Section: New Results
Bayesian Modelling of Sensorimotor Systems and Behaviors
Task Learning for SensoriMotor Based Wheelchair Navigation
The goal of this project is to have a robotic wheelchair being able to autonomously navigate in an indoor dynamic environment. The robot learns to navigate by observing the instructor trying to reproduce and generalize the given task. To reach this goal, many points have to be settled: how the user and the robot communicate, what is a simple behavior, how complex behaviors can be created combining simple ones, how associate a behavior to a task.
In 2007, a list of behaviors to be learnt have been identified, and clustered in three groups: reflex (collision, wandering...), reactive (obstacle avoidance, wall following...) and cognitive (human tracking, path following ...) behaviors. Some of these behaviors have been implemented using Fuzzy Neural Networks.
In 2008, Growing Hidden Markov Models (GHMM) have been used to generate sequences of behaviors  . Each node in the GHMM represents a behavior, and the behaviors are linked between them in a temporal order. For a behavior to occur, the robot must have executed the precedent behaviors already. Each behavior can be linked to one or more behaviors, and each link has a probability to be used, the probability will depend of the past behaviors the robot executed. These probabilities are calculated during learning, observing which behavior the instructor is using the more often.
Experiments have been initiated for a very simple environment (a corridor going to a rectangular room). The robot starts in the corridor, and then the user drives the robot through the corridor, then crosses the room by following the wall on its right side. The goal of this experiment is to choose, from a set of 4 hardcoded behaviors (fuzzy systems incoding: corridor following, left wall following, right wall following, goal reaching), two different behaviors needed to solve the task: corridor following and right wall following. The interaction is done via a poor interface. A map of the environment is presented to the user, who can then click directly on the map to control the robot. A module with an obstacle avoidance system controls the robot for reaching the goal. Once the instructor has shown the task to be accomplished, the system must be able to analyze these instructions. The first step is to decouple this complex task into a sequential list of more basic behaviors. Once the task has been segmented, we have to recognize the behaviors used during the task. The behaviors are encoded in a fuzzy system and new behaviors are learned by the GenSoYager-FNN, a fuzzy neural network developed at the Center for Computational Intelligence (C2I, http://www.c2i.ntu.edu.sg ). We are actually developing the behavior recognition algorithm.
This work is implied in the BACS project.
Brain Controlled Wheelchair
This work has been done at the NTU of Singapore and in cooperation with the NUS Singapore. It is also implied in the BACS project. A brain-computer interface (BCI) is a system that allows direct control of a computer by thought. BCIs have the potential to help people with various disabilities, e.g. individuals suffering from amyotrophic lateral scleroses (ALS), severe cerebral palsy, head trauma, multiple sclerosis, and muscular dystrophies, to communicate or perform ordinary tasks. BCI applications range from typing words, moving a cursor over the screen, gaming, or controlling a TV.
Robotic applications are a different story: controlling a robotic device, such as a wheelchair or a prosthesis, requires continuous and accurate commands. However, due to the poor and noisy signal, information from BCIs can typically be extracted only at a very slow pace (up to several seconds), or with a very high uncertainty. A solution to this conflicting situation is to endow the system with enough autonomy to avoid dangerous situations.
Hence, in  , an EEG BCI based on recognition of three mental states (providing frequent signals but with a relatively low confidence) interacts continuously with automatic behaviors of an autonomous robotic wheelchair to successfully maneuver in the environment. However, this approach requires the user to be constantly alert, which is likely to cause stress.
Our solution  relies on motion guidance and destination selection: virtual guiding paths connect locations of interest in the environment (see figure 22 ). These paths can be traced automatically if an accurate map of the environment is available, or manually by simply pushing the wheelchair once along the desired trajectory. Once a network of guiding paths is available, navigating in the environment simply consists in selecting the desired destination.
