Puneet Singla

Adaptive Output Feedback Control for Spacecraft Rendezvous and Docking Under Measurement Uncertainty

An output feedback structured model reference adaptive control law has been developed for spacecraft rendezvous and docking problems. The effect of bounded output errors on controller performance is studied in detail. Output errors can represent an aggregation of sensor calibration errors, systematic bias, or some stochastic disturbances present in any real sensor measurements or state estimates. The performance of the control laws for stable, bounded tracking of the relative position and attitude trajectories is evaluated, considering unmodeled external as well as parametric disturbances and realistic position and attitude measurement errors. Essential ideas and results from computer simulations are presented to illustrate the performance of the algorithm developed in the paper.

Uncertainty propagation for nonlinear dynamic systems using Gaussian mixture models

A Gaussian-mixture-model approach is proposed for accurate uncertainty propagation through a general nonlinear system. The transition probability density function is approximated by a finite sum of Gaussian density functions for which the parameters (mean and covariance) are propagated using linear propagation theory. Two different approaches are introduced to update the weights of different components of a Gaussian-mixture model for uncertainty propagation through nonlinear system. The first method updates the weights such that they minimize the integral square difference between the true forecast probability density function and its Gaussian-sum approximation. The second method uses the Fokker-Planck-Kohnogorov equation error as feedback to adapt for the amplitude of different Gaussian components while solving a quadratic programming problem. The proposed methods are applied to a variety of problems in the open literature and are argued to be an excellent candidate for higher-dimensional uncertainty-propagation problems.

Adaptive Gaussian Sum Filter for Nonlinear Bayesian Estimation

A nonlinear filter is developed by representing the state probability density function by a finite sum of Gaussian density kernels whose mean and covariance are propagated from one time-step to the next using linear system theory methods such as extended Kalman filter or unscented Kalman filter. The novelty in the proposed method is that the weights of the Gaussian kernels are updated at every time-step, by solving a convex optimization problem posed by requiring the Gaussian sum approximation to satisfy the Fokker-Planck-Kolmogorov equation for continuous-time dynamical systems and the Chapman-Kolmogorov equation for discrete-time dynamical systems. The numerical simulation results show that updating the weights of different mixture components during propagation mode of the filter not only provides us with better state estimates but also with a more accurate state probability density function.

An Approach for Nonlinear Uncertainty Propagation: Application to Orbital Mechanics

An approach for nonlinear propagation of orbit uncertainties is discussed while making use of the Fokker-Planck-Kolmogorov Equation (FPKE). The central idea is to replace evolution of initial conditions for a dynamical system with the evolution of a probability density function (pdf) for state variables. The transition pdf corresponding to dynamical system state vector is approximated by using a nite Gaussian mixture model. The mean and covariance of dierent components of the Gaussian mixture model are propagated through the use of an Unscented Kalman Filter (UKF). Furthermore, the unknown amplitudes corresponding to dierent components of the Gaussian mixture model are found by minimizing the FPKE error over the entire volume of interest. This leads to a convex quadratic minimization problem guaranteed to have a unique solution. The two-body problem model with non-conservative atmospheric drag forces and initial uncertainty will be used to show the ecacy of the ideas developed in this paper.

A probabilistic approach for damage identification and crack mode classification in reinforced concrete structures

Reinforced concrete is subjected to deterioration due to aging, increased load, and natural hazards. To minimize the maintenance costs and to increase the operation lifetime, researchers and practitioners are increasingly interested in improving current nondestructive evaluation technologies or building advanced structural health monitoring strategies. Acoustic emission methods offer an attractive solution for nondestructive evaluation/structural health monitoring of reinforced concrete structures. In particular, monitoring the development of cracks is of large interest because their properties reflect not only the condition of concrete as material but also the condition of the entire system at structural level. This article presents a new probabilistic approach based on Gaussian mixture modeling of acoustic emission to classify crack modes in reinforced concrete structures. Experimental results obtained in a full-scale reinforced concrete shear wall subjected to reversed cyclic loading are used to demonstrate and validate the proposed approach.

