International Conference, April 9th-10th 2013 - Toulon, France

Supported by PACA region, University Sud Toulon Var, Fed. Francaise de Robotique, INRIA, CNRS, Institut Universitaire de France, CART IUT USTV.

**In this conference we aim to evaluate the importance of the Maximum Principle for control theory and optimal control, with a presentation by the founder : the Russian academician Revaz Gamkrelidze, co-author with Lev Pontryagin of the **
**Maximum Principle****.**

**Three families of bio-inspired systems are presented, base on this optimality principle**

**a) the motor control and the Parkinson's disease; in particular for its neural-robotic modeling, by the Pr. Juan Lopez Coronado from University of Cartagena, Spain.
b) modeling of movement disorders (like Parkinson) by machine learning of electro-physiologic recordings, and the Maximum Principle for a better identification of these disorders, by the Dr. Xanadu Halkias, CEO of In Actu Comapny, USA.**

There are many applications in robotics: for example autonomous robotics, robotics in hostile environments (e.g. marine), or for human-computer interaction, ergonomics, as well as intelligent software assistants, in particular for people with movement disorders (like Parkinson).

**Tuesday, April 9th**

12h, Welcome & Lunch

**SESSION 1 - 13h30**

**Introduction session**

**"The Pontryagin's Maximum Principle as a basic tool for Bio-inspired problems in Control and Vision" **

J.-P. Gauthier, Pr at Univ. Sud Toulon-Var-IUF, INRIA, CNRS LSIS

I shall present 3 examples of bio-inspired problems that are tackled by optimal control methods, and in particular by the Pontryagin's maximum principle. The first problem is the problem of motions of the arms, that was the subject of my talk at the (commemorative) centennial anniversary of Lev Pontryagin. In this study, we discovered a biomechanical principle (called the inactivation principle), that allowed to explain the presence of total silence periods in the motion of human arms. The second subject is also an inverse optimal control problem. It is the problem of reconstructing the cost minimized by good plane pilots, for the purpose of giving autonomy to HALE Drones. We have here a general abstract result for a certain class of (inverse) optimal control problems. The third subject is the problem of Validating the theory of Jean Petitot relative to the geometry of vision. In this problem, very special optimal control problems appear, that are in fact problems of Subriemannian geometry. Besides the optimal control questions, there is here the natural presence of certain Hypoelliptic diffusion operators, that can be considered as the equivalent of the heat equation in Riemannian geometry. We present some very recent results of (human-like) image reconstruction, using these operators.

**SESSION 2 - 14h30**

**Motor Planning**

**"Why do humans move the way they do ? Direct and inverse optimal control" **

B. Berret, Ass. Pr. at Univ. Paris Sud

We address the question of motor planning in humans. Assuming that human movements are optimal, the problem is to identify the underlying cost function. Identifying this cost is important as it may unveil the variables possibly represented by the brain during the planning of actions, but also for all the applications in which generating human-like motion is desired: humanoid robotics, neural prosthetics, motor rehabilitation or character animation. Historically, motor control researchers tackled this issue by using direct optimal control approaches: a cost function is designed a priori and then confronted to some experimental data. More recently, inverse optimal control approaches have been considered to objectively infer the cost function (or some of its properties) right from experimental observations. I will first present results about the control of single-joint arm movements. Using Pontryagin's maximum principle and a non-smooth yet physically-sensed cost function (thus a direct approach), we derived an inactivation principle, a singular prediction that we verified experimentally. Actually, the process can be reversed (leading to an inverse approach) by showing that if some optimal trajectories contain such inactivation then the cost function cannot be smooth (with respect to the control variable). Therefore, the cost accounting for human arm movements must include a term similar to the absolute work of torques, i.e. a measure of the mechanical energy expenditure. Second, with the aim of identifying all the components of a possibly composite cost function, I will present a new experimental paradigm involving target redundancy developed to favor the discrimination between cost functions. Based on a family of candidate costs already proposed in the literature, we used state-of-art numerical methods to find out which linear combination accounted the best for the observed arm trajectories. Results show that the observed arm trajectories are best compatible with the goal of moving with both minimal mechanical energy expenditure and maximal joint smoothness.

