Nonlinear system identification by modelling the underlying relationships in observation data is an important application area for artificial neural networks and other learning paradigms. Splines have been used for scattered data interpolation, but the applications have mainly been restricted to low dimensional input spaces. This paper describes ASMOn, a new learning paradigm for higher dimensional data (> 3) based on B-spline interpolation. The models can be trained online, and a method for step-wise model refinement is applied during model training for gradually increasing the modelling capability until the desired or best possible accuracy is obtained. For every refinement step a number of possible refinement actions are evaluated, and the one that gives the highest improvement of the model accuracy is chosen. The model structure is hence adapted to the modelling problem, giving a model of small size and high accuracy. ASMOn has very efficient implementations on serial computers. The scheme has been evaluated on a problem designed for MARS (see Friedman 1988) and the results compare favourably with MARS. The method has also been used to model the actuator dynamics of a hydraulic robot manipulator, and significant improvements in dynamic accuracy in the manipulator control have been obtained.
Recently, Range Imaging (RIM) cameras have become available that capture high resolution range images at video rate. Such cameras measure the distance from the scene for each pixel independently based upon a measured time of flight (TOF). Some cameras, such as the SwissRanger™ SR-3000, measure the TOF based on the phase shift of reflected light from a modulated light source. Such cameras are shown to be susceptible to severe distortions in the measured range due to light scattering within the lens and camera. Earlier work induced using a simplified Gaussian point spread function and inverse filtering to compensate for such distortions. In this work a method is proposed for how to identify and use generally shaped empirical models for the point spread function to get a more accurate compensation. The otherwise difficult inverse problem is solved by using the forward model iteratively, according to well established procedures from image restoration. Each iteration is done as a sequential process, starting with the brightest parts of the image and then moving sequentially to the least bright parts, with each step subtracting the estimated effects from the measurements. This approach gives a faster and more reliable compensation convergence. An average reduction of the error by more than 60% is demonstrated on real images. The computation load corresponds to one or two convolutions of the measured complex image with a real filter of the same size as the image.
Trajectory learning control is a method for generating near to optimal feedforward control for systems that are controlled along a reference trajectory in repeated cycles. Iterative refinements of a stored feedforward control sequence corresponding to one cycle of the control trajectory is computed based upon the recorded trajectory error from the previous cycle. Several learning operators have been proposed in earlier work, and convergence proofs are developed for certain classes of systems, but no satisfactory method for design and analysis of learning operators under the presence of uncertainties in the system model have been presented. This article presents frequency domain methods for analyzing the convergence properties and performance of the learning controller when the amplitude and phase of the system transfer function is assumed to be within specified windows. Experimental results with an industrial robot manipulator confirm the theoretical results.
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