Abstract
People with spinal cord injury (SCI) suffer from a drastic reduction in sitting stability which negatively impacts their postural control. Thus, sitting balance becomes one of the most challenging everyday exercises. To better understand the consequences of this pathology, we have to work with high-sized non-linear biomechanical models implying both theoretical and numerical difficulties. The main goal being to recover unmeasured inputs, the observer should have limited or no simplification at all to provide a better estimation quality. A Proportional Integral-observer (PI-observer) is designed and its convergence is formulated by linear matrix inequalities (LMI) through convex optimization techniques. Using a unique high-sized observer, the LMI constraints problem can quickly reach current solvers limitations regarding the number of unknown parameters required. A way to solve this issue is to design a cascade observer in order to estimate the unmeasurable torques of a human with SCI. This approach consists in decomposing a biomechanical model into interconnected subsystems and to build “local” observers. The relevance of this approach is demonstrated in simulation and with real-time experimental data.
Highlights
People with spinal cord injury (SCI) live with a complete or a partial paralysis of their abdominal and lower back muscles
People living with a SCI sitting position has been described via a so-called S3S model (Blandeau, 2018)
The main goal is to be able to understand the different strategies that can be used by the people with the SCI
Summary
People with spinal cord injury (SCI) live with a complete or a partial paralysis of their abdominal and lower back muscles. In order to be able to get feasible performance solutions, this study proposes to decompose the mechanical model under descriptor forms in interconnected systems, from where descriptor non-linear observers of reduced sizes can be derived from local problems (Lendek et al, 2008) (Gripa et al, 2012). It results in cascaded observers design for descriptor mechanical systems. The fourth part applies this cascade observer way-of-doing to the 2D-S3S model and proposes a solution as a LMI constraints problem to solve. This significant reduction is related to the disturbance which pushes each subject in the direction anterior to what is equivalent to injecting a negative torque (resp. positive) at the level of the trunk (resp. of the shoulder) (Blandeau, 2018)
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