Section: New Results
Modelling and controlling the human sensory-motor system
Modelling and Identification of the Skeletal Muscle under Functional Electrical Stimulation
The objectives of this study were both the modelling of skeletal muscles under FES and the identification of the associated parameters  .
There are two main goals for muscle modelling: 1) the simulation and the synthesis of the movement in order to evaluate a priori the system performance, and 2) the design of advanced control schemes based on reference model. The input of the muscle model is an electrical signal provided by electrical stimulator such as the "PROSTIM" offering the possibility of tuning the amplitude, the pulse width and the frequency of the electrical signal of stimulation, and the outputs are the muscle force and stiffness. The muscle model we developed is composed of three blocks (fig. 1 ):
Mechanical model: an original multi-scale model (from sarcomere up to the whole muscle) was developed and presented in the state space with a set of differential equations. This model integrates both macroscopic (muscle scale) and microscopic (fibre scale) dynamical behavior of the muscle. Two control inputs are involved: a "static" input associated to the rate of fibers recruitment and a "chemical" input for the dynamical activation model. Two models were developed depending on their final use. One includes muscle masses in order to be accurate enough in isometric contraction i.e. without any link movement; the other one is much simpler without masses and dampers to be used in a complex musculoskeletal model (fig. 2 ). In this case, dampers and masses are transferred respectively to the joint and the segments.
Recruitment model: It represents the transfer function between the stimulus parameters (intensity and pulse width) and the percentage of activated muscle fibres. This model is static with a sigmoid like transfer function.
Dynamic activation model: The calcium dynamics that appears between the neural signal action potential activation and the muscle fibers activation is modeled through a linear second order low pass filter followed by a threshold on off activation so that mainly the stimulus frequency (that triggers this dynamics) is involved.
The two last items may evolve because they are actually not based on micro-scale physiological phenomena.
The parameters of the muscle model were identified experimentally in isometric mode on animal with classical techniques of identification such as Levenberg-Marquardt and the Extended Kalman Filter. The cross validations illustrate the pertinence of the model and the quality of the estimate (fig. 3 ).
Closed loop control: Co-contraction case study
Few studies have treated the human muscle as an entire physiological element in a closed loop system. Known by their robustness against unknown perturbation and their accuracy, we used the sliding mode control. Because of the nonlinearity and the presence of a 2 relative degree order system, we have adopted , a 2-order sliding mode controller, which seems necessary to ensure robust control and safer movement of the lower extremities. This latter was applied to a new multi-scale model developed within the DEMAR project. We were able to control two antagonist muscles quadriceps and hamstrings alternatively and simultaneously (the so called co-contraction effect) with the same control vector, increasing the joint stiffness and forcing dynamically the system to behave as a first order one. Satisfactory stability and tracking error were achieved after a finite time delay. The performance of the closed loop system was assessed in the presence of an external force perturbations. The controller showed great accuracy and robustness against these perturbations.
The patient is supposed to be laying supine where only the shank is free to move around the knee joint (Fig. 4 ).
The main goal concerns the computation of the needed stimulation patterns in order to ensure a safe and stiff movement through co-contraction of antagonist muscles for a given desired task, and to defer the muscular fatigue as much as possible. Thus we will compensate most of the non linear effects of the muscle model taking into account the time dependent parameters. Muscles and knee joint models can be rewritten as a non-linear state space function:
Where X represents the state space vector of the forces and stiffness generated by the muscles as well as the knee joint angle and knee angular velocity and U represent the control vector input gathering the recruitment variables and the chemical control inputs of both muscles. The controller was mathematically computed and showed satisfactory stability and position-tracking performance (Fig. 5 )  .
Co-contraction can be defined as the simultaneous activation of the antagonist muscles crossing the same joint.
Since the number of actuator (muscles) is greater than the number of joints (knee), we have a redundancy problem. The force-sharing problem or the stimulation distribution between antagonist muscles was solved based on the optimization of the sum of muscular activities in the antagonist muscles  . Figure 6 shows the control schemes as well the resulted stimulation currents of the antagonist muscles.