For destination selection we use a BCI based on the P300 signal. The user focuses his or her attention on an item within a list of 20 or more while the items are presented in random order (see figure 21 ). A peak of potential appears in the EEG about 300ms after the item of interest was presented (see figure 20 ). Upon detection of the P300 signal, the target is traced back as the item that was presented 300ms earlier. For greater accuracy and reliability the process can be repeated several times. Typically, this kind of interface can achieve a response time in between 10 to 20 seconds with an accuracy close to 100%.
This strategy has the important benefit of requiring minimal input from the subject, therefore minimizing concentration effort, thus fatigue. Moreover, since the trajectories are repeated over time, the predictability of the motion adds confidence in the machine. Lastly, because no complex sensor is required to perceive and interpret the environment, the price of the robotic system is very low, thus allowing a larger number of disabled to afford it.
Two faster BCIs were developped for issuing stop commands within a few seconds. The first one is a modified version of the P300 selection interface: only one out the nine buttons is active (the stop button). With this configuration the false acceptance rate is greatly reduced, thus allowing to reduce the P300 detection threshold, thereby reducing the response time  . The second stop interface relies on a different brain signal: by imagining left or right limb movements, subjects can modify synchronization of the and rhythms in the pre-motor cortex. This type of interface is typically used for 1D or 2D control of a cursor on screen. In our configuration, a stop command is issued when the amount of desynchronization goes beyond a certain threshold. Visual feedback can be provided in the form of a cursor moving left or right proportionally to the amount of desynchronization.
Both interfaces yield a similar response time (approximately 5 seconds) but they have their pros and cons: the P300 stop interface is easy to use but suffers from a relatively high false positive rate (1.3 per 100 seconds); the interface does not suffer from any false positive, however it is relatively difficult to use and may require a long training. It therefore left to the user to decide which interface is more suitable according to his ability.
The slow but accurate P300 selection interface is combined with one of the two interfaces for stopping to form an hybrid BCI. Switching between modalities is controlled by a simple state machine as illustrated on figure 23 .
Bayesian Modelling of Sensorimotor Systems: Application to Handwriting
The goal of the PhD of Estelle Gilet, is to define a Bayesian model of the whole sensorimotor loop involved in handwriting, from visual sensors to the control of the effector  . We aim to implement a simulation of handwriting based on three points: the perception, the representation and the production of letters.
In 2007, we studied the state-of-the-art of the modeling of sensorimotor systems, focusing more precisely on handwriting movements. We focused on the state-of-the-art of the perception of hand trajectory and we examined studies of the kinematic and dynamic aspects of human arm movements.
In 2008, we focused on how the central nervous system represents the sensorimotor plans associated with writing movements. In the motor theories of perception, the perception and the production share the same set of invariants and they must be linked. The model is structured around an abstract internal representation of letters, which acts as a pivot between motor models and sensors models. We assume that a letter is internally represented by a sequence of viapoints, that are part of the whole X, Y trajectory of the letter. We restrict via-points to places in the trajectory where either the X derivative or the Y derivative, or both, are zero. The representation of letters is independent of the effector usually used to perform the movement.
The sensor model (vision) concerns the extraction of via-points from trajectories, using their geometric properties. The motor model concerns general trajectory formation. It is expressed in a cartesian reference frame. An acceleration profile is chosen, that constrains the interpolation. In our case, we used a bang-bang profile, where the arm first applies a maximum force, followed by a maximum negative force. The effector model is made of two parts, related to the geometry of the considered effector (kinematic model) and the control of this effector for general movement production (dynamic model).
Thanks to Bayesian inference, the joint probabilistic distribution can be used to automatically solve cognitive tasks. We define a cognitive task by a probabilistic term to be computed, which we call a question. Our model allows to solve a variety of tasks, like letter reading, recognizing the writer, and letter writing (with different effectors).
This work is done under the joint supervision of Pierre Bessière and Julien Diard of the LPNC laboratory (Laboratoire de Psychologie et NeuroCognition, CNRS, Grenoble). Is is implied in the BACS european project.
