Probabilistic Methodology and Techniques for Artefact Conception and Development

The purpose of this paper is to make a state of the art on probabilistic methodology and techniques for artefact conception and development. It is the 8th deliverable of the BIBA (Bayesian Inspired Brain and Artefacts) project. We first present the incompletness problem as the central difficulty that both living creatures and artefacts have to face: how can they perceive, infer, decide and act efficiently with incomplete and uncertain knowledge?. We then introduce a generic probabilistic formalism called Bayesian Programming. This formalism is then used to review the main probabilistic methodology and techniques. This review is organized in 3 parts: first the probabilistic models from Bayesian networks to Kalman filters and from sensor fusion to CAD systems, second the inference techniques and finally the learning and model acquisition and comparison methodologies. We conclude with the perspectives of the BIBA project as they rise from this state of the art

Approximate Discrete Probability Distribution Representation using a Multi-ResolutionBinary Tree

Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiples random variables. The problem of efficient representation of probability distributions is central in term of computational efficiency in the field of probabilistic reasoning. The main problem arises when dealing with joint probability distributions over a set of random variables: they are always represented using huge probability arrays. In this paper, a new method based on a binary-tree representation is introduced in order to store efficiently very large joint distributions. Our approach approximates any multidimensional joint distributions using an adaptive discretization of the space. We make the assumption that the lower is the probability mass of a particular region of feature space, the larger is the discretization step. This assumption leads to a very optimized representation in term of time and memory. The other advantages of our approach are the ability to refine dynamically the distribution every time it is needed leading to a more accurate representation of the probability distribution and to an anytime representation of the distribution

Expressing Bayesian Fusion as a Product of Distributions: Application in Robotics

More and more fields of applied computer science involve fusion of multiple data sources, such as sensor readings or model decision. However incompleteness of the models prevent the programmer from having an absolute precision over their variables. Therefore bayesian framework can be adequate for such a process as it allows handling of uncertainty.We will be interested in the ability to express any fusion process as a product, for it can lead to reduction of complexity in time and space. We study in this paper various fusion schemes and propose to add a consistency variable to justify the use of a product to compute distribution over the fused variable. We will then show application of this new fusion process to localization of a mobile robot and obstacle avoidance

Expressing Bayesian Fusion as a Product of Distributions: Application to Randomized Hough Transform

Data fusion is a common issue of mobile robotics, computer assisted medical diagnosis or behavioral control of simulated character for instance. However data sources are often noisy, opinion for experts are not known with absolute precision, and motor commands do not act in the same exact manner on the environment. In these cases, classic logic fails to manage efficiently the fusion process. Confronting different knowledge in an uncertain environment can therefore be adequately formalized in the bayesian framework. Besides, bayesian fusion can be expensive in terms of memory usage and processing time. This paper precisely aims at expressing any bayesian fusion process as a product of probability distributions in order to reduce its complexity. We first study both direct and inverse fusion schemes. We show that contrary to direct models, inverse local models need a specific prior in order to allow the fusion to be computed as a product. We therefore propose to add a consistency variable to each local model and we show that these additional variables allow the use of a product of the local distributions in order to compute the global probability distribution over the fused variable. Finally, we take the example of the Randomized Hough Transform. We rewrite it in the bayesian framework, considering that it is a fusion process to extract lines from couples of dots in a picture. As expected, we can find back the expression of the Randomized Hough Transform from the literature with the appropriate assumptions

The Ariadne's Clew Algorithm

We present a new approach to path planning, called the "Ariadne's clew algorithm". It is designed to find paths in high-dimensional continuous spaces and applies to robots with many degrees of freedom in static, as well as dynamic environments - ones where obstacles may move. The Ariadne's clew algorithm comprises two sub-algorithms, called Search and Explore, applied in an interleaved manner. Explore builds a representation of the accessible space while Search looks for the target. Both are posed as optimization problems. We describe a real implementation of the algorithm to plan paths for a six degrees of freedom arm in a dynamic environment where another six degrees of freedom arm is used as a moving obstacle. Experimental results show that a path is found in about one second without any pre-processing

Simulating Vocal Imitation in Infants, using a Growth Articulatory Model and Speech Robotics

In order to shed lights on the cognitive representations likely to underlie early vocal imitation, we tried to simulate Kuhl and Meltzoff's experiment (1996), using Bayesian robotics and a statistical model of the vocal tract that had been fitted to pre-babblers' actual vocalizations. It was shown that audition is compulsory to account for infants' early vocal imitation performance, inasmuch as the simulation of purely visual imitation failed to reproduce infants' score and pattern of imitation. Further, a small number of vocalizations (less than 100!) appeared to be enough for a learning process to provide scores at least as high as those of pre-babblers. Thus, early vocal imitation lies in the reach of a baby robot, with only a few assumptions about learning and imitation

Using Bayesian Programming for Multisensor Multi-Target Tracking in Automative Applications

A prerequisite to the design of future Advanced Driver Assistance Systems for cars is a sensing system providing all the information required for high-level driving assistance tasks. Carsense is a European project whose purpose is to develop such a new sensing system. It will combine different sensors (laser, radar and video) and will rely on the fusion of the information coming from these sensors in order to achieve better accuracy, robustness and an increase of the information content. This paper demonstrates the interest of using probabilistic reasoning techniques to address this challenging multi-sensor data fusion problem. The approach used is called Bayesian Programming. It is a general approach based on an implementation of the Bayesian theory. It was introduced rst to design robot control programs but its scope of application is much broader and it can be used whenever one has to deal with problems involving uncertain or incomplete knowledge

Obstacle Avoidance and Proscriptive Bayesian Programming

Unexpected events and not modeled properties of the robot environment are some of the challenges presented by situated robotics research field. Collision avoidance is a basic security requirement and this paper proposes a probabilistic approach called Bayesian Programming, which aims to deal with the uncertainty, imprecision and incompleteness of the information handled to solve the obstacle avoidance problem. Some examples illustrate the process of embodying the programmer preliminary knowledge into a Bayesian program and experimental results of these examples implementation in an electrical vehicle are described and commented. A video illustration of the developed experiments can be found at http://www.inrialpes.fr/sharp/pub/laplac

Proscriptive Bayesian Programming Application for Collision Avoidance

Evolve safely in an unchanged environment and possibly following an optimal trajectory is one big challenge presented by situated robotics research field. Collision avoidance is a basic security requirement and this paper proposes a solution based on a probabilistic approach called Bayesian Programming. This approach aims to deal with the uncertainty, imprecision and incompleteness of the information handled. Some examples illustrate the process of embodying the programmer preliminary knowledge into a Bayesian program and experimental results of these examples implementation in an electrical vehicle are described and commented. Some videos illustrating these experiments can be found at http://www-laplace.imag.fr

The Design and Implementation of a Bayesian CAD Modeler for Robotic Applications

We present a Bayesian CAD modeler for robotic applications. We address the problem of taking into account the propagation of geometric uncertainties when solving inverse geometric problems. The proposed method may be seen as a generalization of constraint-based approaches in which we explicitly model geometric uncertainties. Using our methodology, a geometric constraint is expressed as a probability distribution on the system parameters and the sensor measurements, instead of a simple equality or inequality. To solve geometric problems in this framework, we propose an original resolution method able to adapt to problem complexity. Using two examples, we show how to apply our approach by providing simulation results using our modeler