Posture estimation and modelling
A new approach aiming posture estimation by only measuring forces exerted on a walker's handles is outlined. The behavior of the system is modeled by an ordinary differential equation (ODE) which includes parameters whose value is uncertain. Since insufficiency in precision while solving ODEs may affect safe decision making, the method proposed is based on the numerical integration of a kinematic and dynamic model of the human body, where force measurements are considered as inputs to the model. In order to guarantee reliability in computation for safe posture estimation, and prevent cases like falling, the numerical methodology to use must be fail-safe from numerical errors introduced by the integration schemes. It must also account for any uncertainties in either initial posture values or with the anthropometric parameters which act in the biomechanical model.
A validated integration method via interval analysis is under investigation. The evaluation of the approach on simulation runs from a three degrees of freedom planar manipulator model and gives promising results (fig. 7 )  .
Early detection of postural modifications and motion monitoring using micro attitude sensors
This work is based on a collaboration with CEA-LETI (Grenoble, France) and INRIA-Rhône-Alpes around R. Héliot PhD thesis.
When controlling postural movements through artificial prosthetic limbs or muscle Functional Electrical Stimulation (FES), an important issue is the enhancement of the interaction of the patient with the artificial system through his valid limb motions. We believe that a clever observation of valid limbs could improve the global postural task by giving to the patient an active role in the control of his deficient limbs. We developed an approach to identify a postural task by observing one limb  ,  . Our objectives are to: 1) detect and identify subject voluntary actions as early as possible after a movement decision is taken, and 2) to monitor the current motion in order to estimate the task state variables. We employed a set of micro sensors (CEA-LETI TRIDENT system) providing us with accelerations and absolute 3D orientations, then implemented specific signal processing methods. Two axes have already been investigated:
Early detection of Sit-to-stand. Trunk sensor acceleration information allows us to detect task initiation 500ms before legs started moving in 10 healthy subjects. This delay is sufficient to envision using this detection in order to control a leg FES system in paraplegic patients. To do this, we employed abrupt change detection methods, which rely on SLR (Sequential Likelihood Ratio) estimates, and reveal to be a powerful tool for such applications  ,  (fig. 8 ).
Gait phase identification in a steady-state walk by observing one leg with two sensors placed unilaterally at the thigh and shank levels during a walking task. 8 healthy subjects and 7 stroke patients have been involved in experiments carried out in Bronderslev rehabilitation center (Denmark). We were able to define a list of events associated to gait cycle phases which could be robustly detected. These results will find application in stroke patient rehabilitation, as part as early therapy, by triggering pre-computed stimulation sequences of deficient leg by observing valid leg. This study has been carried out in collaboration with D. Popovic (SMI, Aalborg, Denmark) during a 3 month stay of R. Héliot in SMI supported by a Marie-Curie grant.
Towards a model-based estimator of muscle length and force using muscle afferent signals for real time FES control
This work is given in the context of motor function rehabilitation via implanted Functional Electro-Stimulation (FES) and is based on a collaboration with SMI (Aalborg, Denmark) started in 2004.
Our ultimate objective is to use natural muscle sensitive fiber information as feedback for the FES artificial controller. This implies online extraction of information from neural activity in a form usable by a closed-loop controller.
In this study, the in-vivo viscoelastic responses of the rabbit skeletal muscle Medial Gastrocnemius (MG) were investigated (fig. 9 -a). 6 anesthetized New Zealand white rabbits were surgically exposed and tested under in-vivo conditions during experiments we ran at Aalborg Hospital, Department of Pathology. A Longitudinal Intrafascicular Electrode (LIFE) was implanted in the tibial branch innervating MG muscle. Muscle state (length variation and force) as well as electroneurogram (ENG) from LIFEs were recorded while applying external mechanical stretches to the muscle. A series of sinusoidal stretch profiles ranging in rate from 0.01 up to 1 Hz were imposed on the muscle. Up to now 2 rabbit set of data were analyzed. Mechanical properties were expressed through a viscoelastic model and ENG signals were analyzed in terms of the single unit responses using simple threshold detection (fig. 9 -b). This approach has the advantage of being a fast and easy method for unit separation that could be implemented for online application  .
Note: This work is supported by an EADS foundation contract with INRIA for M. Djilas PhD thesis (October 2005-September 2008). A EURON financial support starting in November 2005 has also been obtained for this project involving DEMAR and SMI.
Contribution of afferent feedback to posture and gait control
The understanding of human postural reflexes and more precisely defining the contributions of afferent information to posture and locomotion control could be of high importance in FES context. Indeed, this knowledge could be integrated in both the design of control architectures and the modeling of muscle. This research axis is investigated through a collaboration with SMI (Aalborg, Denmark) started in 2003.
