MMC — A Holistic System for a Nonsymbolic Internal Body Representation

Abstract

Contrary to feedforward networks, networks with recurrent connections show dynamic, in the sense of time-dependent properties. Therefore, recurrent networks are well suited to control behavior varying in time and, in this way, are particularly interesting for the solution of motor control tasks in both robots and animals. However, there is only a small theoretical basis concerning the properties of massively parallel recurrent systems. Only a few special types, in particular the Hopfield network, have been investigated in some detail. Here we describe another type of recurrent network that shows interesting properties and that can be applied to solve a basic problem in motor control. To control a multijoint manipulator with revolute joints, the actuators have to control joint angles. Thus, the controller has to provide signals giving angle values, i. e. , it has to operate in joint space coordinates. The task of the manipulator, however, is usually given in another coordinate system, namely in workspace coordinates. In many cases, the workspace coordinates are provided by a visual system. These workspace coordinates could, for example, be given as Cartesian coordinates. Therefore, the controller has to cope with the problem of transformation between workspace and joint space coordinates. Another problem is that the position of the manipulator may be subject to external disturbances. The classical way to solve this problem is to apply negative feedback control. In the feedback loop, the joint space values will therefore be transformed to workspace coordinates. This is called direct transformation. In the feedforward loop, the workspace coordinates have to be transformed into joint space coordinates, which is called inverse transformation. Here, we will concentrate only on kinematic systems. In this case, the transformations are called direct kinematics and inverse kinematics, respectively. If we deal with a redundant system, for example, when we consider a three-joint manipulator which moves in a two-dimensional plane (see Fig. 1), the direct kinematics are easy to calculate, but for the inverse kinematics there is an infinite number of solutions. Therefore, in the case of a redundant system, additional constraints are necessary to permit a unique solution.