Precise computer controlled positioning of robot end effectors using force sensors

A major problem in space applications of robotics and docking of spacecraft is the development of technology for automated precise positioning of mating components with smooth motion and soft contact. To achieve the above objective, a design method was developed for optimally placing the closed-loop poles of a discretized robotic control system at exact prescribed locations inside the unit circle of the complex z-plane. The design method combines the merits of the pole placement and the linear quadratic design approaches. The proposed design procedure is based on the assignment of one real eigenvalue or two complex conjugate (or real) eigenvalues at each design step. The method involves solutions of simple algebraic equations and this is considered to be efficient for on-line or off-line computations. Also, two methods for the linearization of the nonlinear model of a robotic manipulator were presented. Since automatic control of multi-degree freedom robotic manipulators involves high nonlinear equations of systems, a pilot project was proposed involving the control of a one-dimensional system. This simple system can be readily implemented for testing the concepts and algorithms

Improved FFT-based numerical inversion of Laplace transforms via fast Hartley transform algorithm

AbstractThe disadvantages of numerical inversion of the Laplace transform via the conventional fast Fourier transform (FFT) are identified and an improved method is presented to remedy them. The improved method is based on introducing a new integration step length Δω = π/mT for trapezoidal-rule approximation of the Bromwich integral, in which a new parameter m, is introduced for controlling the accuracy of the numerical integration. Naturally, this method leads to multiple sets of complex FFT computations. A new inversion formula is derived such that N equally-spaced samples of the inverse Laplace transform function can be obtained by [m2] + 1 sets of N-point complex FFT computations or by m sets of real fast Hartley transform (FHT) computations