**SESSION 3, POSTER SESSION - 16h**

**"On the inverse optimal control problems of the human locomotion: stability and robustness of the minimizers"**

F. C. Chittaro, Ass. Pr. at Univ Sud Toulon-Var

In recent papers models of the human locomotion by means of an optimal control problem have been proposed. In this paradigm, the trajectories are assumed to be solutions of an optimal control problem whose cost has to be determined. In the approach initiated and developed in [Laumond 2010], goal-oriented human locomotion is understood as the motion in the 3-D space of both its position (x,y) and its orientation r of a person walking from an initial point (x_0,y_0,r) to a final point (x_1,y_1,r_1). The locomotor trajectories are assumed to be the solutions of an optimal control problem, for the cost functions L. The class L of admissible optimal costs can then be divided into two sub-classes L1 and L2 that depend on whether the highest derivative of the angle r explicitly appearing in the cost is the first or the second one. We prove strong convergence result for the solutions of the optimal control problem on the one hand for perturbations of the initial and final points (stability), and on the other hand for perturbations of the cost (robustness). We also develop a test, to be carried out on the experimental data, to determine to which of the two classes L1 and L2 the cost does belong.

**"How humans fly"**

T. Maillot and,
A. Ajami Phd at USTV

The general problem considered is the reconstruction the cost from the observation of trajectories, in a problem of optimal control. It is motivated by the following applied problem, concerning HALE drones: one would like them to decide by themselves for their trajectories, and to behave at least as a good human pilot. This applied question is very similar to the problem of determining what is minimized in human locomotion. These starting points are the reasons for the particular classes of control systems and of costs under consideration. To summarize, our conclusion is that in general, inside these classes, three experiments visiting the same values of the control are needed to reconstruct the cost, and two experiments are in general not enough.

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20h -
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Diner Gala
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**Wednesday, April 10th**

**SESSION 4 - 9h**

**"History of the Maximum Principle"
R. Gamkrelidze, Pr. at the Russian Academy of Sciences **

**break**

__SESSION 5, Learning Neural Dynamics - 11h__

Discussant H. Glotin, Pr at IUF and USTV, CNR LSIS

**"A Model for Altered Neural Network Dynamics related to Prehension Movements in Parkinson Disease"
J. L. Coronado,
Pr. at Politecnica Cartagena ES
* Lunch Buffet at Neptune Palais **

**"Machine Learning Approach for Neuro-degenerative Diseases : Detection and Tremor Arrest in Movement Disorder"
X. Halkias, Dr. at USTV CNRS LSIS and Dir. of In Actu LLC, USA**

Xanadu Halkias received her Master's and PhD from the Electrical Engineering Department of Columbia University, NY and was part of the Laboratory for the Recognition and Organization of Speech and Audio (LabROSA). Her doctorate research focused on advanced signal processing and audio analysis combined with machine learning techniques as they apply to bioacoustics. She also obtained her breadth requirement in biomedical signal processing and computational neuroscience. She is currently a post-doctorate fellow and adjunct professor at the Université du Sud - Toulon working on advanced machine learning and specifically deep architectures and their applications. Xanadu is also the co-founder of In Actu, LLC. The company is based in the US, and houses the patent pending medical invention regarding arresting the tremors of patients who suffer from movement disorders such as Parkinson's disease, Huntington's disease and others. Her talk will focus on the use of machine learning approaches for controlling and alleviating the tremors in these types of neuro-degenerative diseases. The talk will be based on the patent pending invention (US Patent Application US 13/180,865,7/2011) regarding *Systems, Methods and Media for Finding and Matching Tremor Signals*. The concept of the application is based on the known principles of noise cancellation in advanced audio processing as applied to biomedical signals i.e. EMG signals. In addition to the algorithms used for the amplitude and temporal identification of the desired tremors, a machine learning approach is proposed to ensure customized delivery of the cancellation signal. Overall, a non-parametric approach may be suitable in capturing the evolution of the disease depending both in time and in the patient’s actions. Finally, a proposed device is presented with an electromechanical output that may arrest the tremors of patients with movement disorders.

__SESSION 6, General Discussion - 16h__

Discussant P. Gorce, Pr at USTV, Dir. Handibio

"Towards Optimal Control, Machine Learning for Neuro-Robotics"

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20h -
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Diner
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Registration Fees

180 euros, including the coffee breaks, the mid day lunch the 9th and
10th, and the proceedings.

Program committee

**Pr. Glotin, USTV and IUF,
Pr. Gauthier, USTV and IUF,
Pr. Gorce, USTV, dir. Handibio.
contact : glotin, gauthier, gorce @ univ-tln.fr **