Vicente Ruiz de Angulo

BioCD : An efficient algorithm for self-collision and distance computation between highly articulated molecular models

This paper describes an efficient approach to (self) collision detection and distance computations for complex articulated mechanisms such as molecular chains. The proposed algorithm called BioCD is particularly designed for samplingbased motion planning on molecular models described by long kinematic chains possibly including cycles. The algorithm considers that the kinematic chain is structured into a number of rigid groups articulated by preselected degrees of freedom. This structuring is exploited by a two-level spatially-adapted hierarchy. The proposed algorithm is not limited to particular kinematic topologies and allows good collision detection times. BioCD is also tailored to deal with the particularities imposed by the molecular context on collision detection. Experimental results show the effectiveness of the proposed approach which is able to process thousands of (self) collision tests per second on flexible protein models with up to hundreds of degrees of freedom.

Rapid learning of humanoid body schemas with Kinematic Bézier Maps

This paper addresses the problem of hand-eye coordination and, more specifically, tool-eye recalibration of humanoid robots. Inspired by results from neuroscience, a novel method to learn the forward kinematics model as part of the body schema of humanoid robots is presented. By making extensive use of techniques borrowed from the field of computer-aided geometry, the proposed kinematic Bezier maps (KB-Maps) permit reducing this complex problem to a linearly-solvable, although high-dimensional, one. Therefore, in the absence of noise, an exact kinematic model is obtained. This leads to rapid learning which, unlike in other approaches, is combined with good extrapolation capabilities. These promising theoretical advantages have been validated through simulation, and the applicability of the method to real hardware has been demonstrated through experiments on the humanoid robot ARMAR-IIIa.

A deterministic algorithm that emulates learning with random weights

Abstract The expectation of a function of random variables can be modeled as the value of the function in the mean value of the variables plus a penalty term. Here, this penalty term is calculated exactly, and the properties of different approximations are analyzed. Then, a deterministic algorithm for minimizing the expected error of a feedforward network of random weights is presented. Given a particular feedforward network architecture and a training set, this algorithm accurately finds the weight configuration that makes the network response most resistant to a class of weight perturbations. Finally, the study of the most stable configurations of a network unravels some undesirable properties of networks with asymmetric activation functions.

Architecture-Independent Approximation of Functions

We show that minimizing the expected error of a feedforward network over a distribution of weights results in an approximation that tends to be independent of network size as the number of hidden units grows. This minimization can be easily performed, and the complexity of the resulting function implemented by the network is regulated by the variance of the weight distribution. For a fixed variance, there is a number of hidden units above which either the implemented function does not change or the change is slight and tends to zero as the size of the network grows. In sum, the control of the complexity depends on only the variance, not the architecture, provided it is large enough.

Using PSOMs to learn inverse kinematics through virtual decomposition of the robot

We propose a technique to speed up the learning of the inverse kinematics of a robot manipulator by decomposing it into two or more virtual robot arms. Unlike previous decomposition approaches, this one does not place any requirement on the robot architecture and, thus, it is completely general. Parametrized Self-Organizing Maps (PSOM) are particularly adequate for this type of learning, and permit comparing results obtained directly and through the decomposition. Experimentation shows that time reductions of up to two orders of magnitude are easily attained.

Learning Inverse Kinematics via Cross-Point Function Decomposition

The main drawback of using neural networks to approximate the inverse kinematics (IK) of robot arms is the high number of training samples (i.e., robot movements) required to attain an acceptable precision. We propose here a trick, valid for most industrial robots, that greatly reduces the number of movements needed to learn or relearn the IK to a given accuracy. This trick consists in expressing the IK as a composition of learnable functions, each having half the dimensionality of the original mapping. A training scheme to learn these component functions is also proposed. Experimental results obtained by using PSOMs, with and without the decomposition, show that the time savings granted by the proposed scheme grow polynomically with the precision required.

Exploiting single-cycle symmetries in continuous constraint problems

Symmetries in discrete constraint satisfaction problems have been explored and exploited in the last years, but symmetries in continuous constraint problems have not received the same attention. Here we focus on permutations of the variables consisting of one single cycle. We propose a procedure that takes advantage of these symmetries by interacting with a continuous constraint solver without interfering with it. A key concept in this procedure are the classes of symmetric boxes formed by bisecting a n-dimensional cube at the same point in all dimensions at the same time. We analyze these classes and quantify them as a function of the cube dimensionality. Moreover, we propose a simple algorithm to generate the representatives of all these classes for any number of variables at very high rates. A problem example from the chemical field and the cyclic n-roots problem are used to show the performance of the approach in practice.

Neural learning methods yielding functional invariance

This paper investigates the functional invariance of neural network learning methods incorporating a complexity reduction mechanism, such as a regularizer. By functional invariance we mean the property of producing functionally equivalent minima as the size of the network grows, when the smoothing parameters are fixed. We study three different principles on which functional invariance can be based, and try to delimit the conditions under which each of them acts. We find out that, surprisingly, some of the most popular neural learning methods, such as weight-decay and input noise addition, exhibit this interesting property.

Symmetry breaking in numeric constraint problems

Symmetry-breaking constraints in the form of inequalities between variables have been proposed for a few kind of solution symmetries in numeric CSPs. We show that, for the variable symmetries among those, the proposed inequalities are but a specific case of a relaxation of the well-known LEX constraints extensively used for discrete CSPs. We discuss the merits of this relaxation and present experimental evidences of its practical interest.

Neural Learning Invariant to Network Size Changes

This paper investigates the functional invariance of neural network learning methods. By functional invariance we mean the property of producing functionally equivalent minima as the size of the network grows, when the smoothing parameters are fixed. We study three different principles on which functional invariance can be based, and try to delimit the conditions under which each of them acts. We find out that, surprisingly, some of the most popular neural learning methods, such as weight-decay and input noise addition, exhibit this interesting property.