The motion planning problem and exponential stabilisation of a heavy chain. Part I†

A model of a heavy chain system with a punctual load (tip mass) in the form of a system of partial differential equations is interpreted as an abstract semigroup system on a Hilbert state space. Our aim is to solve the output motion planning problem of the same nature as in the case of an unloaded heavy chain (Grabowski, P. (2003 Grabowski, P. 2003. Abstract Semigroup Model of Heavy Chain System with Application to a Motion Planning Problem. Proceedings of 9th IEEE International Conference: Methods and Models in Automation and Robotics. 25–28 August2003, Mi?dzyzdroje, Poland. pp.77–86. (IS1-2-3.PDF) [Google Scholar]), ‘Abstract Semigroup Model of Heavy Chain System with Application to a Motion Planning Problem’, in Proceedings of 9th IEEE International Conference: Methods and Models in Automation and Robotics, 25–28 August, Mi?dzyzdroje, Poland, pp. 77–86 (IS1-2-3.PDF)). In order to solve this problem we first analyse its well-posedness and some basic properties. Next, we solve the output motion planning problem using a substitute of the inverse of the input–output operator represented in terms of the Laplace transforms. A problem of exponential stabilisation is also formulated and solved using a stabiliser of the colocated type. The exponential stabilisation is proved using the method of Lyapunov functionals combined with some frequency-domain tools. The method of Lyapunov functionals can be replaced by the spectral or exact controllability approach as shown in the second part (Grabowski, P. (2008 Grabowski, P. 2008. ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’. Opuscula Mathematica, 28: 481–505. (2008) (Special issue dedicated to the memory of Professor Andrzej Lasota) [Google Scholar]), ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’, Opuscula Mathematica, 28 (2008 Grabowski, P. 2008. ‘The Motion Planning Problem and Exponential Stabilisation of a Heavy Chain. Part II’. Opuscula Mathematica, 28: 481–505. (2008) (Special issue dedicated to the memory of Professor Andrzej Lasota) [Google Scholar]) (Special issue dedicated to the memory of Professor Andrzej Lasota), 481–505) of the present article. A laboratory setup which allows verification of the results in practice is described in detail. Its dynamical model is used as an example to illustrate the theoretical results.     

Analytical stable CGPC design for minimum-phase systems

The continuous-time generalized predictive control (CGPC) using a long horizon cost function has superior robustness as compared to several other control strategies suitable for adaptive control. The main purpose of this paper is to put forward an analytical, explicit stable CGPC control design method for minimum-phase SISO systems that is based on a set of closed-loop characteristics with definite time-domain specifications. Explicit formulae for closed-loop characteristic polynomials are given and then the prototype design characteristic polynomials are catalogued that can serve as a basis for fully analytical design procedure assuring both the nominal stability and nominal performance specifications. A numerical example is given in order to illustrate the approach.     

CHANGES OF RHEOLOGICAL PROPERTIES OF APPLE TISSUE UNDERGOING CONVECTIVE DRYING

ABSTRACT

The aim of this work was to investigate rheological properties of apple cubes undergoing convective drying. Compression-relaxation test was used to follow changes of properties under investigation.

Raw apple appeared to be very heterogeneous material from the rheological point of view. The relationship between stress and strain was concave downwards and the concavity increased until water content of 2·5 g/g d.m. was reached. Then the relationship begun to straighten and for dry material developed stress was linearly dependent on strain. The resistance of deformation decreased with decreasing water content. Analysis of relaxation showed that the rate of relaxation increased with decreasing water content and the unrelaxed stress was smaller the lower was the water content.

Apple cubes undergoing drying are pictured as material composed of three compartments with different rheological properties. The outer layer is dry, inelastic and difficult to deform. Underneath is moist material with no turgor and relatively easy to compress, and the core with properties of raw apples. During drying the second layer grows in expense of the core and porous structure with many voids filled with air is formed. Share of each compartment in the volume of apple cube undergoing drying affects average rheological properties of the material.     

Room Airflow Studies Using Sonic Anemometry

Abstract To ensure prompt response by real-time air monitors to an accidental release of toxic aerosols in a workplace, safety professionals should understand airflow patterns. This understanding can be achieved with validated computational fluid dynamics (CFD) computer simulations, or with experimental techniques, such as measurements with smoke, neutrally buoyant markers, trace gases, or trace aerosol particles. As a supplementary technique to quantify airflows, the use of a state-of-the art, three-dimensional sonic anemometer was explored. This instrument allows for the precise measurements of the air-velocity vector components in the range of a few centimeters per second, which is common in many indoor work environments. Measurements of air velocities and directions at selected locations were made for the purpose of providing data for characterizing fundamental aspects of indoor air movement in two ventilated rooms and for comparison to CFD model predictions. One room was a mockup of a plutonium workroom, and the other was an actual functioning plutonium workroom. In the mockup room, air-velocity vector components were measured at 19 locations at three heights (60, 120 and 180 cm) with average velocities varying from 1.4 cm s^?1 to 9.7 cm s^?1. There were complex flow patterns observed with turbulence intensities from 39% up to 108%. In the plutonium workroom, measurements were made at the breathing-zone height, recording average velocities ranging from 9.9 cm s^?1 to 35.5 cm s^?1 with turbulence intensities from 33% to 108%.     

