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Holonomic Constraints (holonomic + constraint)
Selected AbstractsKinematic modeling of mobile robots by transfer method of augmented generalized coordinatesJOURNAL OF FIELD ROBOTICS (FORMERLY JOURNAL OF ROBOTIC SYSTEMS), Issue 6 2004Wheekuk Kim A kinematic modeling method, which is directly applicable to any type of planar mobile robots, is proposed in this work. Since holonomic constraints have the same differential form as nonholonomic constraints, the instantaneous motion of the mobile robot at current configuration can be modeled as that of a parallel manipulator. A pseudo joint model denoting the interface between the wheel and the ground (i.e., the position of base of the mobile robot) enables the derivation of this equivalent kinematic model. The instantaneous kinematic structures of four different wheels are modeled as multiple pseudo joints. Then, the transfer method of augmented generalized coordinates, which has been popularly employed in modeling of parallel manipulators, is applied to obtain the instantaneous kinematic models of mobile robots. The kinematic models of six different types of planar mobile robots are derived to show the effectiveness of the proposed modeling method. Lastly, for the mobile robot equipped with four conventional wheels, an algorithm estimating a sensed forward solution for the given information of the rotational velocities of the four wheels is discussed. © 2004 Wiley Periodicals, Inc. [source] Use of the Rotation Vector in Brownian Dynamics Simulation of Transient Electro-Optical PropertiesMACROMOLECULAR THEORY AND SIMULATIONS, Issue 1 2009Tom Richard Evensen Abstract We have recently developed a new singularity-free algorithm for Brownian dynamics simulation of free rotational diffusion. The algorithm is rigorously derived from kinetic theory and makes use of the Cartesian components of the rotation vector as the generalized coordinates describing angular orientation. Here, we report on the application of this new algorithm in Brownian dynamics simulations of transient electro-optical properties. This work serves two main purposes. Firstly, it demonstrates the integrity of the new algorithm for BD-simulations of the most common transient electro-optic experiments. Secondly, it provides new insight into the performance of the new algorithm compared to algorithms that make use of the Euler angles. We study the transient electrically induced birefringence in dilute solutions of rigid particles with anisotropic polarization tensor in response to external electric field pulses. The use of both one single electric pulse and two electric pulses with opposite polarity are being analyzed. We document that the new singularity-free algorithm performs flawlessly. We find that, for these types of systems, the new singularity-free algorithm, in general, outperforms similar algorithms based on the Euler angles. In a wider perspective, the most important aspect of this work is that it serves as an important reference for future development of efficient BD-algorithms for studies of more complex systems. These systems include polymers consisting of rigid segments with single-segment translational,rotational coupling, segment,segment fluid-dynamic interactions and holonomic constraints. [source] Brownian Dynamics Simulations of Rotational Diffusion Using the Cartesian Components of the Rotation Vector as Generalized CoordinatesMACROMOLECULAR THEORY AND SIMULATIONS, Issue 7-8 2008Tom Richard Evensen Abstract Here, we report on the first Brownian dynamics (BD) simulations of rotational diffusion using the Cartesian components of the rotation vector as the generalized coordinates. The model system employed in this study consists of freely rotating and non-interacting rigid particles with arbitrary surface topography. The numerical BD algorithm contains no singularities and yields numerical results that are in full agreement with known theoretical results. Because of the absence of singularities, this new algorithm is several orders of magnitude more efficient than a simple BD algorithm employing the Euler angles as the generalized coordinates. The general theory for using generalized coordinates in studies of more complex systems involving both translation, rotation, and fluid dynamic interactions is well known. Consequently, the benefits reported here can readily be extended to such systems. Important examples are segmented polymer chains, with and without holonomic constraints, and liquid crystals. [source] Numerical integration of differential-algebraic equations with mixed holonomic and control constraintsPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2008Mahmud Quasem The present work aims at the incorporation of control (or servo) constraints into finite,dimensional mechanical systems subject to holonomic constraints. In particular, we focus on underactuated systems, defined as systems in which the number of degrees of freedom exceeds the number of inputs. The corresponding equations of motion can be written in the form of differential,algebraic equations (DAEs) with a mixed set of holonomic and control constraints. Apart from closed,loop multibody systems, the present formulation accommodates the so,called rotationless formulation of multibody dynamics. To this end, we apply a specific projection method to the DAEs in terms of redundant coordinates. A similar projection approach has been previously developed in the framework of generalized coordinates by Blajer & Ko,odziejczyk [1]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Shaping stable periodic motions of inertia wheel pendulum: theory and experiment,ASIAN JOURNAL OF CONTROL, Issue 5 2009Leonid B. Freidovich Abstract We consider an underactuated two-link robot called the inertia wheel pendulum. The system consists of a free planar rotational pendulum and a symmetric disk attached to its end, which is directly controlled by a DC-motor. The goal is to create stable oscillations of the pendulum, which is not directly actuated. We exploit a recently proposed feedback-control design strategy based on motion planning via virtual holonomic constraints. This strategy is shown to be useful for design of regulators for achieving orbitally exponentially stable oscillatory motions. The main contribution is a step-by-step procedure on how to achieve oscillations with pre-specified amplitude from a given range and an arbitrary independently chosen period. The theoretical results are verified via experiments with a real hardware setup. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society [source] | ||||||||||