Kinematic Bézier Maps.

The kinematics of a robot with many degrees of freedom is a very complex function. Learning this function for a large workspace with a good precision requires a huge number of training samples, i.e., robot movements. In this paper, we introduce the Kinematic Bézier Map (KB-Map), a parameterizable model without the generality of other systems but whose structure readily incorporates some of the geometric constraints of a kinematic function. In this way, the number of training samples required is drastically reduced. Moreover, the simplicity of the model reduces learning to solving a linear least squares problem. Systematic experiments have been carried out showing the excellent interpolation and extrapolation capabilities of KB-Maps and their relatively low sensitivity to noise.

Self-calibration of a space robot.

We present a neural-network method to recalibrate automatically a commercial robot after undergoing wear or damage, which works on top of the nominal inverse kinematics embedded in its controller. Our starting point has been the work of Ritter et al. (1989, 1992) on the use of extended self-organizing maps to learn the whole inverse kinematics mapping from scratch. Besides adapting their approach to learning only the deviations from the nominal kinematics, we have introduced several modifications to improve the cooperation between neurons. These modifications not only speed up learning by two orders of magnitude, but also produce some desirable side effects, like parameter stability. After extensive experimentation through simulation, the recalibration system has been installed in the REIS robot included in the space-station mock-up at Daimler-Benz Aerospace. Tests performed in this set-up have been constrained by the need to preserve robot integrity, but the results have been concordant with those predicted through simulation.

On-line learning with minimal degradation in feedforward networks.

Dealing with nonstationary processes requires quick adaptation while at the same time avoiding catastrophic forgetting. A neural learning technique that satisfies these requirements, without sacrificing the benefits of distributed representations, is presented. It relies on a formalization of the problem as the minimization of the error over the previously learned input-output patterns, subject to the constraint of perfect encoding of the new pattern. Then this constrained optimization problem is transformed into an unconstrained one with hidden-unit activations as variables. This new formulation leads to an algorithm for solving the problem, which we call learning with minimal degradation (LMD). Some experimental comparisons of the performance of LMD with backpropagation are provided which, besides showing the advantages of using LMD, reveal the dependence of forgetting on the learning rate in backpropagation. We also explain why overtraining affects forgetting and fault tolerance, which are seen as related problems.