Aerospace mission design requires the definition of a nominal trajectory, related to the expected performance of the vehicle, and the corrective actions tailored to compensating nonnominal flight conditions. These deviations may have an environmental nature or can arise from an imperfect vehicle modeling. This research addresses the development of an integrated methodology for optimization, guidance, and control of trajectory and attitude motion of aerospace vehicles, with potential application in several mission scenarios, e.g. atmospheric flight of aircraft and unmanned aerial vehicles, ascent path of launch vehicles, orbit transfers, and interplanetary missions. This unified architecture requires the preliminary modeling of both the aerospace vehicle of interest and the related dynamical environment, and is based on the joint, interactive application of specific algorithms. The indirect heuristic method is being employed for trajectory optimization, due to its capability of yielding the state, costate, and control vectors associated with the optimal path. The vehicle guidance and control will involve the interconnected use of the variable-time-domain neighboring optimal guidance and a constrained proportional-derivative attitude control algorithm. The guidance technique at hand refers to the optimal path as the reference trajectory, whereas the attitude control algorithm must consider some physical constraint related to the actuation system. Gain tuning through suitable optimization algorithms will be used to improve the overall performance of the methodology being developed in this research project. Some applications of practical relevance are being considered as study cases, for the purpose of testing the performance of the unified approach at hand, with the final objective of demonstrating its effectiveness, accuracy, and robustness.
Originality of the proposed research project resides in the numerical techniques for optimization, guidance, and control of aerospace vehicles, as well as in their integration, in the context of a unified architecture.
A general optimization technique termed indirect heuristic method (IHM) has been recently developed by the project leader, and uses the necessary conditions for optimality (i.e., the Pontryagin minimum principle, the Euler-Lagrange equations, and the Weierstrass-Erdmann corner conditions), together with a heuristic algorithm. The control variables are expressed as functions of the adjoint variables, which are subject to the costate equations (and the related boundary conditions). Because the control is determined without assuming any particular functional representation, IHM is capable of circumventing the main disadvantages of using heuristic approaches, while retaining the main advantage, which is the absence of any starting guess. Moreover, satisfaction of all the necessary conditions guarantees optimality of the solution. The recently introduced [1,2], general-purpose variable-time-domain neighboring optimal guidance algorithm (VTD-NOG) has several original features capable of overcoming the main difficulties related to the use of former NOG schemes, in particular the occurrence of singularities and the lack of an efficient law for the iterative real-time update of the time of flight. In fact, adoption of a normalized time domain leads to defining a new, effective updating law for the time of flight, a novel termination criterion, and a new analytical formulation for the sweep method. VTD-NOG identifies the trajectory corrections by assuming that the thrust has a prescribed direction with respect to the vehicle body axes. However, this assumption represents an approximation, and the attitude control system must be capable of maintaining the actual spacecraft orientation sufficiently close to the correct configuration corresponding to the desired thrust direction. To do this, the attitude control system can use thrust vector control (TVC), in conjunction with a proportional-derivative algorithm. If the actuator dynamics is sufficiently faster than the attitude control loop, this approach may be proven [3] to guarantee global convergence of the actual attitude toward the desired attitude. However, a proper saturation action might be necessary in order to avoid excessive angular rates for the thrust deflection, and the present research will address this issue. As the performance of the attitude control system depends on the proper selection of several gain coefficients, a systematic approach for their determination, based on dedicated parameter optimization algorithms, is being investigated as well. Furthermore, the worst-case scenario can be identified and modeled, in order to select these parameters in a robust fashion. This represents a particularly useful and valuable aspect of the research, potentially able to refine the overall methodology and improve its performance.
The general approach at hand is being developed and tested with reference to some applications of practical interest, such as (1) ascent trajectories of launch vehicles, (2) orbit transfers around the Earth, (3) interplanetary trajectories, (4) accurate orbit injection, and (5) atmospheric flight of aircraft or unmanned aerial vehicles. For each application, Monte Carlo campaigns are being performed, in the presence of stochastic deviations from nominal flight conditions. Navigation errors can be modeled as well. The outcomes coming from applying this integrated optimization, guidance, and control methodology are being evaluated with reference to three main properties: (a) effectiveness, i.e. the capability of compensating nonnominal flight conditions, without an excessive degradation of the objective function (minimized in the initial optimization phase), (b) accuracy, i.e. precise satisfaction of the boundary conditions, and (c) robustness, related to the system performance in the most unfavorable conditions.
This research has thus the ultimate purpose of demonstrating that the new optimization, guidance, and control technique at hand indeed represents an effective methodology, capable of overcoming known difficulties and potentially able to outperform alternative techniques described in the scientific literature, with reference to different aerospace mission scenarios.
*References
[1] Pontani M., Cecchetti G., and Teofilatto P., ¿Variable-Time-Domain Neighboring Optimal Guidance, Part 1: Algorithm Structure,¿ Journal of Optimization Theory and Applications, 166(1), 2015, 76-92
[2] Pontani M., Cecchetti G., and Teofilatto P., ¿Variable-Time-Domain Neighboring Optimal Guidance Applied to Space Trajectories,¿ Acta Astronautica, 115, 2015, 102-120
[3] Celani F., "Global and Robust Attitude Control of a Launch Vehicle in Exoatmospheric Flight," 3rd IAA Conference on Dynamics and Control of Space Systems, Moscow, 2017