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Iteration Strategy (iteration + strategy)
Selected AbstractsOptimal Velocity Planning of Wheeled Mobile Robots on Specific Paths in Static and Dynamic EnvironmentsJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 12 2003Marķa Prado This paper deals with optimal temporal-planning of wheeled mobile robots (WMRs) when navigating on predefined spatial paths. A method is proposed to generate a time-optimal velocity profile for any spatial path in static environments or when mobile obstacles are present. The method generates a feasible trajectory to be tracked by fully exploiting velocity, acceleration and deceleration boundaries of the WMR, and by ensuring the continuity of the velocity and acceleration functions. As an additional benefit for the tracking process the jerk is also bounded. The algorithm is not time consuming, since it mostly uses closed mathematical expressions, nonetheless iteration strategies are presented to solve specific situations. However, such situations are not expected to occur when the spatial paths are planned as smooth curves. The success of the algorithm was tested by experimental and simulation results on the WMR "RAM." © 2003 Wiley Periodicals, Inc. [source] Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9-10 2006Koen Hillewaert Abstract We study the efficient use of the discontinuous Galerkin finite element method for the computation of steady solutions of the Euler equations. In particular, we look into a few methods to enhance computational efficiency. In this context we discuss the applicability of two algorithmical simplifications that decrease the computation time associated to quadrature. A simplified version of the quadrature free implementation applicable to general equations of state, and a simplified curved boundary treatment are investigated. We as well investigate two efficient iteration techniques, namely the classical Newton,Krylov method used in computational fluid dynamics codes, and a variant of the multigrid method which uses interpolation orders rather than coarser tesselations to define the auxiliary coarser levels. Copyright © 2005 John Wiley & Sons, Ltd. [source] Fast implementations and rigorous models: Can both be accommodated in NMPC?INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL, Issue 8 2008Victor M. Zavala Abstract In less than two decades, nonlinear model predictive control has evolved from a conceptual framework to an attractive, general approach for the control of constrained nonlinear processes. These advances were realized both through better understanding of stability and robustness properties as well as improved algorithms for dynamic optimization. This study focuses on recent advances in optimization formulations and algorithms, particularly for the simultaneous collocation-based approach. Here, we contrast this approach with competing approaches for online application and discuss further advances to deal with applications of increasing size and complexity. To address these challenges, we adapt the real-time iteration concept, developed in the context of multiple shooting (Real-Time PDE-Constrained Optimization. SIAM: Philadelphia, PA, 2007; 25,52, 3,24), to a collocation-based approach with a full-space nonlinear programming solver. We show that straightforward sensitivity calculations from the Karush,Kuhn,Tucker system also lead to a real-time iteration strategy, with both direct and shifted variants. This approach is demonstrated on a large-scale polymer process, where online calculation effort is reduced by over two orders of magnitude. Copyright © 2007 John Wiley & Sons, Ltd. [source] Computerized calculation scheme for bitoric eikonic intraocular lensesOPHTHALMIC AND PHYSIOLOGICAL OPTICS, Issue 3 2003Achim Langenbucher Abstract Despite full correction of the corneal astigmatism with toric intraocular lenses, the retinal image is distorted and the lateral image-object magnification is different in different meridians. The purpose of this study is to describe an iteration strategy for tracing an axial pencil of rays through the ,optical system eye' containing astigmatic refractive surfaces with their axes at random to calculate a thick bitoric lens implant which eliminates image distortion. The capabilities of this computing scheme are demonstrated with two clinical examples. We present a mathematically straightforward computer-based strategy for the calculation of thick bitoric eikonic lens implants. The iteration algorithm is initialized with a spherical front and a toric back surface and stepwise decreases the image distortion by adding cylinder lenses to the front lens surface corrected by the toric lens back surface. Total magnification can be modulated by varying the front-to-back surface power of the thick lens. [source] Fixed-point type iterations in numerical simulations for static and dynamic elastoplasticityPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Yury Vetyukov Mag. Dynamics of the elastoplastic media is stated in terms of plastic eigenstrains acting upon a background elastic problem with fixed (initial) stiffness. The plastic flow is described by specifically introduced plastic multipliers, which minimizes the number of unknown variables to be determined within the time step. A fixed-point type iteration strategy is suggested for the computation of the plastic multipliers, which has been implemented for the finite element spatial discretization. Numerical experiments show the correctness and the effectiveness of the developed algorithm. [source] | ||||||||||