335 research outputs found
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
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
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
A Framework for Decision-based Consistencies
International audienceConsistencies are properties of constraint networks that can be enforced by appropriate algorithms to reduce the size of the search space to be explored. Recently, many consistencies built upon taking decisions (most often, variable assignments) and stronger than (general- ized) arc consistency have been introduced. In this paper, our ambition is to present a clear picture of decision-based consistencies. We identify four general classes (or levels) of decision-based consistencies, denoted by S∆φ, E∆φ, B∆φ and D∆φ, study their relationships, and show that known consistencies are particular cases of these classes. Interestingly, this gen- eral framework provides us with a better insight into decision-based con- sistencies, and allows us to derive many new consistencies that can be directly integrated and compared with other ones
On The Complexity and Completeness of Static Constraints for Breaking Row and Column Symmetry
We consider a common type of symmetry where we have a matrix of decision
variables with interchangeable rows and columns. A simple and efficient method
to deal with such row and column symmetry is to post symmetry breaking
constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and
negative results on posting such symmetry breaking constraints. On the positive
side, we prove that we can compute in polynomial time a unique representative
of an equivalence class in a matrix model with row and column symmetry if the
number of rows (or of columns) is bounded and in a number of other special
cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are
often effective in practice, they can leave a large number of symmetric
solutions in the worst case. In addition, we prove that propagating DOUBLELEX
completely is NP-hard. Finally we consider how to break row, column and value
symmetry, correcting a result in the literature about the safeness of combining
different symmetry breaking constraints. We end with the first experimental
study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark
problems.Comment: To appear in the Proceedings of the 16th International Conference on
Principles and Practice of Constraint Programming (CP 2010
Domain k-Wise Consistency Made as Simple as Generalized Arc Consistency
Abstract. In Constraint Programming (CP), Generalized Arc Consistency (GAC) is the central property used for making inferences when solving Constraint Satisfaction Problems (CSPs). Developing simple and practical filtering algorithms based on consistencies stronger than GAC is a challenge for the CP community. In this paper, we propose to combine k-Wise Consistency (kWC) with GAC, where kWC states that every tuple in a constraint can be extended to every set of k − 1 additional constraints. Our contribution is as follows. First, we derive a domain-filtering consistency, called Domain k-Wise Consistency (DkWC), from the combination of kWC and GAC. Roughly speaking, this property corresponds to the pruning of values of GAC, when enforced on a CSP previously made kWC. Second, we propose a procedure to enforce DkWC, relying on an encoding of kWC to generate a modified CSP called k-interleaved CSP. Formally, we prove that enforcing GAC on the k-interleaved CSP corresponds to enforcing DkWC on the initial CSP. Consequently, we show that the strong DkWC can be enforced very easily in constraint solvers since the k-interleaved CSP is rather immediate to generate and only existing GAC propagators are required: in a nutshell, DkWC is made as simple and practical as GAC. Our experimental results show the benefits of our approach on a variety of benchmarks.
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