Rolla, MO, United States
Rolla, MO, United States
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Darling J.E.,IST-Rolla | Balakrishnan S.N.,IST-Rolla | D'Souzaz C.,NASA
AIAA Guidance, Navigation, and Control (GNC) Conference | Year: 2013

A neural network based novel state observer, known as the Sigma Point Modified State Observer, is presented. The Sigma Point Modified State Observer uses sigma point filtering techniques, similar to the Unscented Kalman Filter, in combination with a neural network to estimate system states, state error covariance, and system uncertainty in nonlinear systems online. Spacecraft atmospheric reentry simulation results are presented to show the validity of the Sigma Point Modified State Observer to highly nonlinear systems with significant uncertainty.


Harl N.,IST-Rolla | Harl N.,710 University Drive | Balakrishnan S.N.,IST-Rolla | Balakrishnan S.N.,710 University Drive
Journal of Guidance, Control, and Dynamics | Year: 2010

A guidance scheme has been developed for the terminal guidance of an unpowered lifting reentry vehicle during the approach and landing phase. The proposed approach is quite useful for offline trajectory design and allows for trajectories to be generated online through the use of a closed-loop control law. In scenarios in which the reentry vehicle is significantly deviated from its nominal trajectory upon entry into the landing phase, the usefulness of such an online method can be clearly realized. These types of scenarios are of interest for any reentry vehicle, including the space shuttle, since existing guidance approaches during the approach and landing phase involve tracking trajectories created offline. To solve the approach and landing guidance problem, a novel concept called the sliding mode terminal guidance is used in this work. This approach takes advantage of the finite-time-reaching phase of the sliding mode technique to ensure that any desired state constraints can be fulfilled in a finite time. Further, by using a new approach to second-order sliding mode control, analytic solutions are obtained for both the altitude and flight path angle during the reentry process. The end result of this approach is a closed-loop guidance (control) law, which can be used to generate trajectories that depend only on the initial and final conditions of the approach and landing phase. Simulations shown indicate that the method provides some robustness to variations in the initial downrange and velocity. copyright © 2009 by IST-Rolla, Rolla, MO. Published by the American Institute of Aeronautics and Astronautics, Inc.


Harl N.,IST-Rolla | Harl N.,Sandia National Laboratories | Rajagopal K.,IST-Rolla | Balakrishnan S.N.,IST-Rolla
Journal of Guidance, Control, and Dynamics | Year: 2013

A novel technique for estimating uncertainties caused by gravitational perturbations is presented. The approach, called the modified state observer, allows for the estimation of uncertainties in nonlinear dynamics and, in addition, providing estimates of the system states. The observer structure contains neural networks whose outputs are the uncertainties in the system. A useful and important application of this observer is the problem of determining uncertain gravitational perturbations that a satellite may experience when orbiting a body. With future space missions involving other bodies, such as asteroids that produce gravitational perturbations which are highly uncertain and are subjected to unknown physical influences, the modified state observer can be used not only to estimate the states of the satellites, but it can also be used to estimate the uncertainties that could be analyzed further with understanding the physical phenomena. To demonstrate the utility of the modified state observer for this class of problem the technique is applied for two cases: estimating the uncertainty caused by the J2 perturbation for an Earth orbiter and estimating the uncertainty in an asteroid's gravitational field. Simulations are presented, which indicate that the observer can accurately estimate both the periodic nature of these perturbations, as well as the magnitudes. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


Ohlmeyer E.J.,Aerospace Science Applications | Balakrishnan S.N.,IST-Rolla
AIAA Guidance, Navigation, and Control Conference | Year: 2010

