Walking is a challenging activity for people suffering from lower-limb spasticity, that occur for many reasons including neurological diseases such as Cerebral Palsy (CP), spinal cord disorders or strokes (Cerebral Accident for CA). CP is a disorder that affects muscle tone and motor skills, in a way that doesn’t allow persons to move in a coordinated and purposeful way. Spinal cord disorders are due to injuries, infections, blocked blood supply and compression by a tumor or a fracture. For CA, the poor blood flow to the brain results in cells death, which leads to death or, in case of survival, to muscle paralysis. This induce a gait disorder and other disabilities.

The use of a rehabilitation exoskeleton helps to improve the social status of paraplegics. Since the beginning of the second half of the 20th century, exoskeletons witnessed huge progress in the field of gait rehabilitation. this progress is still ongoing in the 21st century while prototypes are being developed and the use of exoskeletons spans worldwide for the paraplegics  rehabilitation.

However, exoskeletons are facing real challenges in this context, especially with regard to control: each patient has their own set of specific movements, their own space and time parameters, kinetic parameters, their own electromyography signals etc…

       Therefore, it is important to find a solution to better control exoskeletons in order to rehabilitate patients and compensate walking disorders to ensure a better recovery.

The walking disorder caused by the spasticity of the muscles, appears by kinematic parameters where the trajectory of the joints during the walk becomes disordered.

     From this point on, understanding normal and abnormal gait is a prerequisite in order to be able to diagnose and analyze any gait disorder or pathology.

     This understanding stems from the extraction of biomedical signals (EMG ) which will be combined to joint kinematics.

      In other words, the idea is to find the relation between the muscle force which cause the joint movement (knee and hip) and the joint angles during a walking cycle to find a steering function for or the control of rehabilitation exoskeleton.

     Paving the way for a better movement compensation for patients.in our work we have tried to find a relation between muscular co-contraction index and gait angle, paving the way for a find a signal for rehabilitation exoskeleton control for paraplegics movement compensation.

    LISV team (system engineering laboratory of Versailles : versailles University ), develops the design of a rehabilitation exoskeleton, this exoskeleton has four degrees of freedom, where the actuators are connected to two active assets the knee and hip and the other two degrees of freedom are passive like springs on the ankles, its advantage is that it is deformable in a way that it can be used by paraplegics of different ages from 10 years.

      We chose to test the cases of Healthy people (HP)  (to determine the baseline) and paraplegics : CP and  CA (for rehabilitation cases) by databases already existing at Endicap laboratory  of Garches Hospital (Raymond Poincare)

          Our thesis goal, is to  find a control method to use  LISV exoskeleton to rehabilitation and to assist paraplegics by regulating their strength required for a successful gait movement. This assistance must be introduced to correct their walking movement without sacrificing the patient control priority, during the gait cycle.

The proposed method for exoskeleton control (neuro-motor) is to find inputs related directly to the following patient’s movement parameters to control Exoskeleton:

     the antagonistic muscles can contract at the same time as the agonists in a large number of circumstances. This is called co-contraction, which characterizes the simultaneous activation of the agonist and antagonist muscles within the same joint and acting on the same plane Olney, 1985

       Muscle co-contraction is an important variable that can be used to evaluate the function of the walking muscle causing movement of a joint such as the knee and hip.

    When it comes to bi-articular muscles such as the quadriceps and hamstrings that affect the same at the hip and knee, for example,

      In normal human movement, the presence of the agonist-antagonist co-contraction and its degree remain incompletely elucidated (Smith, 1981, Damiano, 1993).

        The level of antagonistic co-contraction seems to increase proportionally with the speed of the movement (Wachholder and Altenburger 1925, Barnett and Harding, 1955), to vary with the degree of inertia during the movement (Lestienne and Bouisset, 1968), according to the muscular group considered. (Patton and Mortensen, 1971) and according to the type of agonist contraction, being superior in concentric rather than eccentric mode (Kellis and Unnhitan, 1999).

        In isometric conditions, the antagonistic co-contraction seems to increase according to the agonist activation, being proportionally higher during the maximal voluntary contraction (Yang and Winter, 1983, Hébert et al., 1991); it also appears to be dependent on the position of other joint segments (eg forearm position in pronation or supination on the upper limb), and angular variations (Funk et al., 1987).

