Constrained Dynamic Optimization of Sit-to-Stand Motion Driven by Bézier Curves

Abstract

The purpose of this work is twofold: first, to synthesize a motion pattern imitating sit-to-stand (STS) and second, to compare the kinematics and dynamics of the resulting motion to healthy STS. Predicting STS in simulation inspired the creation of three models: a biomechanical model, a motion model, and performance criteria as a model of preference. First, the human is represented as three rigid links in the sagittal plane. This model captures aspects of joint, foot, and buttocks physiology, which makes it the most comprehensive planar model for predicting STS to date. Second, candidate STS trajectories are described geometrically by a set of Bézier curves which seem well suited to predictive biomechanical simulations. Third, with the assumption that healthy people naturally prioritize mechanical efficiency, disinclination to a motion is described as a cost function of joint torques, and for the first time, physical infeasibility including slipping and falling. This new dynamic optimization routine allows for motions of gradually increasing complexity while the model's performance is improving. Using these models and optimal control strategy together has produced gross motion patterns characteristic of healthy STS when compared with normative data from the literature.