G. Payre

Nonlinear oscillations and chaotic motions in a road vehicle system with driver steering control

The nonlinear dynamics of a differential system describing the motion of a vehicle driven by a pilot is examined. In a first step, the stability of the system near the critical speed is analyzed by the bifurcation method in order to characterize its behavior after a loss of stability. It is shown that a Hopf bifurcation takes place, the stability of limit cycles depending mainly on the vehicle and pilot model parameters. In a second step, the front wheels of the vehicle are assumed to be subjected to a periodic disturbance. Chaotic and hyperchaotic motions are found to occur for some range of the speed parameter. Numerical simulations, such as bifurcation diagrams, Poincaré maps, Fourier spectrums, projection of trajectories, and Lyapunov exponents are used to establish the existence of chaotic attractors. Multiple attractors may coexist for some values of the speed, and basins of attraction for such attractors are shown to have fractal geometries.

Path planning based on fluid mechanics for mobile robots using unstructured terrain models

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.

Global bifurcation analysis of a nonlinear road vehicle system

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.

Parameters estimation of an aquatic biological system by the adjoint method

Simulation models are currently used to predict environmental impacts. However, models must be adapted to the peculiarities of the given situation and one of these adaptations consists in the calibration of certain model parameters. The calibration is made by an optimization technique in which parameters must be adjusted to fit to the data coming from one sampling station.

Optimal design of the shape of a space radiator

This paper surveys the theory and numerical solution for the design of a minimum weight thermal radiator with constraint on the input temperature.

OPTIMAL DESIGN OF A RADIATING FIN FOR COMMUNICATIONS SATELLITES

Abstract This paper is motivated by the design of a minimum weight thermal radiator or radiating fin for communication satellites. As a first step towards the solution of this problem we present an efficient finite element method to solve the non-linear boundary-value problem describing the temperature distribution. It leads to a non-linear programming problem. Steepest descent, conjugate gradient and Newton’s method are compared. Numerical experiments are presented. This basic tool will be used many times in the iteration process to find the optimal shape.

Optimal and Suboptimal Design of Thermal Diffusers for Communication Satellites a

Abstract The object of this paper is to present recent developments in the design of mass-optimized thermal diffusers with a priori specifications on the input power flux and a bound on the output power flux. This problem arises in connection with the use of high power solid state devices (HPSSD’s) in future Canadian communication satellites. In DELFOUR, PAYRE and ZOLESIO (1981a), we have announced some results on the optimal design using the techniques of shape optimal design (cf. J.CEA (1976, 1978)), J.P.ZOLESIO (1981, 1979, 1973, 1977)). In this paper we also consider suboptimal designs (e.g. doublers) and compare them with the optimal one. A similar problem was studied by Ph. DESTLIYNDER (1976). However the present design differs in the fact that we have a constraint on the normal derivative on a piece of the boundary surface instead of a constraint on the maximum temperature in the domain or body of the diffuser.

KINEMATICS AND DYNAMICS OF SKI-TRACKED VEHICLES

SUMMARY A snow vehicle is modelized as a system of rigid bodies and the equations of motion are obtained within the framework of the differential algebraic equations formalism, and also, through the Kane dynamic formalism. Problems arising from the ski or track contact constraints with a given hard rigid profile are discussed. A constitutive model for snow compaction is assumed and external forces and moments, that condition the dynamic of this type of vehicle, are evaluated. A pilot, modelized by a four-bar mechanism and a viscoelastic seat is added to the system and simulations are reported, revealing some of the important characteristics of this type of vehicle. The role of the animation is also stressed for the purpose of vehicle design.

Numerical Computation of Eigenvalues for Linear Structures by Kuhn's Method

Abstract In this paper we adapt the combinatorial method developed by H. Kuhn to the computation of the eigenvalues of a structure made up of N connected beams. Among its advantages over computations based on finite element models are its accuracy, its speed, and the posibility to easily obtain eigenvalues of large modulus. Two adaptations of H. Kuhns original method are presented: one with fixed size rectangles and one with variable size rectangles. The scaling of the function characterizing the eigenvalues is also discussed. This question is especially important in the computation of roots of large modulus. Several numerical tests are presented