This paper describes a series of system design and performance studies for a notional air-launched interceptor intended for boost phase interception of a ballistic missile target. A candidate launch platform for the interceptor is an unmanned air vehicle loitering in airspace near the target launch site. A notional target from the open literature is used for analysis. The conceptual interceptor is designed from first principles using standard methods. Designs for two target tracking filters based on the Extended Kalman Filter (EKF) and the Unscented Kalman Filter (UKF) are developed. Then tracking accuracy is quantified as a function of measurement noise levels. The effects of tracking errors and prediction interval on errors in the Predicted Intercept Point (PIP) is determined. Then an evaluation of how the PIP errors affect interceptor terminal performance is conducted, using heading errors and line-of-sight pointing errors as metrics. The performance of the candidate system design is then assessed. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


Harl N.,IST-Rolla | Rajagopal K.,Toomey Hall | Balakrishnan S.N.,IST-Rolla
AIAA Guidance, Navigation, and Control Conference 2011 | Year: 2011

A novel technique for estimating uncertainties caused by gravitational perturbations is presented. The approach, called the Modified State Observer (MSO), allows for the estimation of uncertainties in nonlinear dynamics while in addition providing estimates of the system states. The observer structure contains neural networks whose outputs are the uncertainties in the system. A useful and important application of this observer is the problem of determining uncertainties with an inaccurate gravity mode that a satellite may experience when orbiting a body. With future space missions involving other bodies such as asteroids that produce gravitational perturbations which are highly uncertain and are subjected to unknown physical influences, the MSO can be used not only to estimate the states of the satellites, it can be used to estimate the uncertainties that could further be analyzed further in understanding the physical phenomena. To demonstrate the utility of the MSO for this class of problem, the technique is applied for three cases: estimating the uncertainty caused by the J2 perturbation for Earth and Mars orbiters, and estimating the uncertainty in an asteroid's gravitational field. Simulations are presented which indicate that the observer can accurately estimate both the periodic nature of these perturbations as well as the magnitudes. © 2011 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


Harl N.,IST-Rolla | Balakrishnan S.N.,IST-Rolla | Phillips C.,U.S. Navy
AIAA Guidance, Navigation, and Control Conference | Year: 2010

A novel method for the integrated guidance and control of a missile, called Sliding Mode Integrated Guidance and Control (SMIGC), is derived. In this formulation, the guidance and control systems are developed together and implemented in a single loop. One benefit of this "integrated" approach is that beneficial synergies between the guidance and control subsystems can be exploited. The design process can also be significantly reduced since only one control architecture must be designed. SMIGC makes use of the finite-time reaching phase of the sliding mode technique to ensure that a desired constraint, the Predicted Impact Point (PIP) heading error, is achieved in a finite time. Furthermore, the robustness of sliding mode to uncertainties is combined with a novel method for accounting for target acceleration to yield acceptable miss distances against maneuvering targets. An interesting and desirable aspect of the controller is that it does not require full information about the target acceleration. Further, to fully understand the effects of target acceleration on the problem, an in-depth target acceleration uncertainty analysis is performed. The effectiveness of the SMIGC approach is demonstrated through a series of simulations with a 6-DOF nonlinear missile model that includes all aerodynamic effects against maneuvering targets. Representative numerical results show that against agile targets, SMIGC obtains a high Hit-to-Kill accuracy consistently with reasonable fin deflections. Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


Grant
Agency: National Aeronautics and Space Administration | Branch: | Program: SBIR | Phase: Phase I | Award Amount: 99.45K | Year: 2010

Spacecraft need accurate position and velocity estimates in order to control their orbits. Some missions require more accurate estimates than others, but nearly all missions need some type of orbit determination. IST-Rolla seeks to provide highly accurate algorithms that do not overpower the spacecraft's computer. Many new, powerful algorithms exist such as the particle filter and the unscented Kalman filter, but most of them involve integrating several state vectors, and those integrations devour the computing power available. IST-Rolla will implement the è-D technique, the cost based filter (CBF), and the neural network estimator for orbit determination(developed by IST-Rolla Engineers) and analyze the results. These filters are nonlinear and might provide better accuracy than the extended Kalman filter (EKF) which is widely used, without being computationally cumbersome as the particle filter and unscented Kalman filter. The theta-D technique approximates the solution to the filter-related Ricatti Equation. The CBF is an attempt to formulation of the filter under an 'optimal' framework. The neural network estimator works to estimate the modeling errors online so that the estimates become more accurate.