An In-Network Querying Framework for Wireless Sensor Networks

In contrast to traditional wireless sensor network (WSN) applications that perform only data collection and aggregation, the new generation of information processing applications such as pursuit-evasion games, tracking, evacuation, and disaster relief applications require in-network information storage and querying. Due to the resource limitations of WSNs, it is challenging to implement in-network querying in a distributed, lightweight, resilient, and energy-efficient manner. We address these challenges by exploiting location information and the geometry of the network and propose an in-network querying framework, namely, the Distributed Quad-Tree (DQT). DQT is distance sensitive for querying of an event: the cost of answering a query for an event is at most a constant factor (2radic(2) in our case) of the distance *d* to the event. DQT construction is local and does not require any communication. Moreover, due to its minimalist infrastructure and stateless nature, DQT shows graceful resilience to node failures and topology changes. Since event-based querying is inherently limited to the anticipated types of inquiries, we further extend our framework to achieve complex range-based querying. To this end, we use a multiresolution algorithm, which is optimal with respect to least square errors that models the data in a decentralized way. Our model-based scheme answers queries with approximate values accompanied by certainty levels with increased resolution at lower layers of the DQT hierarchy. Our analysis and experiments show that our framework achieves distance sensitivity and resiliency for event-based querying, as well as greatly reduces the cost of complex range querying.

The Conjugate Unscented Transform — An approach to evaluate multi-dimensional expectation integrals

This paper presents an extension to the unscented transformation to evaluate expectation integrals in general N-dimensional space by satisfying higher order moment equations. New sets of sigma points are defined to satisfy moment equations up to eighth order. The proposed methodology can be used as an efficient alternative to Gaussian quadrature rule with significantly reduced number of function evaluations but without any loss in accuracy. Numerical simulation results illustrates the effectiveness of the proposed methodology in computing high dimension expectation integrals with significantly reduced number of function evaluations.

Polynomial-chaos-based Bayesian approach for state and parameter estimations

Two new recursive approaches have been developed to provide accurate estimates for posterior moments of both parameters and system states while making use of the generalized polynomial-chaos framework for uncertainty propagation. The main idea of the generalized polynomial-chaos method is to expand random state and input parameter variables involved in a stochastic differential/difference equation in a polynomial expansion. These polynomials are associated with the prior probability density function for the input parameters. Later, Galerkin projection is used to obtain a deterministic system of equations for the expansion coefficients. The first proposed approach provides means to update prior expansion coefficients by constraining the polynomial-chaos expansion to satisfy a specified number of posterior moment constraints derived from Bayes’s rule. The second proposed approach makes use of the minimum variance formulation to update generalized polynomial-chaos coefficients. The main advantage of the prop...

Optimal Linear Attitude Estimator

An optimal linear attitude estimator is presented for the case of a single-point real-time estimation of spacecraft attitude using the minimum-element attitude parameterization: Rodrigues (or Gibbs) vector g. The optimality criterion, which does not coincide with Wahbas constrained criterion, is rigorously quadratic and unconstrained. The singularity, which occurs when the principal angle is π, can easily be avoided by one rotation. The attitude accuracy tests show that the proposed method provides a precision comparable with those fully complying with the Wahba optimality definition. Finally, computational speed tests demonstrate that the proposed method belongs to the class of the fastest optimal attitude estimation algorithms.

Nonlinear uncertainty propagation for perturbed two-body orbits

The main objective of this paper is to present the development of the computational methodology, based on the Gaussian mixture model, that enables accurate propagation of the probability density function through the mathematical models for orbit propagation. The key idea is to approximate the density function associated with orbit states by a sum of Gaussian kernels. The unscented transformation is used to propagate each Gaussian kernel locally through nonlinear orbit dynamical models. Furthermore, a convex optimization problem is formulated by forcing the Gaussian mixture model approximation to satisfy the Kolmogorov equation at every time instant to solve for the amplitudes of Gaussian kernels. Finally, a Bayesian framework is used on the Gaussian mixture model to assimilate observational data with model forecasts. This methodology effectively decouples a large uncertainty propagation problem into many small problems. A major advantage of the proposed approach is that it does not require the knowledge o...