Displaying similar documents to “Interval analysis for certified numerical solution of problems in robotics”

A novel interval arithmetic approach for solving differential-algebraic equations with VALENCIA-IVP

Andreas Rauh, Michael Brill, Clemens Günther (2009)

International Journal of Applied Mathematics and Computer Science

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The theoretical background and the implementation of a new interval arithmetic approach for solving sets of differentialalgebraic equations (DAEs) are presented. The proposed approach computes guaranteed enclosures of all reachable states of dynamical systems described by sets of DAEs with uncertainties in both initial conditions and system parameters. The algorithm is based on VALENCIA-IVP, which has been developed recently for the computation of verified enclosures of the solution...

Computing and Visualizing Solution Sets of Interval Linear Systems

Krämer, Walter (2007)

Serdica Journal of Computing

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The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006 The computation of the exact solution set of an interval linear system is a nontrivial task [2, 13]. Even in two and three dimensions a lot of work has to be done. We demonstrate two different realizations. The first approach (see [16]) is based on Java, Java3D, and the BigRational package [21]. An applet allows modifications of the matrix coefficients...

Visual simultaneous localisation and map-building supported by structured landmarks

Robert Bączyk, Andrzej Kasiński (2010)

International Journal of Applied Mathematics and Computer Science

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Visual simultaneous localisation and map-building systems which take advantage of some landmarks other than point-wise environment features are not frequently reported. In the following paper the method of using the operational map of robot surrounding, which is complemented with visible structured passive landmarks, is described. These landmarks are used to improve self-localisation accuracy of the robot camera and to reduce the size of the Kalman-filter state-vector with respect to...

Introduction to the Maple Power Tool Intpakx

Krämer, Walter (2007)

Serdica Journal of Computing

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The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006 The Maple Power Tool intpakX [24] de nes Maple types for real intervals and complex disc intervals. On the level of basic operations, intpakX includes the four basic arithmetic operators, including extended interval division as an extra function. Furthermore, there are power, square, square root, logarithm and exponential functions, a set of standard...

A verified method for solving piecewise smooth initial value problems

Ekaterina Auer, Stefan Kiel, Andreas Rauh (2013)

International Journal of Applied Mathematics and Computer Science

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In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short...

Supporting locomotive functions of a six-legged walking robot

Krzysztof Walas, Dominik Belter (2011)

International Journal of Applied Mathematics and Computer Science

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This paper presents a method for building a foothold selection module as well as methods for the stability check for a multi-legged walking robot. The foothold selection decision maker is shaped automatically, without expert knowledge. The robot learns how to select appropriate footholds by walking on rough terrain or by testing ground primitives. The gathered knowledge is then used to find a relation between slippages and the obtained local shape of the terrain, which is further employed...

A Solver for Complex-Valued Parametric Linear Systems

Popova, Evgenija, Kolev, Lyubomir, Krämer, Walter (2010)

Serdica Journal of Computing

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This work reports on a new software for solving linear systems involving affine-linear dependencies between complex-valued interval parameters. We discuss the implementation of a parametric residual iteration for linear interval systems by advanced communication between the system Mathematica and the library C-XSC supporting rigorous complex interval arithmetic. An example of AC electrical circuit illustrates the use of the presented software. * This work was partly supported...

Optimization of thrust allocation in the propulsion system of an underwater vehicle

Jerzy Garus (2004)

International Journal of Applied Mathematics and Computer Science

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The paper addresses methods of thrust distribution in a propulsion system for an unmanned underwater vehicle. It concentrates on finding an optimal thrust allocation for desired values of forces and moments acting on the vehicle. Special attention is paid to the unconstrained thrust allocation. The proposed methods are developed using a configuration matrix describing the layout of thrusters in the propulsion system. The paper includes algorithms of thrust distribution for both faultless...

Uncertainty models of vision sensors in mobile robot positioning

Piotr Skrzypczyński (2005)

International Journal of Applied Mathematics and Computer Science

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This paper discusses how uncertainty models of vision-based positioning sensors can be used to support the planning and optimization of positioning actions for mobile robots. Two sensor types are considered: a global vision with overhead cameras, and an on-board camera observing artificial landmarks. The developed sensor models are applied to optimize robot positioning actions in a distributed system of mobile robots and monitoring sensors, and to plan the sequence of actions for a robot...