Grant
Agency: National Aeronautics and Space Administration | Branch: | Program: SBIR | Phase: Phase II | Award Amount: 598.97K | Year: 2011

IST-Rolla developed two nonlinear filters for spacecraft orbit determination during the Phase I contract. The theta-D filter and the cost based filter, CBF, were developed and used in various orbit determination scenarios. The scenarios were application to low Earth orbit, range only, and range and range rate estimation. The modified state observer was also developed to estimate uncertainty in the dynamic model besides estimation of orbital states.Phase I research showed that there is a problem with the linear-like form that is used by many nonlinear filters such as the State Dependant Riccati Equation filter (SDRE filter), and the theta-D and CBF. A study of the observability led to important discoveries about the lack of observabilty in some formulations. Detailed study of the working of the proposed nonlinear filters in terms of observability and their application to more precise orbit determination and model uncertainty estimation will be undertaken in Phase II.Also learned from Phase I, IST-Rolla will focus more on how and where these nonlinear filters can help NASA. There will be three main applications studied during Phase II: interplanetary orbit determination, space debris tracking, and interplanetary landing spacecraft tracking. These applications were chosen because of their relevance to current NASA missions and the nonlinearity of the measurements involved should show the need for the nonlinear filters. Furthermore, working algorithms and software will be given to NASA to test on ongoing applications.


Grant
Agency: Department of Defense | Branch: Missile Defense Agency | Program: SBIR | Phase: Phase II | Award Amount: 249.88K | Year: 2010

This proposal seeks to develop guidance algorithms and estimation schemes to intercept targets when they are boosting or on their ascent trajectory. Effective algorithma to work against such threats need to be robust, efficient and accurate due to the uncertainies in the target burn times and their intent. Furthermore, they could be manuevering. The guidance algorithms to be developed are based on optimality and robustness. These techniques will further be compared with the Lambert Guidance. To improve the effectiveness of the guidance algorithms, new algorithms are based that rae robust to time-delay. A major part of the effort will be to find analytical expressions to develop PIP estimation against a multistage boosting target whose burn times are unknown. The proposed algorithms will be tested in a 6 DOF environment. Performance of different guidance techniques proposed will be tested under various scenarios and compared for their accuracy and performance.


Grant
Agency: Department of Defense | Branch: Air Force | Program: SBIR | Phase: Phase I | Award Amount: 149.25K | Year: 2011

ABSTRACT: This proposal seeks to develop a novel tool wear monitoring technology using a neural network-based observer. In this methodology simple models of the wear process and another related machining process, such as force, are developed. The model development does not require lengthy analysis or experimentation since the methodology inherently accounts for the uncertainty in the models. The monitoring methodology measures the related machining process signal, as well as other available signals, and a neural network-based observer is used to estimate model uncertainties and the tool wear state. This information can be used to ensure tools are changed in a timely manner. Preliminary simulation studies show the promise of the proposed monitoring technology and this proposal seeks to further develop this methodology and prove it with real machining data of Ti6Al4V. BENEFIT: The proposed tool wear monitoring methodology will allow manufactures to dramatically increase the productivity and quality of their manufacturing operations. The ability to cost-effectively monitor the state of cutting tools in real time will provide the means to prevent cutting tools from being taken out of service before they have been fully utilized or from being taken out of service after they are too worn to be reground or, worse yet, they wear to the point of breakage. The proposed technology will minimize tool changes and costly downtime, allow cutting tools to be utilized longer, and will minimize incidents of tool breakage that ruin parts, which is particularly costly in a finishing operation of a part that undergone days, or even weeks, of processing. The commercial impact will be tremendous since the proposed technology can be applied to any machining operation.

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