### Browsing by Author "Yang, R."

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Item Geometric Phases, Anholonomy, and Optimal Movement(1991) Krishnaprasad, Perinkulam S.; Yang, R.; ISRIn the search for useful strategies for movement of robotic systems (e.g. manipulators, platforms) in constrained environments (e.g. in space, underwater), there appear to be new principles emerging from a deeper geometric understanding of optimal movements of nonholonomically constrained systems. In our work, we have exploited some new formulas for geometric phase shifts to derive effective control strategies. The theory of connections in principal bundles provides the proper framework for questions of the type addressed in this paper. we outline the essentials of this theory. A related optimal control problem and its localizations are also considered.Item Neural Networks for Tactile Perception.(1987) Pati, Y.C.; Friedman, Daniel E.; Krishnaprasad, Perinkulam S.; Yao, C.T.; Peckar, M.C.; Yang, R.; Marrian, C.R.K.; ISRIntegrated tactile sensors appear to be essential for dextrous control of multifingered robotic hands. Such sensors would feature (1) compliant contact surfaces, (2) high resolution surface stress transduction, (3) local signal conditioning, and (4) local computation to recover contact surface stress. The last-mentioned item pertains to the basic inverse problem of tactile perception and the real time solution of this inverse problem is our primary concern. We think that good solutions to this problem (i.e., algorithms + implementations) will be needed for realizing dextrous hand control via tactile serving. In this paper we describe a processor chip designed to solve the mathematical inversion problem utilizing neural network principles. Simulations indicate that this chip can function in the presence of large amounts of electrical noise. In addition the effect of processing induced variability in sensor response can also be minimized using the maximum entropy estimate method described below. The tactile sensor design we refer to is the one reported in [1]. This particular design is based on piezo- resistive transduction via an array of diffuse resistors in silicon. Surface load on a compliant layer is transformed into resistance changes proportional to biaxial strains. Initial testing of the sensor has yielded repeatable, linear characteristics. The signal conditioning chip which acts as an interface between the sensor array and subsequent processor chips has also been fabricated. The neural network chip described in this paper has been simulated at the system level. The simulation results for this network based on a particular linear elastic model (described in section 2) of the compliant contact layer. We consider in the simulations some of the errors introduced by process variability in VLSI implementation. The simulations carried out using SIMNON a general purpose nonlinear simulation package developed at Lund Institute of Technology, Sweden (kindly provided us by Professor Astrom), are described in section 4.Item Nonholonomic Geometry, Mechanics and Control(1992) Yang, R.; Krishnaprasad, P.S.; ISRThis dissertation is concerned with dynamic modeling and kinematic control of constrained mechanical systems with symmetry from a geometric point of view. Constraints are defined via the characteristics of distributions or codistributions on the tangent bundle (velocity phase space) of configuration space. Lie symmetry groups acting on the systems are assumed to leave both Lagrangian and constraints invariant. As a special case of mechanical systems with holonomic constraints, we rigorously analyze the kinematics and dynamics of floating, planar four-bar linkages. The analyses include topological description of the configuration space, symplectic and Poisson reductions of the dynamics and bifurcation of relative equilibria. for kinematic control of nonholonomic systems, we mainly study the related optimal control problem for a system consisting of a rigid body with two oscillators. In particular, the intrinsic formulation and explicit solvability of necessary conditions for the optimal control are investigated from a Hamiltonian point of view. In the study of the dynamics of Lagrangian systems with constraints, the nonholonomic distributions are defined via arbitrary choices of principal connections. We show that, under our hypotheses on constraints and exterior force, the dynamics of a nonholonomic Lagrangian system with non-Abelian symmetry can be reduced to a lower dimensional space determined by the principal fiber bundle. The reduced dynamic equations are formulated explicitly. This formulation generalizes the one for classical Chaplygin systems which possess Abelian symmetry, and the one having non-Abelian symmetry but with linear constraints. In addition, if a special principal connection, that is, the mechanical connection by Kummer and Smale, is considered, our formulation for nonholonomic systems also leads to the one in Lagrangian reduction discovered recently by Marsden and Scheurle. The results of this dissertation have direct application in space robotics and nonholonomic motion planning in robotics.Item On the Dynamics of Floating Four-Bar Linkages.