, and compared with that of a commercial branch-and-bound solver on an original 0–1 integer linear programming formulation of the problem. A fast-computation near-optimal transfer strategy, which cleverly exploits the J2 perturbation to achieve the correct alignment between the orbital planes, is used to pre-calculate the ΔV spent by the spacecraft to move between any pair of debris on a discrete grid of departure/arrival epochs. Numerical results are presented for a 21-debris cluster, by analyzing the effect of the debris score distribution, of the total mission time, and of the maximum transfer duration on the computational time required by the different algorithms to optimally solve the problem

Deep learning techniques for autonomous spacecraft guidance during proximity operations

This paper investigates the use of deep learning techniques for real-time optimal spacecraft guidance during terminal rendezvous maneuvers, in presence of both operational constraints and stochastic effects, such as an inaccurate knowledge of the initial spacecraft state and the presence of random in-flight disturbances. The performance of two well-studied deep learning methods, behavioral cloning (BC) and reinforcement learning (RL), is investigated on a linear multi-impulsive rendezvous mission. To this aim, a multilayer perceptron network, with custom architecture, is designed to map any observation of the actual spacecraft relative position and velocity to the propellant-optimal control action, which corresponds to a bounded-magnitude impulsive velocity variation. In the BC approach, the deep neural network is trained by supervised learning on a set of optimal trajectories, generated by routinely solving the deterministic optimal control problem via convex optimization, starting from scattered initial conditions. Conversely, in the RL approach, a state-of-the-art actor–critic algorithm, proximal policy optimization, is used for training the network through repeated interactions with the stochastic environment. Eventually, the robustness and propellant efficiency of the obtained closed-loop control policies are assessed and compared by means of a Monte Carlo analysis, carried out by considering different test cases with increasing levels of perturbations

Tracking filter integration in the adaptive augmenting controller of a launch vehicle

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Meta-Reinforcement Learning for Adaptive Spacecraft Guidance during Multi-Target Missions

In this paper, a meta-reinforcement learning approach is used to generate a guidance algorithm capable of carrying out multi-target missions. Specifically, two models are trained to learn how to realize multiple fuel-optimal low-thrust rendezvous maneuvers between circular co-planar orbits with close radii. The first model is entirely based on a Multilayer Perceptron (MLP) neural network, while the second one also relies on a Long Short-Term Memory (LSTM) layer, which provides augmented generalization capability by incorporating memory-dependent internal states. The two networks are trained via Proximal Policy Optimization (PPO) on a wide distribution of transfers, which encompasses all possible trajectories connecting any pair of targets of a given set, and in a given time window. The aim is to produce a nearly-optimal guidance law that could be directly used for any transfer leg of the actual multi-target mission. To assess the validity of the proposed approach, a sensitivity analysis on a single leg is carried out by varying the radius either of the initial or the final orbit, the transfer time, and the initial phase angle between the chaser and the target. The results show that the LSTM-equipped network is able to better reconstruct the optimal control in almost all the analyzed scenarios, and, at the same time, to achieve, in average, a lower value of the terminal constraint violation