The VFO-Driven Motion Planning and Feedback Control in Polygonal Worlds for a Unicycle with Bounded Curvature of Motion

Integrated motion planning and control for the purposes of maneuvering mobile robots under state- and input constraints is a problem of vital practical importance in applications of mobile robots such as autonomous transportation. Those constraints arise naturally in practice due to specifics of robot mechanical construction and the presence of obstacles in motion environment. In contrast to approaches focusing on feedback control design under the assumption of given reference motion or motion planning with neglection of subsequent feedback motion execution, we adopt a controller-driven motion planning paradigm, which has recently gained attention of many researchers. It postulates design of motion planning algorithms dedicated to specific feedback control policies, which compute a sequence of feedback control subtasks instead of classically planned open-loop controls or parametric paths. In this spirit, we propose a motion planning algorithm driven by the VFO (Vector Field Orientation) control law for the waypoint-following task. Presented analysis of the VFO control law reveals its beneficial properties, which are subsequently utilized to solve a generally nonlinear and non-convex optimal motion planning problem by formulating it as a mixed-integer linear program (MILP). The solution proposed in this paper yields a waypoint sequence, which is designed for execution by application of the VFO control law to drive a robot to a prescribed final configuration under an input constraint imposed by bounded curvature of robot motion and state constraints resulting from a convex decomposition of task space. Satisfaction of these constraints is guaranteed analytically and exactly, i.e., without utilization of numerical approximations. Moreover, for a given discrete set of possible waypoint orientations, the proposed algorithm computes plans optimal w.r.t. given cost functional, which can be any convex linear combination of quantities such as robot path length, curvature of robot motion, distance to imposed state constraints, etc. Furthermore, the planning algorithm exploits the possibility of both forward or backward movement of the robot to allow maneuvering in demanding environments. Generated waypoint sequences are a compact representation of a motion plan, which can be immediately executed with the VFO controller without any additional post-processing. Validity of the proposed approach has been confirmed by simulation studies and experimental motion execution with a laboratory-scale mobile robot.     

Accurate Implicit–Explicit General Linear Methods with Inherent Runge–Kutta Stability

We investigate implicit–explicit (IMEX) general linear methods (GLMs) with inherent Runge–Kutta stability (IRKS) for differential systems with non-stiff and stiff processes. The construction of such formulas starts with implicit GLMs with IRKS which are A- and L-stable, and then we ‘remove’ implicitness in non-stiff terms by extrapolating unknown stage derivatives by stage derivatives which are already computed by the method. Then we search for IMEX schemes with large regions of absolute stability of the ‘explicit part’ of the method assuming that the ‘implicit part’ of the scheme is \(A(\alpha )\)-stable for some \(\alpha \in (0,\pi /2]\). Examples of highly stable IMEX GLMs are provided of order \(1\le p\le 4\). Numerical examples are also given which illustrate good performance of these schemes.     

Sulphidation of an oxidic CoMo/Al2O3 catalyst under practical conditions: different kinds of sulphur species

The sulphidation of a CoMo/Al₂O₃ hydrotreating catalyst was studied under pressure and flow conditions close to industrial practice. The sulphiding mixture contained equal amounts of H₂S and CH₄ diluted in hydrogen under 3.9 MPa total pressure. The oxidic precursor was flushed by the reagent gas at 40°C for 10 h, then the temperature was raised to 400°C within 2 h. Mass variation was continuously recorded by means of a suspension magnetic balance, and the gas phase was analysed by mass spectrometry. Sulphur contents were also determined at intermediate temperatures by chemical analyses. Thus, mass variations due to the presence of adsorbed species or to the formation of CoMo sulphides could be distinguished. The rapid gain in mass noted at 40°C was mostly due to adsorption of H₂S over the oxidic solid, since it increased with H₂S partial pressure. At this stage, however, a small amount of the reactive oxygen was already exchanged for sulphur. Upon raising the temperature, the mass decreased due to a combination of desorption and sulphiding steps. Above 140°C, H₂S consumption was evidenced, together with water production, and the rate of sulphiding increased with the H₂S partial pressure. At 300°C, the mass variation was close to that expected for complete transformation into Co₉S₈ and MoS₂. Above 350°C, the mass further increased due to the replacement of adsorbed water by H₂S. At 400°C, an important excess mass was observed at all H₂S partial pressures. Thus, the adsorption sites on the metal sulphides are essentially saturated by H₂S species under practical conditions.     

Simulation of Fluctuating Populations of Microorganisms and Macroorganisms with Models Having a Normal Random Variate Term

Fluctuating populations of micro- and macroorganisms play a major role in the stability and safety of food and agricultural products. In recent years such populations have been described by ‘chaotic’ models, most notably the discrete logistic function. This model's major limitations, however, are that it implies determinism and that it can account for neither population explosions nor extinction. Consequently, it is suggested that in order to simulate realistic population histories, the growth rate constant, r, in the original discrete logistic function X_n+1=rX_n(1-X_n) can be replaced by a randomly varying term, r_n. The latter can be defined as r_n=r₀ exp(kZ_rn) where r₀ is a characteristic constant, Z_rn a normal random variate produced by a normally distributed random number generator and k its chosen standard deviation. Theoretically, the magnitude of such r_n (and its corresponding X_n) can be anywhere in the range 0<X_n<∞. However, the magnitude of k can be selected so that X_n>1 is a very rare event. In the special case of widely fluctuating populations dominated by random factors, the model can be replaced by N_n/N₀=exp(k′Z_rn), where N₀ is a characteristic number. In this form the model can account for occasional aperiodic population explosions, and if a lower limit to a viable number is also set (eg N/N₀>0·01), for extinction events as well. The flexibility of the two models is demonstrated with simulated population evolution patterns of different kinds. © 1997 SCI.     

Expected and unexpected plastic behavior at the micron scale: An in situ μLaue tensile study

The study of mechanical properties in micron- and submicron-sized metal crystals raises fundamental questions about the influence of size on different aspects of plasticity. In situ characterization of the microstructure evolution during loading is necessary to understand the physics underlying crystal deformation. In situ μLaue diffraction is able to provide unique statistical information on the evolution of type and density of stored dislocations. Here we show macroscopically expected and unexpected plastic behavior at low strains, observed during in situ μLaue tensile tests on micron-sized, single slip oriented Cu samples. Regardless of the initial behavior, a steady state is reached which qualifies a technical yield criterion at the micron scale.     

High-damping carbon nanotube hinged micromirrors

New developments in digital mirror devices (DMDs) require suspension hinges with a good damping and high temperature stability. Carbon nanotubes (CNTs) offer these unique properties. Herein it is shown how CNT hinges can be integrated in micromirrors. The image illustrates a micromirror with a CNT suspension, and a typical overdamped stepresponse (Q-factor < 0.5).     

Modal dynamics in multimode fibers

The dynamics of modes and their states of polarizations in multimode fibers as a function of time, space, and wavelength are experimentally and theoretically investigated. The results reveal that the states of polarizations are displaced in Poincaré sphere representation when varying the angular orientations of the polarization at the incident light. Such displacements, which complicate the interpretation of the results, are overcome by resorting to modified Poincaré sphere representation. With such modification it should be possible to predict the output modes and their state of polarization when the input mode and state of polarization are known.