Ana Barjau

Holonomy in mobile robots

The search for a simple and accurate odometry is a main concern when working with mobile robots. This article presents a general analysis of the problem and proposes a particular solution to improve the odometry. The three crucial kinematical aspects of mobile robots (mobility, control, and positioning) are reviewed in detail for vehicles based both in conventional and in omnidirectional wheels. The latter case is more suitable from a maneuvering point of view as it provides the robot frame with the three Degrees Of Freedom (DOF) of plane motion without singular configurations. Moreover, a suitable design of the omnidirectional wheels leads to a strictly invariant Jacobian matrix and thus to a linear control equation with constant coefficients. It is shown that such vehicles may have a holonomic behavior when moving under suitable kinematical restrictions without constraining their trajectory. In that case, the odometry is algebraic (instead of integrative) and thus more accurate. An application case is presented.

Alternatives to the impulse response h(t) to describe the acoustical behavior of conical ducts

In unidimensional acoustical systems, the impulse response h(t) at the input section, which describes the pressure evolution originated at this section by the introduction of a flow unit impulse through it, relates pressure p(t) and flow u(t) at the input section by means of the convolution product p=h*u. If damping and radiation are small, it is interesting to find other functions of faster decay than h(t) in order to improve the convolution convergence. As alternatives to h(t), this article studies the impulse responses h’(t) and h‘(t), which correspond to the modified systems that result when coupling the original acoustical system input section to a cylindrical anechoic termination and a conical anechoic termination, respectively. These functions h’(t) and h‘(t) are related to the plane‐wave reflection function Rp−(t) and spherical‐wave reflection function Rs−(t), respectively. The comparison of these three impulse responses shows that the use of h’(t) and h‘(t), though of faster decay than h(t) in pr...

Time-domain simulation of acoustical waveguides with arbitrarily spaced discontinuities

The multiconvolution algorithm [Martinez et al., J. Acoust. Soc. Am. 84, 1620–1627 (1988)] to calculate the impulse response or reflection function of a musical instrument air column has proved to be useful, but it has the limitation that the spacing between discontinuites is constrained to be some multiple of cΔt (for phase velocity c and time step Δt). This paper presents an improved method, the continuous-time interpolated multiconvolution (CTIM), where such a limitation has been removed. The response of an air column, modeled as an arbitrary one-dimensional acoustic waveguide constructed using cylindrical or conical bore segments with viscothermal damping and tone-hole discontinuities, is obtained through continuous-time convolutions between analytical reflection and transmission functions and discrete-time pressure signals. The arbitrary spacing between discontinuites is accounted for by interpolation of the discrete-time pressure signals. Many musical instrument air columns possess tone holes that ...

Study of woodwind-like systems through nonlinear differential equations. Part II. Real geometry

Idealized woodwind models assume a well-localized nonlinearity coupled to a linear bore whose mathematical description is usually expressed through a convolution product. For the case of the simplest bore geometries, cylindrical and conical, the convolution can be transformed into a delayed differential equation. When including in it the nonlinearity, the usual concepts of nonlinear dynamical systems allow a better understanding of the system’s evolution. In this paper they are applied to the cylindrical and conical geometries and some characteristics of their behaviors are analyzed at the threshold of oscillation through an analytical study. It is shown that their dynamics cannot be reduced to a finite number of degrees of freedom (effective dynamics). Finally numerical simulations reveal peculiar characteristics of the direct and inverse bifurcations involved in such simple systems for quadratic and cubic nonlinearities respectively.

On the time‐domain description of conical bores

Traditionally the description of the acoustical behavior of a bore has been done in the frequency domain through the acoustical impedance or the reflection coefficient. Whenever the time‐domain response of it (impulse response, reflection function) has been needed, it has usually been obtained through the Fourier transform (FT) of the corresponding frequency‐domain function. However, there are a number of cases in which this approach is unsuitable because the FT leads to noncausal functions which cannot be understood physically as impulse responses or reflection functions. In such cases the time‐domain calculation is unavoidable. This calculation leads to exponentially growing functions which obviously do not accept an FT. This article presents the time‐domain calculation of the main basic functions (reflection and transmission functions associated with a single discontinuity, impulse responses of anechoic bores) which are needed to obtain the input reflection function and the impulse responses of a bore....