(1989) Yang, R.; Krishnaprasad, Perinkulam S.; ISRThe hamiltonian structure of floating, planar four-bar linkages is discussed. The geometry of configuration space is related to the classical theory of mechanisms due to Grashof. For generic value of kinematic parameters, the techniques of symplectic (and Poisson) reduction apply.Item On the Dynamics of Floating Four-Bar Linkages. II. Bifurcations of Relative Equilibria(1990) Yang, R.; Krishnaprasad, Perinkulam S.; ISRContinuing our program to understand the geometry and dynamics of floating four-bar linkages, we explore the relative equilibria of an assembly that admits symmetric configurations. We show that a symmetric configuration is a relative equilibrium. As we vary certain kinematic parameters which preserve the symmetry, a symmetric relative equilibrium is bifurcated. The type of bifurcations can be either supercritical or subcritical pitchfork. The stability of the relative equilibria at symmetric configurations is investigated. Elementary techniques of singularity theory are applied in the analysis of the bifurcations. This investigation illustrates the possible rich dynamics in multibody systems with closed loop structure even with a small number of degrees of freedom.Item On the Geometry and Dynamics of Floating Four-Bar Linkages(1992) Yang, R.; Krishnaprasad, Perinkulam S.; ISRIn this paper, we investigate the kinematics and dynamics of floating, planar four-bar linkages. The geometry of configuration space is analyzed through the classical theory of mechanisms due to Grashof. The techniques of symplectic and Poisson reduction are used to understand the dynamics of the system. Bifurcations of relative equilibria for linkages admitting symmetric shapes are studied using the techniques of singularity theory. The problem of reconstruction of the full dynamics and its relation to geometric phases is discussed through some examples. This research reveals that a coupled mechanical system with kinematic loops possesses richer and more complicated dynamical aspects in comparison with systems which have the same number of degrees of freedom, but no kinematic loops.Item Optimal Control of a Rigid Body with Two Oscillators(1993) Yang, R.; Krishnaprasad, Perinkulam S.; Dayawansa, Wijesuriya P.; ISRThis paper is concerned with the exploration of reduction and explicit solvability of optimal control problems on principal bundles with connections from a Hamiltonian point of view. The particular mechanical system we consider is a rigid body with two driven oscillators, for which the bundle structure is (SO (3) x 者, 者, SO (3)). The optimal control problem is posed by considering a special nonholonomic variational problem, in which the nonholonomic distribution is defined via a connection. The necessary conditions for the optimal control problem are determined intrinsically by a Hamiltonian formulation. The necessary conditions admit the structure group of the principal bundle as a symmetry group of the system. Thus the problem is amendable to Poisson reduction. Under suitable hypotheses and approximations, we find that the reduced system possesses additional symmetry which is isomorphic to S1. Applying Poisson reduction again, we obtain a further reduced system and corresponding first integral. These reductions imply explicit solvability for suitable values of parameters.Item Tactile Perception for Multifingered Hands(1987) Yang, R.; Krishnaprasad, P.S.; ISRRecently, tactile sensors mounted on robot fingers have been identified as essential sensory devices for the control of multifingered robotic hands. A basic tactile sensing task is to determine the force distribution on the contact area between the fingers and grasped object. To increase the grasp stability and to protect the fragile sensors, a kind of elastic material is required to cover the tactile sensors. This thesis derives the relationship between the surface force profile and the stress or strain profile measured by tactile sensors beneath the contract surface for simplified situations. This relationship can be described by integral equations of convolution type, or more generally, integral equations of the first kind with two unknown functions. The algorithms for numerical inversion in real time, an analog network for solving the regularization problem is discussed. Finally, as an application of the tactile sensors, the equilibrium condition for stable grasping by a two-fingered robotic hand is derived.Item Tactile Sensing and Inverse Problems.(1987) Yang, R.; Krishnaprasad, Perinkulam S.; ISRThe goal of this paper is to study how a surface force profile may be estimated from the information on strain or stress distribution detected by tactile sensors. This problem is referred to as the inverse problem since we can consider the stress or strain within an elastic material as the response due to surface loading. This inverse problem can be treated as a deconvolution problem or, more generally, as the problem of solving an operator equation of the firat kind. It is of interest to determine how such an ill-posed problem may be solved using appropriate regularization (Tikhonov 1977). In this paper, we will not consider the effects of the noises (or suppose the observations have been passed through some kind of filter) and only pay attention to deriving particular operators, analyzing their properties and using the Discrete Fourier Transform (DFT) approach to solve the associated equations.