Mobile robots using a 360° field of view LIDAR ranging sensor can generate enormous 3D point clouds. To reduce the quantity of data in memory a compression can lead to unstructured environment models such as irregular meshes. This kind of structure can contain deformed cells and the path planning can be cumbersome. This paper presents a path planning method based on fluid mechanics able to deal with unstructured terrain models. The algorithm uses the finite element method to compute a velocity potential function free from local minima. Then, several streamlines are computed as a road map and the optimal path is selected among the candidate paths. The approach is implemented on the Canadian Space Agency (CSA) Mars Robotics Testbed (MRT) rover and tested at the CSA Mars Emulation Terrain (MET). To confirm the feasibility of the method, the path planner has been tested on 284 LIDAR scans collected in a realistic outdoor challenging terrain.

Methane is a greenhouse gas, emitted from sources such as landfills. This paper presents a steady state model of methane biofiltration taking into consideration the impact of various parameters, such as the inlet methane concentration, the gas superficial velocity and the packing bed average temperature, on the methane biofilter efficiency. More specifically, the model developed here considers that the average bed temperature is influenced by the elimination capacity of methane in the biofilter, which is function of the methane inlet load. When using this model, it is possible to estimate the biofilter performance in terms of parameters, such as the conversion, elimination capacity and carbon dioxide production. Comparison of the model generated performance values with experimental data in the range of methane concentrations varying from 1500 to 9500 ppmv yields satisfactory results (<2–10% error, depending on the inlet methane concentration and on the performance parameter).

The modeling of physical phenomena is most often conveyed through partial differential equations governing continuous fields. Computational approaches are used afterwards in order to approximate the solutions to these equations. In doing so, a discretized version of the initial model must be set up using one of the numerous available methods. This paper illustrates how influence graphs (weighted digraphs with geometrical attributes) may behave in the same way as differential operators in so far as a set of appropriate conditions of consistency are satisfied. These conditions are written explicitly for the most often used cases, including differential boundary operators. On the one hand, a consistent neighborhood may be regarded as a generalization of a classical finite difference scheme. On the other hand, a consistent influence graph is a discrete object modeling a physical behavior as well as its continuous counterpart. Numerical experimentations address firstly the second order diffusion model and lastly the fourth order Kirchhoff theory of plate deflection.

This paper introduces directed graphs on which the evolution of a physical quantity depends only on local neighborhoods. These graphs are then used to model transfer phenomena occurring under a convective mode or a diffusive mode. The conditions under which the state associated to such graphs approaches the solution of a diffusion-convection partial differential model are established. An algorithm permitting to determine consistent neighborhoods is described and recognized as a generalization of the finite difference method. Examples of application are presented in order to illustrate the practical applicability of these concepts.

In this paper, we investigate the stability properties of a cylindrical grinding process. The dynamical model of the process includes two inherent delayed forcing terms, one from workpiece regeneration and the other from grinding wheel regeneration. The prediction of chatter onset is carried out by computing the spectrum of the doubly delayed differential equations for any set of physical and operational parameters. Stability diagrams are plotted in parameter space. The stability behavior obtained from this analysis is verified to be consistent with direct simulation results. A sensitivity analysis approach is also proposed, and can be used to lead an unstable process to a stable state by optimally varying one of the operational parameters.

This paper investigates the global stability behavior present near a bifurcation point of a nonlinear road vehicle system. The nonlinear behavior of the system is determined by reducing its dimensions according to the center manifold theory applied to a nongeneric case. A generalized Hopf bifurcation is analyzed by unfolding the limit cycle mean amplitude equation into a two-parameter space. The numerical application of the analytical framework demonstrates the coexistence of two limit cycles for certain ranges of physical and driver parameter values.

This paper develops the differential equations governing the motion of spatial networks to which mechanical features such as masses, stiffness coefficients, tensions and bending moments have been associated. These networks generalize the concept of particle systems introduced for the simulation of flexible bodies and extend their application to elastic models. The network deformation is shown to be related to the internal tensions and moments by a set of vectors, the directors of the network. A numerical example describing a rotating flexible beam is presented.

In this paper, linear stability and chaotic motion of a time-delayednonlinear vehicle system are studied. The stability is determined bycomputing the spectrum associated with a system of linear retardedfunctional differential equations, which reveals that a loss ofstability occurs following a Hopf bifurcation. Beyond the critical valuefor linear stability, the system exhibits limit cycle motions.Subharmonic, quasi-periodic and chaotic motions are observed for asystem excited by a periodic disturbance.

In the present paper, a new mathematical model describing the physical, chemical and biological phenomena involved in the process of contaminant removal in biofilters is developed. In addition to the contaminant, the key components of the present theoretical model are carbon dioxide and oxygen. The model predicts the concentration profile of the key components in the gas phase, the biofilm and the sorption liquid retained in the solid particles composing the filter bed at both steady and transient regimes. The model equations were solved numerically and comparison between theory and experiment showed that the model results for styrene and carbon dioxide concentration profiles were in very good agreement with experimental data for the biofiltration of styrene vapors at steady state. The analysis of oxygen concentration profile in the biofilm predicted by the theoretical model revealed that oxygen limitation does not occur under the operating styrene biodegradation rate in the biofilter. (C) 2003 Society of Chemical Industry.

Upwind finite element schemes remove spurious oscillations that occur in the solution of diffusion convection equations. Up to now these schemes lose part of their accuracy when the Peclet is large. As an improvement, it is proposed to move the integration nodes along the ‘streamlines’ before evaluating the elementary convection matrices. The displacements of the nodes along the streamlines, which are one-dimensional manifolds, are calculated analogously to well-known one-dimensional formulae. The last section of this paper illustrates this new method with the help of four examples which show its validity.