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Use of Orthogonal Functions for Model Predictive Control of Biomechanical Sit-to-Stand

As far back as Weiner, orthonormal basis functions were proposed for expressing the response of linear dynamical systems. Later, such functions were found useful for controller design in the case of linear time-invariant systems. This study explores the use of orthonormal functions in model predictive controller design for biomechanical sit-to-stand (STS) movement. Due to its simplicity and flexibility, model predictive control (MPC) has been popular in process control applications. MPC assumes finite prediction and control horizons, and optimizes a quadratic cost of state and incremental control variables subject to state and input constraints. In this study, MPC controller design technique is applied to a multi-segment biomechanical model, tasked to mimic physiological STS movement. Two sets of orthogonal functions, that is, Laguerre and Kautz functions, were explored. In both cases, MPC design generated physiologically constrained torques at ankle, knee, and hip joints that facilitated smooth STS movement. The MPC framework can be extended to controller design for other voluntary movements in a model based environment.