Robot Phonotaxis with Dynamic Sound-source Localization

Abstract-We address two key goals pertaining to autonomous mobile robots: one, to develop fast accurate sensory capabilities -at present, the localization of sound sources -and second, the integration of such sensory modules with other robot functions, especially its motor control and navigation. A primary motivation for this work was to devise effective means to guide robotic navigation in environments with acoustic sources. We recently designed and built a biomimetic sound-source localization apparatus. In contrast to the popular use of time-of-arrival differences in free field microphone arrays, our system is based on the principles observed in nature, where directional acoustic sensing evolved to rely on diffraction about the head with only two ears. In this paper we present an integrated robot phonotaxis system which utilizes the robot's movement to resolve fronthack localization ambiguity. Our system achieves high angular localization acuity ( & Z 0 ) and it was successfully tested in localizing a single broadband source and moving towards it within a cluttered laboratory environment

Affine differential geometry analysis of human arm movements

Humans interact with their environment through sensory information and motor actions. These interactions may be understood via the underlying geometry of both perception and action. While the motor space is typically considered by default to be Euclidean, persistent behavioral observations point to a different underlying geometric structure. These observed regularities include the “two-thirds power law” which connects path curvature with velocity, and “local isochrony” which prescribes the relation between movement time and its extent. Starting with these empirical observations, we have developed a mathematical framework based on differential geometry, Lie group theory and Cartan’s moving frame method for the analysis of human hand trajectories. We also use this method to identify possible motion primitives, i.e., elementary building blocks from which more complicated movements are constructed. We show that a natural geometric description of continuous repetitive hand trajectories is not Euclidean but equi-affine. Specifically, equi-affine velocity is piecewise constant along movement segments, and movement execution time for a given segment is proportional to its equi-affine arc-length. Using this mathematical framework, we then analyze experimentally recorded drawing movements. To examine movement segmentation and classification, the two fundamental equi-affine differential invariants—equi-affine arc-length and curvature are calculated for the recorded movements. We also discuss the possible role of conic sections, i.e., curves with constant equi-affine curvature, as motor primitives and focus in more detail on parabolas, the equi-affine geodesics. Finally, we explore possible schemes for the internal neural coding of motor commands by showing that the equi-affine framework is compatible with the common model of population coding of the hand velocity vector when combined with a simple assumption on its dynamics. We then discuss several alternative explanations for the role that the equi-affine metric may play in internal representations of motion perception and production

Prospective Hardware Implementation Of The CHIR Neural Network Algorithm

I review the recently developed Choice of Internal Representations (CHIR) training algorithm for multi-layer perceptrons, with an emphasis on relevant properties for hardware implementation. A comparison to the common error back-propagation algorithm shows that there are potential advantages in realizing CHIR in hardware. I. INTRODUCTION Much effort is being invested in recent years to realize neural networks (NN) in hardware and in particular, on-chip learning (as reflected, for example, in the series of special issues of IEEE-TNN dedicated to the subject). An important role is played by the training algorithm and its characteristics which bear upon the hardware implementation. Naturally, the majority of standard NN algorithms have been considered for implementation to date [10]. The most popular algorithm for multi-layer perceptrons (MLP) is the error back-propagation (BP) and its variants [1, 8] which are based on two elements: 1. training by gradient descent over an error functio..

Geometric Methods in The Study of Human Motor Control

Various approaches have been followed to date in the theoretical analysis and modeling of human motor functions. Most notable are notions taken from the fields of control engineering, information theory, and various computational approaches. However, several aspects of motor behaviour have not been dealt with in a satisfactory way so far. For example, the spaces of motor degrees of freedom are customarily considered to be linear even when they are not, and their geometric structure is often ignored. In order to address these issues we apply some general and powerful tools from differential geometry. We demonstrate their usefulness to the field by examining several questions that have arisen in the study of the oculomotor system and smooth movements of the hand. In particular, we have achieved the following results: the clarification of aspects relating to eye rotations and the control strategy known as Donders' law and Listing's law; the identification of binocular motor space as the L..

The Geometry of Eye Rotations and Listing's Law

We analyse the geometry of eye rotations, and in particular saccades, using basic Lie group theory and differential geometry. Various parameterizations of rotations are related through a unifying mathematical treatment, and transformations between co-ordinate systems are computed using the Campbell-Baker-Hausdorff formula. Next, we describe Listing's law by means of the Lie algebra so(3). This enables us to demonstrate a direct connection to Donders' law, by showing that eye orientations are restricted to the quotient space SO(3)/SO(2). The latter is equivalent to the sphere S²; which is exactly the space of gaze directions. Our analysis provides a mathematical framework for studying the oculomotor system and could also be extended to investigate the geometry of multi-joint arm movements

Three-Dimensional Arm Movements at Constant Equi-Affine Speed

It has long been acknowledged that planar hand drawing movements conform to a relationship between movement speed and shape, such that movement speed is inversely proportional to the curvature to the power of one-third. Previous literature has detailed potential explanations for the power-law’s existence as well as systematic deviations from it. However, the case of speed-shape relations for three-dimensional (3D) drawing movements has remained largely unstudied. In this paper we first derive a generalization of the planar power law to 3D movements, which is based on the principle that this power law implies motion at constant equi-affine speed. This generalization results in a 3D power law where speed is inversely related to the one-third power of the curvature multiplied by the one-sixth power of the torsion. Next, we present data from human 3D scribbling movements, and compare the obtained speed-shape relation to that predicted by the 3D power law. Our results indicate that the introduction of the torsion term into the 3D power law accounts for significantly more of the variance in speed-shape relations of the movement data and that the obtained exponents are very close to the predicted values