Rough terrain mapping and classification for foothold selection in a walking robot

Although legged locomotion over a moderately rugged terrain can be accomplished by employing simple reactions to the ground contact information, a more effective approach, which allows predictively avoiding obstacles, requires a model of the environment and a control algorithm that takes this model into account when planning footsteps and leg movements. This article addresses the issues of terrain perception and modeling and foothold selection in a walking robot. An integrated system is presented that allows a legged robot to traverse previously unseen, uneven terrain using only onboard perception, provided that a reasonable general path is known. An efficient method for real‐time building of a local elevation map from sparse two‐dimensional (2D) range measurements of a miniature 2D laser scanner is described. The terrain mapping module supports a foothold selection algorithm, which employs unsupervised learning to create an adaptive decision surface. The robot can learn from realistic simulations; therefore no a priori expert‐given rules or parameters are used. The usefulness of our approach is demonstrated in experiments with the six‐legged robot Messor. We discuss the lessons learned in field tests and the modifications to our system that turned out to be essential for successful operation under real‐world conditions. © 2011 Wiley Periodicals, Inc.     

Synthesis and surface properties of chemodegradable anionic surfactants: Sodium carboxylates of cis-1,3-dioxane derivatives

The 2-n-alkyl-5-carboxy-5-methyl-1,3-dioxanes were obtained in good yield from the reaction of aliphatic aldehydes with 2,2-bis(hydroxymethyl)propionic acid in dichloromethane solution, catalyzed by p-toluenesulfonic acid monohydrate. Nuclear magnetic resonance analysis indicated that they were pure cis-isomers with the axial configuration of the carboxylic group at the C-5 carbon atom of the 1,3-dioxane ring. The acids were converted, with retention of the configuration, to their sodium salts by reaction with sodium methoxide or sodium hydroxide in methanol. The physicochemical properties of the acids and sodium salts, as well as their surface properties at the aqueous solution-air interface, were determined. Critical micelle concentration, surface excess concentration, surface area demand per molecule of sodium salts at the monomolecular surface layer, and standard free energy of micellization were determined based on surface tension measurements. Part XXXIV in the series: Chemical Structure and Surface Activity. Part XXXIII: A. Piasecki, A. Sokolowski, B. Burczyk, R. Gancarz, and U. Kotlewska, Synthesis, Surface Properties and Hydrolysis of Chemodegradable Anionic Surfactants: Diastereomerically Pure cis- and trans-2,5-Disubstituted-1,3-dioxanes. J. Colloid Interface Sci. 192:74–82 (1997).     

Investigation of water film properties on graphite surfaces

Isotherms of water adsorption and desorption from graphite surfaces have been determined. Thermal analysis curves of water thermodesorption from graphite surfaces have also been determined. From the experimental data the energetic changes accompanying water adsorption and desorption processes were calculated. A mechanism for water adsorption has been proposed, and conclusions concerning the structure and other properties of water films on graphite surfaces have been made.     

Generality and legibility in mobile manipulation

This article investigates methods for achieving more general manipulation capabilities for mobile manipulation platforms, which produce legible behavior in human living environments. To achieve generality and legibility, we combine two control mechanisms. First of all, experience- and observation-based learning of skills is applied to routine tasks, so that the repetitive and stereotypical character of everyday activity is exploited. Second, we use planning, reasoning, and search for novel tasks which have no stereotypical solution. We apply these ideas to the learning and use of action-related places, to the model-based visual recognition and localization of objects, and the learning and application of reaching strategies and motions from humans. We demonstrate the integration of these mechanisms into a single low-level control system for autonomous manipulation platforms.     

Some Remarks on the Classification of Water Vapor Sorption Isotherms and Blahovec and Yanniotis Isotherm Equation

Mathematical analysis was performed on equations describing water vapor sorption isotherms. It was shown that an identity exists between the Blahovec and Yanniotis (BY), D'Arcy and Watt (DW), and generalized D'Arcy and Watt (GDW) models. The original BY model has been modified to account for temperature dependence of the model parameters. This modification enables the application of this model to describe sorption data obtained at different temperatures. A new method for classification of sorption isotherms has been proposed that is much simpler than the classification established by Blahovec and Yanniotis.