A continuous-time analog moment calculating circuit

Abstract

A circuit has been developed which performs a continuoustime analog computation of the f m t two moments of a discrete distribution of currents. The circuit is intended for use with tactile sensor arrays and it is assumed that there are currents available which are proportional to the sum of the forces applied to the elements in each column and row. The zeroth moment then corresponds to the total force on the array and the first moments of the row and column sums correspond to the means of the pressure distributions in the two directions. The circuit comprises a canonical cell which is repeated once for each input current (i.e., once for each column or row) and a divider circuit which is used once for each distribution (i.e., one for the row distribution and one for the column distribution). The reveating canonical cell uses onlv five transistors and can be cascadeTd to work with an NxM a&y for any values of N and M. Background It has long been recognized that the next generation of robots will require 'smart tactile sensors in addition to vision and the standard sensors used to control motion [1,21. Smart tactile sensors could perform some preliminary data reduction in order to reduce the volume of data sent to a digital controller, and would also facilitate the implementation of local feedback control loops in the gripper thereby freeing the central controller for higher level tasks. It is not clear at this time how much processing should be performed locally, but it is clear that the total force and the center of contact of the force would both be useful for obtaining and maintaining a stable grasp, and that moments. in particular, would be useful 131. Continuous-time analog control is usually capable of responding more rapidly than digital control. For low-level functions like total force it may make sense to use analog control loops. The circuit described here provides a total force output (the zeroth moment) in addition to outputs for the mean (the first moment) of the pressure distribution for both the row and column sums. If the pressure distribution is unimodal, which is likely for a curved finger on an articulated hand, then the mean is a measure of the location of the contact. Figure 1 shows the assumed architecture of the sensor array. Each individual element, called a tactel, has two open-collector current outputs. The tactel outputs are tied together to produce row and column sums. As shown in the figure, the column sums represent discrete samples of the pressure distribution in the x direction while the row sums represent discrete samples of the pressure distribution in they direction. The "ray would usually be covered with an elastic layer so that point loads applied between sensors would produce a response. Figure 1 also shows the canonical circuit block, hereinafter called the cell, associated with each row and column. The first two moments of the discrete force dismbutions are given by the following sums. where J-0 is the zeroth moment, (or p ) is the first moment, and f (n) is the sum of the forces in the nth row or column.