A New, General Perturbative Guidance for Space Vehicles

Acta Astronautica, 2018

Future human or robotic missions to the Moon will require efficient ascent path and accurate orbit injection maneuvers, because the dynamical conditions at injection affect the subsequent phases of spaceflight. This research is focused on the original combination of two techniques applied to lunar ascent modules, i.e. (i) the recentlyintroduced variable-time-domain neighboring optimal guidance (VTD-NOG), and (ii) a constrained proportionalderivative (CPD) attitude control algorithm. VTD-NOG belongs to the class of implicit guidance approaches, aimed at finding the corrective control actions capable of maintaining the spacecraft sufficiently close to the reference trajectory. CPD pursues the desired attitude using thrust vector control and side jet system, while constraining the rates of both the thrust deflection angle and the roll control torque. After determining the optimal two-dimensional ascent path, which represents the reference trajectory, VTD-NOG & CPD is applied in the presence of nonnominal flight conditions, namely those due to navigation and actuation errors, incorrect initial position, unpredictable oscillations of the propulsive thrust, and imperfect modeling of the spacecraft mass distribution and variation. These stochastic deviations are simulated in the context of extensive Monte Carlo campaigns, and yield three-dimensional perturbed trajectories. The numerical results obtained in this work unequivocally demonstrate that VTD-NOG & CPD represents an accurate and effective methodology for guidance and control of lunar ascent path and orbit injection.

2012

This paper presents a comprehensive review of spacecraft guidance algorithms for asteroid intercept and rendezvous missions. Classical proportional navigation (PN) guidance is reviewed first, followed by pulsed PN guidance, augmented PN guidance, predictive feedback guidance, Lambert guidance, and other guidance laws based on orbit perturbation theory. Optimal feedback guidance laws satisfying various terminal constraints are also discussed. Finally, the zero-effort-velocity (ZEV) error, analogous to the well-known zero-effort-miss (ZEM) distance, is introduced, leading to a generalized ZEM/ZEV guidance law. These various feedback guidance laws can be easily applied to real asteroid intercept and rendezvous missions. However, differing mission requirements and spacecraft capabilities will require continued research on terminal-phase guidance laws.

Aerotecnica Missili & Spazio

This research is focused on the analysis, design, and numerical testing of a feedback guidance algorithm for autonomous (unmanned) close-range maneuvering of a chaser spacecraft, in the context of orbital rendezvous with a target vehicle. The relative dynamics of the two vehicles, placed in nearby low Earth orbits, is modeled using the nonlinear Battin–Giorgi equations of relative motion, with the inclusion of all the relevant perturbations, i.e. several harmonics of the geopotential, atmospheric drag, solar radiation pressure, and third body gravitational pull due to Moon and Sun. Unlike several former contributions in the scientific literature, this research considers the orbit perturbing actions on both vehicles, proving that this is crucial for a successful maneuver. Feedback linearization provides the theoretical foundation for the definition and development of a guidance algorithm that is capable of driving the chaser vehicle toward the target spacecraft. Moreover, discrete-va...

Automatica, 2002

This paper addresses the computation of the required trajectory correction maneuvers for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launch vehicle. By combining dynamical systems theory with optimal control techniques, we are able to provide a compelling portrait of the complex landscape of the trajectory design space. This approach enables automation of the analysis to perform parametric studies that simply were not available to mission designers a few years ago, such as how the magnitude of the errors and the timing of the ÿrst trajectory correction maneuver a ects the correction V. The impetus for combining dynamical systems theory and optimal control in this problem arises from design issues for the Genesis Discovery Mission being developed for NASA by the Jet Propulsion Laboratory.

Journal of Aerospace …, 2010

A closed-loop time-optimal control strategy for the highly nonlinear problem of the lunar landing mission by using the perturbation technique is developed in this study. The first part of the study considers analytical solution for an optimal control policy of variable mass spacecraft, while it descents on the surface of the moon in the variable gravitational field of it. To validate the accuracy of perturbation solution, a numerical approach based on steepest descent method is employed. The second part considers analytical derivation of an optimal feedback guidance solution by employing the neighboring optimal control ͑NOC͒ law when effects of imperfection in the dynamic model or disturbing noises have been taken into account. The technique of NOC produces time-varying feedback gains that minimize the performance index to the second order for perturbations from a nominal optimal path. The robustness of the designed NOC law is examined with applying sinusoidal noises. From the study of the simulation results, it may be concluded that the developed optimal guidance laws may be used in real world spacecraft applications.