Positive afferent feedback to the human soleus muscle during quiet standing
The ankle plantar flexors of a quietly standing person must produce a certain level of contraction in order to maintain an upright posture. We found evidence that a significant part of this background contraction in the soleus muscle may be due to ongoing force sensitive feedback. Valid subjects were asked to stand quietly on a moveable platform with arms crossed and eyes open, while the platform was, in random intervals, either moved forward, accelerated downwards, or rotated around the ankle joint (dorsiflexion). The downward acceleration of the platform caused a near instantaneous reduction in body weight, proportional to the acceleration, and a drop in averaged rectified EMG of the ankle plantarflexors was found at a short latency. The size of the EMG drop increased monotonically with the amount of downward acceleration from 0.2g to 0.8g, suggesting a gradual feedback from force sensitive receptors. Ischaemia at the level of the thigh abolished or reduced the drop in EMG, suggesting a peripheral origin, whereas ischaemic nerve block applied above the ankle joint had no reducing effect on the short latency reflex or the drop in EMG. Muscle tendon vibration applied at the Achilles' tendon had a decreasing effect on the amplitude of SOL responses, suggesting that group Ia afferent may be involved. Our results suggested that the short-latency drop in EMG in the soleus muscle, as was seen in the downward perturbation, might be due to a decrease in positive afferent feedback due to the sudden decrease in bodyweight. This implies the existence of an ongoing afferent feedback loop towards the soleus motoneuronal pool from force sensitive receptors. Our findings suggested that both Ia and Ib afferents play a role in the responses observed for downward perturbations.
Loss of ground support produces a decrement in SOL EMG during human walking
Sensory feedback from proprioceptive afferents is known to contribute to the enhancement of extensor locomotor muscle activity in cat and human walking. The soleus muscle (SOL) EMG is transiently depressed after a rapid plantar flexion perturbation during human treadmill walking. The objective of the present study was to investigate if a similar decrease in the SOL EMG is observed following a sudden loss in ground support. 8 volunteers walked at a self-selected speed such that the right foot struck a custom-made robotic platform positioned in the middle of the walkway. On random trials the ground support was rapidly removed by accelerating the platform downward at 7.85 m. s-2 ( 0.8 g ) for 8 cm . The perturbations were presented during the right foot stance phase with approximately 1 perturbation for every 8 control steps. The perturbations were delivered at early, mid, or late stance phase, and timed by the heel strike. Control step and perturbed step records were collected until approximately 15 perturbations were obtained for each of the 3 phases of stance. The removal of the support surface resulted in a transient drop in the SOL EMG by approximately 20% with respect to the control step EMG irrespective of the stance phase time. The EMG decline had a mean onset latency of 41 ms with respect to the removal of the support surface and was preceded 20 ms earlier by a slow ankle plantar flexion. The head tilted forward with a mean onset latency of 14 ms (i.e. 27 ms prior to the decline in SOL EMG). The short delays between the onset of the ankle/head movement and the onset of the EMG decline suggests that spindle afferents from the ankle and neck are not responsible for this response. We suggest that the removal of feedback from group Ib receptors may be implicated in this response; however, a vestibular response cannot be ruled out with the present experimental paradigm  .
Bipedal Locomotion: Towards Unified Concepts in Robotics and Neuroscience
This research axis is investigated through a collaboration with Développement et Pathologie de l'Action (DPA) group (Marseille) started in 2002.
We carry out a joint discussion on the functional bases of bipedal locomotion and how could they be controlled? The originality of this work is to synthesize two approaches: automatic/control and neurosciences, in order to take advantage of the knowledge concerning the adaptability and reactivity performances of humans, and of the rich tools and formal concepts available in biped robotics. Indeed, we claim that the theoretical framework of robotics can benefit human postural control description by formally expressing the experimental concepts used in neuroscience. Inversely, biological knowledge of the human posture and gait can inspire biped robot design and control. We attempted to provide common theoretical framework to formally express concepts in gait and posture control. This unification of definitions would be useful not only for the furtherment of human movement analysis, but also for the transfer of knowledge from neuroscience to robotics and vice-versa.  . We also believe that these concepts will find application in FES context for the development of controller architectures.