‘Jacobix’: A hardwired instant Jacobian calculator

Abstract

This paper describes an analog electronic circuit that performs matrix multiplications without using a μP. I t was developed for an in-house designed force-torque sensor (FTS), which consists of a metal-frame structure, having three to six strain gauges (pairs) mounted in a certain geometrical configuration. The geometry of the FTS is such that certain linear combinations of instantaneous signals from all the strain gauges can be used to compute the force and torque applied to it. This basically requires multiplication of all the strain gauges' outputs with a special matrix, called a Jacobian. Now, the straight forward approach of using an A/D chip to acquire signals from the gauges and subsequent computation using a DSP has certain shortcomings. Firstly, the applied force on the FTS may change abruptly even before the sequential polling of all the six gauges are completed-resulting in wrong force computation. Secondly, the processor boards, complete with suitable A/D, D/A ports and memory are expensive and need dust free housing. In humid, noisy and dusty field situations, these components may easily get damaged. As an alternative, we have developed a circuit that not only reads all the strain gauges online in parallel, but also computes the force and torque components instantaneously, that too at a tiny fraction of the cost of a computer.