Sensor hybridization using neural networks for rocket terminal guidance

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Abstract

The Guidance, Navigation and Control (GNC) of air and space vehicles, including artillery rockets, has been one of the spearheads of research in the aerospace field in recent times. Increasing the accuracy of these ballistic projectiles is the major goal. Using Global Navigation Satellite Systems (GNSS) and inertial navigation systems, accuracy may be detached from range. However, during the terminal stage of flight, when movement is governed by highly changing nonlinear forces and moments, GNC strategies based on these systems cause enormous errors in determining attitude and position. These effects can be diminished using additional sensors, independent of jamming and cumulative errors, such as the quadrant photo-detector semi-active laser. This paper proposes a novel non-linear hybridization algorithm, which is based on neural networks, to feed GNC systems while complexity and costs are reduced. It fuses the information from multi-sensor signals, such as GNSS, inertial navigation systems, and semi-active lasers, to predict the line of sight vector, which joins the target and the projectile and drives the flight. As compared to traditional approaches, the use of a neural network presents the advantage that once the network is trained, it is no longer necessary to know the physical-mathematical foundations that govern the dynamics of flight. Instead, it is the network that learns the dynamics. Six-degree-of-freedom non-linear simulations, which are based on real flight dynamics, are used to train the neural networks in the hybridization process. Once training is finished, the approach is tested and simulated together with modified proportional navigation techniques and control methods. Monte Carlo analysis is conducted to determine the suitability of the closed-loop performance across a full spectrum of uncertainty conditions regarding launch, sensor performance, atmospheric, and thrust.

Introduction

Global Navigation Satellite Systems (GNSS) signals are widely utilized in the present days for aerospace applications. Regrettably, as the requirement of the application for which it is designed increases, the reliability decreases inversely proportional. One of the effects is the reduced signal/noise relationship caused by the attenuation and loss of the GNSS signal. So, independent sources of navigation data are needed to mitigate these effects and reduce interference.

The use of devices which are independent of external perturbations such as Inertial Navigation Systems (INS), or more concretely Inertial Measurement Units (IMUs), does not mitigate the fact that they feature important lacks, such as incorrect initialization of navigation system, inertial sensor (accelerometer and gyroscope) imperfections which are the trigger for cumulative errors, and imperfections in implemented dynamics model. Despite of this fact, Inertial Navigation Systems are excellent for GNC data acquisition when they are hybridized with GNSS receivers, which minimize the drift in INS [7], [5].

However, counter-posed objectives such as precision and cost have always been set as primordial characteristics for artillery rocket performance. “Collateral damage” is minimized when precision increases and viability for a military action can be suppressed by non-allowable values of it [13]. To maintain an acceptable precision level while reducing costs, less precise devices may substitute expensive systems as long as reachability and persistence of the GNSS signal is guaranteed to actualize the inertial system to limit overall drift. However, high uncertainty is featured in many scenarios. An alternative to lower collateral damage and costs is merging data of a few low cost sensors, which makes possible increases in accuracy levels.

The advantages of coordinated combination of information have appeared in numerous land warfare, antisubmarine and strategic air applications [36]. Information combination strategies for 6 degrees of freedom rockets are depicted in [27]. The main issues in using various sorts of INS augmented with GNSS updates have been considered by [30]. Notwithstanding INS/GNSS hybridization, a set of nonlinear observers are presented by [2]. In case that various sensors are available, they may be additional contributions to a filter, e.g., the Kalman filter [7], [5].

As in [7], [5], the need to grow new Guidance, Navigation and Control (GNC) frameworks has spurred research on stability and controllability of these aerospace devices. In [11] a novel guidance law is presented. It uses observations consisting solely of seeker line-of-sight angle measurements and their rate of change. [44], [3] present cooperative techniques for various missiles based on the conventional Proportional Navigation (PN). In [31] a target-missile-defender engagement is considered, in which the missile attempts to intercept the target and the defender tries to prevent this interception via missile's interception. An attitude control-framework device for a spinning sounding rocket, which depends on a proportional, integral, and derivative (PID) controller, is created in [19]. Proportional-derivative GNC laws for the terminal stage are proposed in [18], [37]. The line of sight is recreated in [26]. In [43], a limited time concurrent sliding-mode GNC law with terminal angle of impact limitation is introduced. An overall scheme concerning the guidance and autopilot modules for a class of spin-stabilized balance controlled artillery devices is introduced in [34].

Yet, even in GNSS/IMU hybrid devices, there exist obscure unsettling influences, such as irregular estimations, which might be predominant during terminal guidance for low-cost gadgets. Other methods, which are based on image recognition using multi-spectral cameras and other sensors, are deeply used in navigation and aerospace applications [29] at a high cost. Hence, advancement on new algorithms which may easily fulfill the required precision levels and low cost requirements during terminal guidance is a foundation in research on ballistic artillery devices. For instance, present day laser guided ballistic rockets are incorporating IMU, GPS and laser guidance capacity, offering high accuracy and all-climate assault capacity [6], [42].

Semi Active Laser Kits (SAL) have been created to improve exactness in guided rockets. SAL are applied in many designing ambit, for instance in calculating rotational speed of objects or in estimating slight dynamics of laser spots [41], [8]. Probably, the best favourable position of these devices is its high precision for GNC during the last periods of the guidance, when contrasted with its minimal cost efforts.