Journal of Aerospace Engineering, 2020

Recently, low-thrust propulsion is gaining a strong interest by the research community, and already found application in some mission scenarios. This paper proposes an integrated guidance and control methodology, termed VTD-NOG & PD-RM, and applies it to orbit transfers from a low Earth orbit (LEO) to a geostationary orbit (GEO), using low-thrust. The variable time-domain neighboring optimal guidance (VTD-NOG) is a closedloop guidance approach based on minimization of the second differential of the objective functional along the perturbed path, and avoids the singularities that occur using alternate neighboring optimal guidance algorithms. VTD-NOG finds the trajectory corrections considering the thrust direction as the control input. A proportionalderivative scheme based on rotation matrices (PD-RM) is used in order to drive the actual thrust direction toward the desired one determined by VTD-NOG. Reaction wheels are tailored to actuate attitude control. In the numerical simulations, thrust magnitude oscillations, displaced initial conditions, and gravitational perturbations are modeled. Extensive Monte Carlo campaigns show that orbit insertion at GEO occurs with excellent accuracy, thus proving that VTD-NOG & PD-RM represents an effective architecture for guidance and control of lowthrust Earth orbit transfers.

International Journal of Modelling, Identification and Control, 2014

This paper attempts to compare the two methods of Takagi-Sugeno (TS) fuzzy logic and neighbouring optimal control (NOC), for closed-loop guidance laws of low-thrust spacecraft system equations. At first, the open-loop optimal guidance is considered as the optimal thrust steering program that will transfer the vehicle from an inclined low earth orbit to a high earth orbit. Secondly, proper closed-loop guidance laws are achieved, as the novelty of this work, to examine the robustness of the two methods with respect to min-effort criterion for low-thrust spacecrafts. This performance index will be better than customary min-time and will be investigated as a new trend in this field for closed-loop guidance. The results illustrate the viability and efficiency of TS and NOC methods as closed-loop guidance laws for low-thrust orbital manoeuvres regarding the robustness of this guidance against disturbances. Finally, results illustrate a better method to achieve closed-loop guidance for low-thrust spacecraft manoeuvres.

Acta Astronautica, 2014

Optimal feedback control is classically based on linear approximations, whose accuracy drops off rapidly in highly nonlinear dynamics. Several nonlinear optimal feedback control strategies have appeared in recent years. Among them, differential algebraic techniques have been used to tackle nonlinearities by expanding the solution of the optimal control problem about a reference trajectory and reducing the computation of optimal feedback control laws to the evaluation of high order polynomials. However, the resulting high order method could not handle control saturation constraints, which remain a critical facet of nonlinear optimal feedback control. This work introduces the management of saturating actuators in the differential algebraic method.

Journal of Aerospace Engineering, 2018

Future human or robotic missions to the Moon will require efficient ascent path and accurate orbit injection maneuvers, because the dynamical conditions at injection affect the subsequent phases of spaceflight. This research is focused on the original combination of two techniques applied to lunar ascent modules, i.e. (i) the recently-introduced variable-time-domain neighboring optimal guidance (VTD-NOG), and (ii) a constrained proportional-derivative (CPD) attitude control algorithm. VTD-NOG belongs to the class of feedback implicit guidance approaches, aimed at finding the corrective control actions capable of maintaining the spacecraft sufficiently close to the reference trajectory. CPD pursues the desired attitude using thrust vector control, while constraining the rate of the thrust deflection angle. The numerical results unequivocally demonstrate that the joint use of VTD-NOG and CPD represents an accurate and effective methodology for guidance and control of lunar ascent path and orbit injection, in the presence of nonnominal flight conditions .

IFAC Proceedings Volumes, 2000

This paper addresses the computation of the required trajectory correction maneuvers (TCM) for a halo orbit space mission to compensate for the launch velocity errors introduced by inaccuracies of the launch vehicle. By combining dynamical systems theory with optimal control techniques, we produce a portrait of the complex landscape of the trajectory design space. This approach enables parametric studies not available to mission designers a few years ago, such as how the magnitude of the errors and the timing of the first TCM affect the correction ∆V. The impetus for combining dynamical systems theory and optimal control in this problem arises from design issues for the Genesis Discovery mission being developed for NASA by the Jet Propulsion Laboratory.