Delayed models for simplified musical instruments.

Most musical instruments contain, at their very basis, a continuous vibrating element (string or air column) which can be treated as a one-dimensional system. Its oscillation is obtained either through an initial condition or by means of a continuous energy input through a nonlinear device. In both cases and as a first approach, the excitation can be localized at one single point, and the continuous system can be considered as a linear one. The coupling between these two elements is often represented through a convolution integral. This convolution will be rewritten here in a way that different phenomena taking place in the continuous element (internal losses, radiation at the ends...) are separated. Different choices in the formulation of these processes and some mathematical manipulation will lead to either algebraic iterative or delayed differential equations. These equations are valid for any form of energy input. Once this energy input is defined, they can be used to simulate the behavior of different instruments in a more efficient way than that of traditional convolution. Moreover, these equations allow an analytical analysis of possible regimes using the tools of nonlinear dynamical systems (NLDS). The case of woodwinds will be emphasized throughout the paper, while that of strings will be presented briefly for the sake of completeness.

A weighted cost function to deal with the muscle force sharing problem in injured subjects: A single case study

The human body is an over-actuated multi-body system, as each joint degree of freedom can be controlled by more than one muscle. Solving the force-sharing problem (i.e. finding out how the resultant joint torque is shared among the muscles actuating that joint) calls for an optimization process where a cost function, representing the strategy followed by the central nervous system to activate muscles, is minimized. The main contribution of the present study has been the particular formulation of that cost function for the case of the pathological gait of a single subject suffering from anterior cruciate ligament rupture. Our hypothesis was that the central nervous system does not weight equally the muscles when trying to compensate for a lower limb injury during gait (in contrast to what is the usual practice for healthy gait where all muscles are weighted equally). This hypothesis is supported by the fact that muscle activity in injured individuals differs from that of healthy subjects. Different functions were tested until we finally came out with a cost function that was consistent with experimental electromyography measurements and inverse dynamics results for a subject suffering this particular pathology.

Calibration for mobile robots with an invariant Jacobian

The kinematics of some mobile robots is described through a strictly invariant Jacobian matrix [J]. This is the case for robots with three degrees of freedom and suitable omnidirectional wheels, and that for robots with conventional wheels and differential kinematics. This article proposes a calibration technique for the matrix [J] of such robots. It is based on four accurate configuration measurements associated with particular nominal motions where the generalized velocities maintain a constant proportional relationship. As a consequence, the nominal trajectories are arcs of circumference and may be part of the actual trajectories of the robot. An application example is presented.

On the one-dimensional acoustic propagation in conical ducts with stationary mean flow

This paper proposes a direct time-domain calculation of the time-domain responses of anechoic conical tubes with steady weak mean flow. The starting point is the approximated linear one-dimensional wave equation governing the velocity potential for the case of steady flow with low Mach number. A traveling solution with general space-dependent propagation velocity is then proposed from which the inward and outward pressure and velocity impulse responses can be obtained. The results include the well-known responses of conical and cylindrical ducts with zero mean flow.

Differential formulation: A powerful tool for woodwind instrument numerical simulations

A woodwind instrument is well described by a linear resonator introducing a delay and a nonlinear excitator without delay. Thus one can model the woodwind instrument with two simple equations (one in the Fourier domain, the other one in the time domain) calling out the acoustical pressure, flow, and admittance of the resonator. Under some conditions, these two equations can be rewritten as a single nonlinear differential equation with delay, the degree of which depends on the resonator’s geometry. As an example, a cone can be described by a second‐order differential equation which transforms into a first‐order one for a cylinder. This differential formulation has some advantages: The minimal phase space dimension transitions to chaos are clearly displayed; moreover, resulting numerical algorithms are much quicker and more stable than those obtained by integral or Fourier transform methods; the control parameter is directly related to the resonator losses (which is easy to control). And last, it’s a powerf...