Classical Many-particle Clusters in Two Dimensions

We report on a study of a classical, finite system of confined particles in two dimensions with a two-body repulsive interaction. We first develop a simple analytical method to obtain equilibrium configurations and energies for few particles. When the confinement is harmonic, we prove that the first transition from a single shell occurs when the number of particles changes from five to six. The shell structure in the case of an arbitrary number of particles is shown to be independent of the strength of the interaction but dependent only on its functional form. It is also independent of the magnetic field strength when included. We further study the effect of the functional form of the confinement potential on the shell structure. Finally we report some interesting results when a three-body interaction is included, albeit in a particular model.Comment: Minor corrections, a few references added. To appear in J. Phys: Condensed Matte

Deforming the Maxwell-Sim Algebra

The Maxwell alegbra is a non-central extension of the Poincar\'e algebra, in which the momentum generators no longer commute, but satisfy $[P_\mu,P_\nu]=Z_{\mu\nu}$. The charges $Z_{\mu\nu}$ commute with the momenta, and transform tensorially under the action of the angular momentum generators. If one constructs an action for a massive particle, invariant under these symmetries, one finds that it satisfies the equations of motion of a charged particle interacting with a constant electromagnetic field via the Lorentz force. In this paper, we explore the analogous constructions where one starts instead with the ISim subalgebra of Poincar\'e, this being the symmetry algebra of Very Special Relativity. It admits an analogous non-central extension, and we find that a particle action invariant under this Maxwell-Sim algebra again describes a particle subject to the ordinary Lorentz force. One can also deform the ISim algebra to DISim$_b$, where $b$ is a non-trivial dimensionless parameter. We find that the motion described by an action invariant under the corresponding Maxwell-DISim algebra is that of a particle interacting via a Finslerian modification of the Lorentz force.Comment: Appendix on Lifshitz and Schrodinger algebras adde

Newton-Hooke spacetimes, Hpp-waves and the cosmological constant

We show explicitly how the Newton-Hooke groups act as symmetries of the equations of motion of non-relativistic cosmological models with a cosmological constant. We give the action on the associated non-relativistic spacetimes and show how these may be obtained from a null reduction of 5-dimensional homogeneous pp-wave Lorentzian spacetimes. This allows us to realize the Newton-Hooke groups and their Bargmann type central extensions as subgroups of the isometry groups of the pp-wave spacetimes. The extended Schrodinger type conformal group is identified and its action on the equations of motion given. The non-relativistic conformal symmetries also have applications to time-dependent harmonic oscillators. Finally we comment on a possible application to Gao's generalization of the matrix model.Comment: 21 page

A framework integrating statistical and social cues to teach a humanoid robot new skills

Bringing robots as collaborative partners into homes presents various challenges to human-robot interaction. Robots will need to interact with untrained users in environments that are originally designed for humans. Compared to their industrial homologous form, humanoid robots can not be preprogrammed with an initial set of behaviours. They should adapt their skills to a huge range of possible tasks without needing to change the environments and tools to fit their needs. The rise of these humanoids implies an inherent social dimension to this technology, where the end-users should be able to teach new skills to these robots in an intuitive manner, relying only on their experience in teaching new skills to other human partners. Our research aims at designing a generic Robot Programming by Demonstration (RPD) framework based on a probabilistic representation of the task constraints, which allows to integrate information from cross-situational statistics and from various social cues such as joint attention or vocal intonation. This paper presents our ongoing research towards bringing user- friendly human-robot teaching systems that would speed up the skill transfer process

Learning of Gestures by Imitation in a Humanoid Robot

In this chapter, we explore the issue of encoding, recognizing, generalizing and reproducing arbitrary gestures. We address one major and generic issue, namely how to discover the essence of a gesture, i.e. how to find a representation of the data that encapsulates only the key aspects of the gesture, and discards the intrinsic variability across people motions. The model is tested and validated in a humanoid robot, using kinematics data of human motion. In order for the robot to learn new skills by imitation, it must be endowed with the ability to generalize over multiple demonstrations. To achieve this, the robot must encode multivariate time-dependent data in an efficient way. Principal Component Analysis and Hidden Markov Models are used to reduce the dimensionality of the dataset and to extract the primitives of the motion. The model takes inspiration in a recent trend of research that aims at defining a formal mathematical framework for imitation learning. In particular, it stresses the fact that the observed elements of a demonstration, and the organization of these elements should be stochastically described to have a robust robotic application. It bears similarities with theoretical models of animal imitation, and offers at the same time a probabilistic description of the data, more suitable for a real-world application

What is the Teacher's Role in Robot Programming by Demonstration? - Toward Benchmarks for Improved Learning

Robot programming by demonstration (RPD) covers methods by which a robot learns new skills through human guidance. We present an interactive, multimodal RPD framework using active teaching methods that places the human teacher in the robot's learning loop. Two experiments are presented in which observational learning is first used to demonstrate a manipulation skill to a HOAP-3 humanoid robot by using motion sensors attached to the teacher's body. Then, putting the robot through the motion, the teacher incrementally refines the robot's skill by moving its arms manually, providing the appropriate scaffolds to reproduce the action. An incremental teaching scenario is proposed based on insights from various fields addressing developmental, psychological, and social issues related to teaching mechanisms in humans. Based on this analysis, different benchmarks are suggested to evaluate the setup further

Stochastic Gesture Production and Recognition Model for a Humanoid Robot

Robot Programming by Demonstration (PbD) aims at developing adaptive and robust controllers to enable the robot to learn new skills by observing and imitating a human demonstration. While the vast majority of PbD works focused on systems that learn a specific subset of tasks, our work explores the problem of recognition, generalization, and reproduction of tasks in a unified mathematical framework. The approach makes abstraction of the task and dataset at hand to tackle the general issue of learning which of the features are the relevant ones to imitate. In this paper, we present an implementation of this framework to the determination of the optimal strategy to reproduce arbitrary gestures. The model is tested and validated on a humanoid robot, using recordings of the kinematics of the demonstrator's arm motion. The hand path and joint angle trajectories are encoded in Hidden Markov Models. The system uses the optimal prediction of the models to generate the reproduction of the motion

PDA Interface for Humanoid Robots

To fulfill a need for natural, user-friendly means of interacting and reprogramming toy and humanoid robots, a growing trend of robotics research investigates the integration of methods for gesture recognition and natural speech processing. Unfortunately, efficient methods for speech and vision processing remain computationally expensive and, thus, cannot be easily exploited on cost- and size-limited platforms. Personal Digital Assistants (PDAs) are ideal low-cost platforms to provide simple speech and vision-based communication for a robot. This paper investigates the use of Personal Digital Assistant (PDA) interfaces to provide multi-modal means of interacting with humanoid robots. We present PDA applications in which the robot can track and imitate the user's arm and head motions, and can learn a simple vocabulary to label objects and actions by associating the user's verbal utterance with the user's gestures. The PDA applications are tested on two humanoid platforms: a mini doll-shaped robot, Robota, used as an educational toy with children, and DB, a full body 30 degrees of freedom humanoid robot

A Humanoid Robot Drawing Human Portraits

This paper presents the creation of a robot capable of drawing artistic portraits. The application is purely entertaining and based on existing tools for face detection and image reconstruction, as well as classical tools for trajectory planning of a 4 DOFs robot arm. The innovation of the application lies in the care we took to make the whole process as human-like as possible. The robot's motions and its drawings follow a style characteristic to humans. The portraits conserve the esthetics features of the original images. The whole process is interactive, using speech recognition and speech synthesis to conduct the scenario