Acta Astronautica, 2014

A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems.

Journal of Guidance, Control, and Dynamics, 2013

The performance of the zero-effort-miss/zero-effort-velocity (ZEM/ZEV) feedback guidance algorithm is evaluated through practical space application examples. The ZEM/ZEV feedback guidance algorithm is in general not an optimal solution; however, it is an optimal solution in a uniform gravitational environment. It is also conceptually simple and easy to implement, and thus has great potential for autonomous on-board implementation. It is shown that, for some classic ballistic missile intercept and asteroid intercept scenarios, the ZEM/ZEV algorithm can even compete with corresponding open-loop optimal solutions, while its feedback characteristics make it more suitable to deal with uncertainties and perturbations. By employing the ZEM/ZEV algorithm in the highly nonlinear orbital transfer and raising problems and comparing with corresponding open-loop optimal solutions, its simplicity and near-optimality are further verified.

Journal of Aerospace Engineering, Sciences and Applications, 2008

Space trajectory design always requires the solution of an optimal control problem in order to maximize the payload launch-mass ratio while achieving the primary mission goals. A certain level of approximation always characterizes the dynamical models adopted to perform the design process. Furthermore the state identification is usually affected by navigation errors. Thus, after the nominal optimal solution is computed, a control strategy that assures the execution of mission goals in the real scenario must be implemented. In this frame differential algebraic techniques are here proposed as an effective alternative tool to design the guidance law. By using differential algebra the final state dependency on initial conditions, environmental and control parameters is represented by high order Taylor series expansions. The mission constraints can then be solved to high order using a so-called high order partial inversion of the polynomial relationship for every admissible uncertainty. The control strategy is eventually reduced to a simple function evaluation. The performances of the proposed methods are assessed by two examples of space mission trajectory design: a continuous propelled Earth-Mars transfer and an aerocapture maneuver at Mars.

IFAC-PapersOnLine, 2018

The design of optimal or sub-optimal guidance laws for aerospace vehicles remains a challenging task because of its computation difficulties. Recently in literature computationally efficient technique named as MPSC (model predictive spread control) has been proposed to overcome this problem. It combine nonlinear optimal control theory and approximate dynamic programming philosophies and hence embed effective trajectory optimization concepts into guidance law. Here objective is to show the application of MPSC to the generation of guidance law for astronautical as well as atmospheric aerospace vehicles. Here, four different cases were taken, a successful landing of an aircraft, an optimal re-entry guidance path of a spacecraft, an interception of ground target by air launched missile and interception against incoming air target. Performance of the proposed MPSC guidance is demonstrated using a 3DOF simulation which clearly shows the effectiveness of the MPSC guidance law for various application model.  Recently in literature, a nonlinear model predictive static programming (MPSP) technique (Padhi (2009)) which is a combination of nonlinear optimal control theory (Yang (2005)-Cannon (2004)) and dynamic programming (Werbos (1992)) has been proposed. The philosophy is quite similar to optimal control theory based approach. The advantage of this approach is that the control action is guaranteed to be smooth

International Conference on Aerospace Sciences and Aviation Technology, 2007

The feedback optimal control problem in low-thrust interplanetary trajectory design is studied in this paper. The problem is tackled by solving the Hamilton-Jacobi-Bellman equation via a generating function technique devised for linear systems. Instead of solving the classical optimal control problem, this technique allows us to derive closed loop control laws in the preliminary design phase. The idea of the work consists in applying a globally diffeomorphic linearizing transformation that rearranges the original nonlinear two-body dynamics into a linear system of ordinary differential equations written in new variables. The generating function technique is then applied to this new dynamical system, the feedback optimal control is solved, and the variables are back transformed in the original ones. We circumvent in this way the problem of expanding the vector field and truncating higher-order terms because no accuracy is lost in the undertaken approach. This technique can be applied to any planet-to-planet transfer; it has been successfully tested here for the classical Earth-Mars low-thrust transfer.