Showing papers by "John B. Moore published in 1996"

Dextrous hand grasping force optimization

Abstract: A key goal in dextrous robotic hand grasping is to balance external forces and at the same time achieve grasp stability and minimum grasping energy by choosing an appropriate set of internal grasping forces. Since it appears that there is no direct algebraic optimization approach, a recursive optimization, which is adaptive for application in a dynamic environment, is required. One key observation in this paper is that friction force limit constraints and force balancing constraints are equivalent to the positive definiteness of a certain matrix subject to linear constraints. Based on this observation, we formulate the task of grasping force optimization as an optimization problem on the smooth manifold of linearly constrained positive definite matrices for which there are known globally exponentially convergent solutions via gradient flows. There are a number of versions depending on the Riemannian metric chosen, each with its advantages, Schemes involving second derivative information for quadratic convergence are also studied. Several forms of constrained gradient flows are developed for point contact and soft-finger contact friction models. The physical meaning of the cost index used for the gradient flows is discussed in the context of grasping force optimization. A discretized version for real-time applicability is presented. Numerical examples demonstrate the simplicity, the good numerical properties, and optimality of the approach.

Simultaneous Schur decomposition of several matrices to achieve automatic pairing in multidimensional harmonic retrieval problems

Abstract: This paper presents a new Jacobi-type method to calculate a simultaneous Schur decomposition (SSD) of several real-valued, non-symmetric matrices by minimizing an appropriate cost function. Thereby, the SSD reveals the “average eigenstructure” of these non-symmetric matrices. This enables an R-dimensional extension of Unitary ESPRIT to estimate several undamped R-dimensional modes or frequencies along with their correct pairing in multidimensional harmonic retrieval problems. Unitary ESPRIT is an ESPRIT-type high-resolution frequency estimation technique that is formulated in terms of real-valued computations throughout. For each of the R dimensions, the corresponding frequency estimates are obtained from the real eigenvalues of a real-valued matrix. The SSD jointly estimates the eigenvalues of all R matrices and, thereby, achieves automatic pairing of the estimated R-dimensional modes via a closed-form procedure, that neither requires any search nor any other heuristic pairing strategy. Finally, we show how R-dimensional harmonic retrieval problems (with R ≥ 3) occur in array signal processing and model-based object recognition applications.

Gradient algorithms for principal component analysis

Abstract: The problem of princip~l component analysis of a symmetric matrix (finding a p-dimensional eigenspace associated with the largest p eigenvalues) can be viewed as a smooth optimization problem on a homogeneous space. A solution in terms of the limiting value of a continuous-time dynamical system is presented, A discretization of the dynamical system is proposed that exploits the geometry of the homogeneous space. The relationship between the proposed algorithm and classical methods are investigated.

Structure and convergence of conventional Jacobi-type methods minimizing the off-norm function

Abstract: Conventional Jacobi-type methods for the diagonalization of real symmetric matrices can be seen as achieving the optimization of the off-norm function on a homogeneous space. The critical point structure of this function is studied in detail. Conventional Jacobi-type algorithms are rederived, and their convergence properties are studied using the tools of global analysis.

Interleaved Pulse Train Spectrum Estimation

Abstract: In this paper we consider signals consisting of a finite though unknown number of periodic time-interleaved pulse trains. For such signals, we present a novel approach for determining both the number of pulse trains present and the frequency of each pulse train. Our approach requires only the time of arrival data of each pulse. It is robust to noisy time of arrival data and missing pulses, and above all is very computationally efficient. If N is the number of pulses being processed, the computation required is of the order of N log N.

Risk-sensitive maximum likelihood sequence estimation

Abstract: In this brief, we consider risk-sensitive Maximum Likelihood sequence estimation for hidden Markov models with finite-discrete states. An algorithm is proposed which is essentially a risk-sensitive variation of the Viterbi algorithm. Simulation studies show that the risk-sensitive algorithm is more robust to uncertainties in the transition probability matrix of the Markov chain. Similar estimation results are also obtained for continuous-range state models.

Stable linear fractional transformations with applications to stabilization and multistage H∞ control design

Abstract: Stable linear fractional transformations (SLET's) resulting from a 2 × 2-block unit Z in the ring of stable real rational proper matrices are considered in this paper. Several general properties are obtained. The problem of representing a plant as a SLFT of another plant such that the order of the original plant is exactly equal to the sums of the orders of the SLET and of the new plant is solved. All such representations can be found by searching for all matching pairs of stable invariant subspaces associated with the plant. In relation to applications of SLFT's, it is shown that if two plants are related by a SLFT, then a one-to-one correspondence between their two respective sets of all stabilizing controllers can be established via a different SLFT. Also, it is shown how to decompose a standard H∞ control problem by means of SLFT into two individual H∞ subproblems, the first involving a nominal plant model and the second involving a certain frequency-shaped approximation error.

On Finite-dimensional Risk-sensitive Estimation

Abstract: In this paper, we address the finite-dimensionality issues regarding discrete-time risk-sensitive estimation for stochastic nonlinear systems. We show that for a bilinear system with an unknown parameter, finite-dimensional risk-sensitive estimates can be obtained. A necessary condition is obtained for nonlinear systems with no process noise such that one can obtain finite-dimensional risk-sensitive estimates.