Models and Tools for Bayesian Inference
This work has been done in collaboration with our Start-up Probayes. ProBT is a C++ library for developing efficient Bayesian software   . This library has two main components: (i) a friendly Application Program Interface (API) for building Bayesian models and (ii) a high-performance Bayesian inference and learning engine allowing execution of the probability calculus in exact or approximate ways.
The aim of ProBT is to provide a programming tool that facilitates the creation of Bayesian models and their reusability ( http://www.probayes.com/spip.php?rubrique57 ). Its main idea is to use “probability expressions” as basic bricks to build more complex probabilistic models. The numerical evaluation of these expressions is accomplished just-in-time: computation is done when numerical representations of the corresponding target distributions are required. This property allows designing advanced features such as submodel reuse and distributed inference. Therefore, constructing symbolic representations of expressions is a central issue in ProBT.
Since a few years the main development of ProBT has been carried out by Probayes: a spin-off born from the e-motion project. Both, e-motion and Probayes, are part of the European project Bayesian Approach to Cognitive Systems (BACS). The development of ProBT has been effectuated taking into account the goals of the BACS project partners.
Bayesian modelling of the superior colliculus
Among the various possible criteria guiding eye movement selection, we investigate the role of position uncertainty in the peripheral visual eld. In particular, we suggest that, in everyday life situations of object tracking, eye movement selection probably includes a principle of reduction of uncertainty.
To do so, we confront the movement predictions of computational models with human results from a psychophysical task. This task is a freely moving eye version of the Multiple Object Tracking task with the eye movements possibly compensating for lower peripheral resolution.
We design several Bayesian models of increasing complexity, whose layered structures are inspired by the neurobiology of the brain areas implied in eye movement selection.
Finally, we compare the relative performances of these models with regard to the prediction of the recorded human movements, and show the advantage of taking explicitly into account uncertainty for the prediction of eye movements.
This work as been done in collaboration with LPPA-Collège de France and with the Max Planck Institute in Tuebingen. A common publication in Biological Cybernetics (in press) describes this work in details  .
Biochemical Probabilistic Inference
Participant : Pierre Bessière.
Biochemical Probabilistic Inference is a new area of research which started in 2008 in close collaboration with LPPA-College de France and ProBAYES.
Living organisms need to quickly react without waiting for a perfect evaluation of the consequences of their action. For instance, we perceive objects from retinal stimulation without the need for a complete knowledge of the underlying light-matter interactions. To account for this ability to reason with incomplete knowledge, it has been recently proposed that the brain works as a probabilistic machine, evaluating probability distribution over cognitively relevant variables. A number of Bayesian models have been shown to efficiently account for perceptive and behavioural tasks. However, little is known about the way subjective probabilities are represented and processed in the brain.
Numerous biochemical cellular signalling pathways have now been unravelled. These mechanisms involve the strong coupling of macromolecular assemblies, membrane voltage and diffusible messengers, including intracellular Ca2+ and other chemical substrates like cyclic nucleotides. Since transition between allosteric states and messenger diffusion are mainly powered by thermal agitation, descriptive models at the molecular level are also based on probabilistic relationships between biophysical and biochemical state variables.
Our proposal is based on the existence of a deep structural similarity between the probabilistic computation required at the macroscopic level to account for cognitive, perceptive and sensory motor abilities and the biochemical interactions of macromolecular assemblies and messengers involved in cellular signalling mechanisms.
Our working hypothesis is then that biochemical processes constitute the nanoscale components of cognitive Bayesian inferences.
To prove this hypothesis, we plan to develop: 1. A comprehensive and coherent formalism to handle both macroscopic and microscopic levels of description, 2. A software package to emulate complex biochemical interactions and to demonstrate the plausibility of our working hypothesis.
Finally, we wish to explore, through the search for new partners for future projects, the possibility to design artificial systems mimicking the biochemical interactions and working on similar principles and nanoscale space-time grain. In the future, this could open the way to the development of revolutionary probabilistic machines. An ADR proposal has been submitted on this topic.