Considering what has been depicted, sensor hybridization techniques [29], [28] for viable and robust estimations that take into account autonomy, accuracy and minimal cost are a current need. In this sense, a promising direction is the one offered by Machine Learning (ML) procedures. They offer multitudinous options and innovative solutions of particular interest for GNC applications, where their foray is still latter and shallow, yet with no doubt promising. In this line, there have been successful attempts in controlling other dynamic processes employing Artificial Neural Networks (ANN) [1].

Moreover, the utilization of ML strategies for the estimation of parameters dependent on the dynamics of aviation vehicles presents the bit of leeway that once the algorithm is calibrated or trained, it is not important to know the physical-mathematical establishments that rule the flight mechanics. These algorithms, for the input signals, may restore the data that can later be utilized inside the GNC device, such that the subsequent solutions will fit the genuine output ([32], [21]). Notice that this does not hold true for traditional methods for sensor signal hybridization. For such approaches, it is necessary to know the dynamics governing the movement of the vehicle. And furthermore, as accuracy requirements increase, the tuning becomes more complex, calling for high-complexity tuning methods.

However, the application of these strategies depends largely on the representativity and amount of real input and output data employed for training. This fact implies that desired performance stability and convergence is restricted to the trained mission envelope. Other control approaches, which could ensure convergence and stability parameters under the proposed uncertain conditions, might also be employed for this type of application. For instance, adaptive control that uses adaptation laws to online estimate unknown system parameter variations for various mission envelopes [9], [14], [15].

The objective of this paper is to improve the current strategies for terminal guidance applying a powerful hybridization calculation, introducing ML procedures. The goal is to acquire a precise vector among rocket and target from a blend of various sensors data acquisitions to be utilized within a GNC device.

Contributions

The main contribution of this scientific research is the study of Machine Learning techniques, i.e., Neural Network (NN) algorithms, to hybridize GNSS/IMU and semi-active laser quadrant photo-detectors signals. With them, it is aimed to predict the line of sight, i.e., the vector linking target and rocket, during terminal guidance to improve the accuracy at the impact. Consequently, the advantage of this hybrid system over the GNSS/IMU option is the capability to avoid drift and modify final impact angles during the terminal phase.

An approach based on different combinations of neural networks and training algorithms, which predict line of sight dynamics during terminal phase, is presented. GNSS/IMU and semi-active laser (SAL) quadrant photo-detectors data are the inputs for the NN. After that, the predicted line of sight is integrated on a modified proportional navigation guidance law and on a control system, which is based on a rotatory technique. As controller, it is proposed a robust double-input double-output algorithm, which manages the substantial coupling among the normal and lateral projectile nonlinear dynamics.

Additionally, a flight dynamics model that reproduces the highly spinning movement of the rocket is utilized. This model considers non linear aerodynamic forces and moments and it has been validated to build up a realistic simulation campaign. [7], [5] Indeed, the obtained results exhibit exactness and applicability under non deterministic environment, launch and projectile conditions.

As stated before, the presented approach depends on the amount of available data for training, which means stability and convergence may be restricted to the trained mission envelope. However, note that the type of vehicle presented in this paper is non-reusable and training has been performed for a wide variety of launching, flight, and impact point conditions to resemble realistic settings, i.e., for a comprehensive set of missions. Overall, the methodology results in good enough quality results (including response to uncertainty in several conditions and characteristics), showing good GNC performances. Therefore, the presented research poses a path for a generalized and systematic application of NN/Machine Learning for GNC Strategies.

This paper is organized as follows. In Section 2, the system modeling is described in detail. Section 3 describes navigation, guidance and control algorithms. Section 4 exposes simulations results. Finally, discussion and conclusions are presented.

Section snippets

Plant modeling

This section is focused on the plant description, the nonlinear flight dynamics model, sensor and actuation models, and the developed hybridization for GNC purposes.

GNC algorithm definition

Proposed navigation, guidance and control algorithms are described in this section.

Numerical simulations

The previously described dynamics nonlinear conditions are integrated forward in time utilizing a fixed time step Runge-Kutta method of fourth grade to get a single flight path. In [7], it is shown the validation of this modeling and solving approach for ballistic flights. So as to exhibit the precision of the outcomes given by the novel methodology introduced here, which depends on neural networks, they are contrasted with the outcomes acquired in [7] and [4]. The methodology in [7] highlights

Conclusions

A novel methodology, which depends on an innovative hybridization among semi-active laser quadrant photo-detector, GNSS and IMU has been created. Little errors of 1 m in GNSS/IMU frameworks may instigate huge mistakes in line of sight vector computation. Note that when separation to target is small, these errors may bring high angular errors in line of sight. The proposed approach can improve the exactness of line of sight calculation during the terminal GNC, enhancing the accuracy on impact

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

This research was supported by Project Grant F663 - AAGNCS by the “Dirección General de Investigación e Innovación Tecnológica, Consejería de Ciencia, Universidades e Innovación, Comunidad de Madrid” and “Universidad Rey Juan Carlos”. The authors would like to thank Lieutenant Colonel Jesús Sánchez (NMT) of the National Institute for Aerospace Technology (INTA) for the solid modeling of the concept. The authors also thank the comments and suggestions raised by the anonymous reviewers.

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