A Forward Backward Algorithm for ML State and Sequence Estimation

Abstract: The classical Viterbi algorithm is used to estimate the maximum likelihood state sequence from a block of observed data. It achieves this by maximising a forward path probability measure. In an analogous manner a backward path probability measure can be generated which leads to the development of a Viterbi forwardbackward algorithm. This algorithm computes an “a posteriori maximum path probability” for each state at a given time. The resulting probability distribution across all possible state at time t can be used as a soft output for further processing. Maximising a posteriori maximum path probability at each time gives the same state sequence as obtained from the classical Viterbi algorithm.

Adaptive estimation of HMM transition probabilities

Abstract: This paper presents new schemes for recursive estimation of the state transition probabilities for hidden Markov models (HMMs) via recursive prediction error (RPE) methods. These new schemes are designed to be consistent and well conditioned, compared to the previous RPE schemes which are known to be ill-conditioned in low noise environments. The RPE algorithms proposed in this paper, although requiring less computational effort than the previous algorithms are still of order N/sup 4/, each time instant, where N is the number of Markov states. Extended least squares algorithms are also presented which less computational effort (order N/sup 2/ per time instant) but for which no convergence results are presented. A consistent algorithm for simultaneous estimation of the state output levels and the state transition probabilities is also presented and discussed. Implementation aspects of all proposed algorithms are discussed, and simulation studies are presented to illustrate convergence and convergence rates.

Hybrid Algorithms For Maximum Likelihood And Maximum A Posterior Sequence Estimation

Abstract: This paper presents two methods of processing data generated by a hidden Markov model (HMM) such that the resulting state estimates are related to both the maximum likelihood (ML) estimates (generated by the Viterbi algorithm) and maximum a posreriori (MAP) estimates (generated by the HMM forwardbackward algorithm). Both algorithms contain a tuneable parameter which selects the tendency of the processing to replicate ML or MAP estimates. In the limit the algorithms reproduce the ML and MAP estimates exactly.

On-line estimation and identification of HMMs with grouped state values

Abstract: This paper presents a signal-processing scheme for the class of lumpable or weakly lumpable hidden Markov models (HMMs) which have state values clustered into groups. Attention is focused not only on state estimation for known models but also on on-line model identification. The approach taken employs a new technique whereby separate state estimators are used for each group of state values. The state estimator for each group estimates the discrete states in that group together with an associated flag state which represents all the other groups. The result is that the computational complexity is greatly reduced. Hidden Markov model parameters associated with lumpable or weakly lumpable Markov chains can be identified on-line using available techniques such as the recursive prediction error (RPE) approach taken in this paper. These techniques estimate the transition probabilities and discrete state values of the Markov chain on-line. Other parameters, such as the noise density associated with the observations, can also be identified.

Multiple-prediction-horizon recursive identification of hidden Markov models

Abstract: This paper considers on-line identification of hidden Markov models via multiple-prediction-horizon recursive prediction error (RPE) methods. Working with multiple-prediction-horizons ensures that there is consistent parameter estimation, under appropriate excitation conditions. Simulation studies are included to illustrate the advantages of the proposed approach when compared to standard methods (which do not ensure consistent parameter estimation).

An Hmm Soft-Output Decoder for Qam Signals with a Clustered Constellation

Abstract: This paper presents a new HMM soft-output decoder for QAM signals transmitted through narrow-band flat-fading channels, in the case where the signal constellation has points which are clustered into groups. Parallel HMM filters are used for QAM detection, with one filter for each group of constellation points. This greatly reduces the number of computations required. A Kalman Filter (KF) is then applied for channel estimation. The resulting adaptive algorithms appear as coupled KF and HMM filters. As well as having reduced computations, this approach does not require so called ‘hard-decoding-decisions’ to be made, which result s in better robustness to noise.

Optimal HMM Processing Of Differentially Phase Modulated Communication Systems

Abstract: This paper investigates demodulation of differentially phase modulated signals (DPMS) using optimal HMM filters. The optimal HMM filter presented in the paper is computationally of order N 3 per time instant, where N is the number of message symbols. Previously, optimal HMM filters have been of computational order N 4 per time instant. Also, suboptimal HMM filters have be proposed of computation order N 2 per time instant. The approach presented in this paper uses two coupled HMM filters and exploits knowledge of their interdependence to achieve computational gains. A simulation study is also presented.

Pose Estimation of Quadratic Surface Using Gradient Flow Approach

Abstract: A key problem in robotics is the estimation of the location and orientation of 3-D curved objects from surface measurement data. This is termed pose estimation. We assume that parts of 3-D curved objects are approximated to quadratic surfaces. Fundamental task is to estimate the pose of quadratic surface from measured data. A solutions for this task facilitates pose estimation for more complex object. Our

Optimal HMM processing of differentially phase modulated communication systems

Abstract: This paper investigates demodulation of differentially phase modulated signals DPMS using optimal HMM filters. The optimal HMM filter presented in the paper is computationally of order N3 per time instant, where N is the number of message symbols. Previously, optimal HMM filters have been of computational order N4 per time instant. Also, suboptimal HMM filters have be proposed of computation order N2 per time instant. The approach presented in this paper uses two coupled HMM filters and exploits knowledge of ...