The solution of inverse kinematics and trajectory planning with performance criteria for a redundant manipulator is proposed with modification in fuzzy c-means. A new fuzzy clustering model based on a new generalized validity index based on weighted within-scatter metrics and betweencluster scatter metrics for the manipulator is proposed. In order to understand the proposed algorithm and to show its performance, two simulation studies of trajectory planning with manipulability criteria for a redundant manipulator are modeled to solve the problems of finding association rules in the data and of setting up an appropriate classification procedures. The problem of redundant manipulator (which is a multi-input, multi-output nonlinear system) is new in terms of solution by clustering method. The proposed algorithm for the trajectory planning of the manipulator is simulated using Matlab®. All practical steps, from data acquisition to model validation, are illustrated using a 4 degree of freedom robot manipulator. The simulated results are compared with the numerical methods of the trajectory planning. The results are presented graphically. The proposed method has the advantage of simplicity, flexibility, and good tracking performance.
SummaryThis paper aims at estimating the tremor torque using extended Kalman filter (EKF) applied to a two-link 3-DOF robot with nonlinear dynamics modelled using Lie-group and Lie-algebra theory. Later, it is generalised to d number of links with (d + 1) -DOF. The configuration of each link at any time is described by its rotation relative to the preceding link. Using this formulation, an elegant formula for the kinetic energy of the (d + 1) -DOF system is obtained as a quadratic form in the angular velocities with coefficients being highly nonlinear trigonometric functions of the angles. Properties of the Lie algebra generators and the Lie adjoint map are used to arrive at this expression. Further, the gravitational potential energy and the torque potential energy are expressed as nonlinear trigonometrical functions of the angles using properties of the SO(3) group. The input torque comprises a nonrandom intentional torque component and a highly nonlinear tremor torque component. The tremor torque is modelled as a stochastic differential equation (sde) satisfying Ornstein–Uhlenbeck (OU) process with diffusion and damping coefficients. Further, the tremor is treated as the disturbance. The Euler–Lagrange equations for the angles are derived. These form a system of sdes, and the EKF is used to get a more accurate disturbance estimate than that provided by the usual disturbance observer. The EKF is based on noisy angle measurements and yields as a bonus the angle and angular velocity estimates on a real-time basis. The parameters in the OU process model of the tremor torque, and parameters of the Fourier components of the intentional torque have also been estimated.
Sodium Thiosulphate, Polymorphism, Solid ElectrolyteNa2S2C>3 crystallizes in 4 modifications. The familiar monoclinic a-form stable at ambient temperature transforms into the trigonal /3-form at 330 °C which at 388 °C converts to bcc y-Na2S203. These transformations are reversible. Unstable orthorhombic a'-Na2S2C>3(Pna 2i) is obtained by dehydration of the pentahydrate or by cooling the ß-phase.The y-phase decomposes in sealed ampoule to Na2SC>4 and NaSs; decomposition is slow below and rapid above 440 °C. Equilibrium displacement by distillation of sulphur accelerates decomposition even for /?-Na2S203, and maintaining low sulphur pressure by pumping gives Na2S03. ß-and y-Na2S2C>3 are superionic conductors; a dynamic model is presented for the /3-structure with Na+ conduction pathways originating from oscillation of the S0O3 2-tetrahedra. Structural relationships can be derived with respect to the arrangement of the thiosulphate groups.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.