ERCIM News No.42 - July 2000 [contents]

### Modelling Non-linear Phenomena in Joints of Robots with Neural Networks

by Jozef Suchy

Some types of artificial neural networks have the potential to model non-linear relations between input and output variables of systems. The structure of this non-linearity need not be known in advance. Joints of robots are known to posses non-linear properties like friction, non-linear stiffness or backlash. Usual way how to model these phenomena is to assume some analytical model and to identify its para-meters. At the Faculty of Natural Sciences of Matej Bel University, an approach is based on using the convenient measurements, which enable to model the joint of a robot as non-linear system.

Knowledge of non-linearity in joints of geared robots may be very important. Friction, eg, causes that part of the moment generated by the motor in the joint is lost to overcome the friction moment of the joint. If these losses of the moment caused by friction, stiffness/ compliance (eg compliance of harmonic drive), and backlash were known in advance one could compensate for them by generating some extra torque. This may be significant in those situations where it is important that some amount of torque is transferred through the joint without losses. Typical example is the so-called force or compliance control of robots.

With this type of robot control one desires that the robot apply some well-defined force or moment to the working environment. This force depends in general on torque in all joints. If the torque in some joint is insufficient, it may not be possible to generate the desired force or moment in the environment. Besides, as the amount of lost torque is not known, the Cartesian force may be generated with low precision.

In current practice the problem is solved by force feedback. The 6-component force/torque sensors are used to measure the intensity of contact (three Cartesian forces and three Cartesian moments) and the measured forces or moments are fed back. On this basis the motor currents, which are equivalent to the torque are controlled in such a way that the desired Cartesian values are attained. Disadvantage of this approach is the use of comparatively expensive sophisticated sensor and also narrower bandwidth caused by additional control loops.

On the contrary, this problem is not so serious with direct drive robots where the absence of gearing removes the majority of sources of non-linearity. In principle, using direct drive robots, the intensity of contact with the environment could be satisfactorily controlled by defining equivalent joint’s torque. As there are only minor losses of torque in joints in this case, the equivalent joint’s torque may be computed by multiplying the desired Cartesian force/moment with transposed Jacobi matrix of the manipulator.

We have begun neural network modelling with the most significant non-linear phenomenon in robot joints – friction. To separate friction from other phenomena we used data measured on one joint of direct drive robot EDDA built at the Institute of Robotics, University of Technology, Braunschweig, Germany. In spite of absence of gearing, some friction is still present in joints. It was our desire to utilize as simple measurements as possible. We developed methodology of modelling joint friction with ANN for this simple two-degree-of-freedom robot based on the measurements of angular position and of corresponding current. However, the knowledge of dynamic model of the manipulator was assumed.

Methodology is based on obtaining friction data from the knowledge of angular position, motor current/moment and from the dynamical model of the manipulator. This leads to the inevitability to compute angular acceleration. As the by-product, also this procedure was developed, which works satisfactorily.

Multi-layer perceptron network was used in most of cases for the modelling although it was worked also with CMAC neural network. The inputs to the network are present and past values of angular position and past values of friction torque. The output of the network is actual value of friction torque. Network was learnt by back-propagation algorithm with the momentum term and with the adaptive learning rate. The batch version of the algorithm was used. The number of training epochs was chosen as 10 000, while the training set consisted of 2000 samples. The sum square error was diminished to 0.707 on the training set and to 2.95 for the whole set of samples. It goes out from this that the friction torque is modelled with good quality.

There was also experimented with the depth of history of signals used for modelling as it was assumed that the structure of non-linearity including the order of the system is not known. It goes out from these experiments that the system of first or second order sufficiently model the joint properties. This procedure makes up for the procedure of system’s order identification.

One may object that friction changes with time and depends on temperature. Temperature dependence may be modelled if the additional measurement of temperature is available. Temperature and temperature gradient would be possibly further inputs to the ANN. However, in the present time such measurements are not available for us. This possibility is the subject of our further research.

There is the potential to make this method adaptive, which means that the measurements could be performed continually and the model would be up-dated on their basis. This does not in principle need any extra sensors, as the sensors needed are available in every joint. Would the model be built also on the basis of temperature measurement, simple temperature measuring scheme would have to be built.

An attempt has also been made to model complex properties of the joint. This research will continue in the future. One goal of this research consists in constructing what we call generalised Jacobi matrix, ie Jacobi matrix, which includes also the properties of joints. Such a matrix could serve to transform the Cartesian forces and moments to joint torque or motor current.

This work was performed due to the grants of the Slovak Scientific Grant Agency VEGA.