       The level of antagonistic co-contraction may also be partially dependent on sex and age (Kelly and Unnithan 1999, Osternig et al., 1995, Baratta et al., 1988, Morse et al. for others (Seger and Thorstensson, 1994, Frost et al., 1997, Unnithan et al., 1996b, Spiegel et al., 1996, Peterson and Martin, 2010).

      In the functional operating condition, antagonistic co- contraction is a common feature of several muscles. For example, the hamstrings and the femoral right are described as simultaneously active in order to provide support for the trunk when walking (Carlsöö and Nordstrand, 1968).

      Antagonistic co-contractions seems to be a rule as soon as a precision requirement arises (Smith, 1981, Humprey, 1982, Aagaard et al., 2000) constituting a central element of the means by which the nervous system adjusts movements at all times. even after learning dynamics (Darainy and Ostry, 2008) reflecting the adaptive character of the neuromuscular system according to the desired movement (Bouisset and Lestienne, 1974).

      A more elaborate view was proposed by Basmajian in 1977, which suggested that motor skill acquisition is expressed by selective inhibition of unnecessary muscle activities rather than activation of additional motor units. Antagonist co-contraction is thus rather an indicator of the degree of learning, in the same way as in the child under development.

     During children motor development , the movement is characterized by a sequence of massive antagonistic co-contractions in the first months of life, and a reciprocal inhibition gradually more and more widespread, which becomes fully functional in a nervous system. mature (Thelen et al., 1983, Gatev, 1972).

      As postulate disciples, some authors report that the degree of antagonistic co-contraction may decrease after the learning phenomenon, although the effects are not lasting over time (Carolane and Cafarelli, 1992, Gribble et al., 2003).

        Thus, the antagonistic co-contraction could reflect a defect of strategy of the nervous system when there is an uncertainty of the task to be performed as in the case of the elderly who, having often difficulties in controlling the level of force reduction, adopt co-activation of antagonists (Spiegel et al., 1996, Seidler-Dobrin et al., 1998), or cases of central fatigue occurrence (Rodrigues et al., 2009) .

        Of the existing co-contraction index that are commonly used to quantify the co-contraction of muscle activities, the ratio of antagonistic activity to total muscle activities

EMG Normalization:

The many factors involved in the EMG signal represent obstacles to the direct comparison of EMG amplitudes in microvolts between different subjects as well as for the same subject tested at different sessions. One solution is then to standardize the electrical units, ie to express the intensity of the EMG with respect to a reference value. Different methods exist for calculating this value reference, especially in the study of walking, and the criterion of ideal normalization does not yet enjoy a unanimous consensus (Yang and Winter, 1984). A reference value used in the majority of studies is that obtained during maximal isometric contraction (Perry 1992, De Luca 1997). Apart from the interpolated stimulation method (Denny-Brown and Sherrington, 1928), the aim is to test the subject during maximal isometric effort by measuring the EMG of the muscle in parallel. The average of the IEMG or the RMS is then read as reference values. Relative values are then derived, expressed as a percentage of the reference value. Admittedly, this measure does not make it possible to obtain the actual maximum voluntary force of which a subject is capable, representing a potential source of error (Allen et al., 1995). However, it has a high intra-individual reproducibility index (Allen et al., 1995), and a better intra and inter-individual reproducibility score than dynamic EMG values \cite{Knutson_1994}.

This normalization method can be used for the quantification of agonist recruitment but also for the quantification of antagonistic recruitment in the estimation of co-contraction degree (Gracies et al., 2009, Vinti et al., 2012ab, Table 1, index 3). In the literature, for the quantification of antagonistic co-contraction under static or dynamic, physiological conditions \cite{Knutson1994,Kellis2003} (Olney, 1985, Solomonow et al., 1986, 1987, 1988, Knutson et al., 1994, Falconer and Winter, 1995) and pathological (Unnithan et al., 1996ab, Frost et al., 1997, Levin et al., 1994, 2000, Ikeda et al., 1998, Gracies et al., 2009, Vinti et al., 2012ab ), various methods have been used ranging from simple electromyographic measurements (Knutson et al., 1994; Unnhitan et al., 1996ab) to advanced mathematical models (Olney, 1985, Solomonow et al., 1986).