A nonlinear modelling approach to quantify sitting control in individuals with sensorimotor impairments

Few biomechanical models of sitting stability have been proposed over the last decades and most of them control the trunk position through a lumbar torque. Unfortunately, this type of model is not valid for individuals living with a complete thoracic spinal cord injury (SCI) who generally experience paralysis of their abdominal and lower back muscles. Instead, individuals with SCI often engage their upper limbs as a compensatory strategy to control their sitting position. A new nonlinear biomechanical model is introduced to take into consideration the influence of the upper limbs for sitting control study of people living with SCI. The inherent nonlinearity of the model is taken into account via the Takagi-Sugeno (T-S) framework. To estimate the internal controlling torques without measurements, an unknown input observer (UIO) is created. Its convergence is expressed by linear matrix inequalities (LMI), which are solved by convex optimization techniques. Numerical simulations with perturbations are used to assess the adequacy of the methodology and preliminary experimental data of one person living with SCI performing a sitting stabilization exercise is used to estimate internal torques of the upper limbs. The main contribution of this work is to provide a way to estimate human joint torques without invasive measurements; the results highlight the validity of both goals of this article, the nonlinear biomechanical modelling and the UIO methodology.