Directed Evidential Networks with Conditional Belief Functions

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Evidential Network with Conditional Belief Functions for an Adaptive Training in Informed Virtual Environment Lo¨c Fricoteaux, Indira Thouvenin, J´ rˆ me Olive and Paul George ı eo

Abstract Simulators have been used for many years to learn driving, piloting, steering, etc. but they often provide the same training for each learner, no matter his/her performance. In this paper, we present the GULLIVER system, which determines the most appropriate aids to display for learner guiding in a fluvial-navigation training simulator. GULLIVER is a decision-making system based on an evidential network with conditional belief functions. This evidential network allows graphically representing inference rules on uncertain data coming from learner observation. Several sensors and a predictive model are used to collect these data about learner performance. Then the evidential network is used to infer in real time the best guiding to display to learner in informed virtual environment.

1 Introduction
Virtual reality can provide, in comparison with classical training, many advantages [1]. In the case of fluvial navigation, training in virtual environment allows to simply modify environmental conditions (wind, current, etc.), which has an impact on the behavior of the ship. Another advantage of training in virtual reality is the strong coupling between the user and the virtual environment. The virtual world must credibly answers to user’s actions. We use an informed virtual environment (IVE: environment including knowledge-based models and providing an action/perception coupling) for fluvial navigation training. The purpose of our work is to provide the best learner guiding (set of aids) in real time based on learner observation. We propose an adaptive system: the learner’s behavior is taken into account for the choice of the aids to display [3]. On the opposite side, non-adaptive systems [4] are easier to build but the aids will not be adapted to the learner’s performance. For example, novice learners will not have enough help and experienced ones will have Lo¨c Fricoteaux, Indira Thouvenin, J´ rˆ me Olive and Paul George ı eo Heudiasyc Laboratory UMR CNRS 6599, Compi` gne, France, e-mail: firstname.lastname@utc.fr e

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Lo¨c Fricoteaux, Indira Thouvenin, J´ rˆ me Olive and Paul George ı eo

too much help. As fluvial navigation is a complex task, there is no complete procedure to follow to know how to navigate (there is only a navigation code). With a procedural approach, errors can be easily detected by comparing learner’s actions with good actions to perform [3]. With a non-procedural approach [6], the system is more complex to build but is adapted to the training of complex tasks. Thus, our system is based on this approach. Errors are mainly detected according to a predictive model (the future position of the ship), therefore this detection is uncertain and this has to be taken into account by the decision-making module in the choice of the best guiding. We also use physiological sensors to detect learner’s state (for example the stress level with a heart rate variability sensor), which gives uncertain data about the user’s state due to sensor reliability and uncertainty of data interpretation. All data coming from learner observation has to be expressed in a common formal framework to allow making decision. We use the Dempster-Shafer (DS) theory [9] to take the uncertainty of these data into account. Comparing to the theory of probability, the DS theory allows modeling ignorance explicitly, which is useful in our case since we can have incomplete data about learner’s actual situation. To represent influences between variables (i.e. variables about learner’s errors and possible feedbacks to avoid these errors) and to reason on these variables, directed graphs are widely used. In the case of probabilistic inference, Bayesian networks (BN) are used [7]. With belief functions, the equivalent network is called an Evidential Network...
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