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.

InverseMuscleNET: Alternative Machine Learning Solution to Static Optimization and Inverse Muscle Modeling

“…It is noteworthy to mention that every single computational technique for muscle variable computations has limitations in analytical expressions and suffers from unrealistic assumptions in the muscle models. The model parameters identified with measurements that are subject to error, require an iterative optimization loop, and results in estimated muscle activations that may not be correct (Norman-Gerum and McPhee, 2018 ).…”

“…Sensitivities and difficulties in fitting and identifying the relevant muscle parameters (Millard et al, 2019 ; Serrancolí et al, 2020 ), in addition to uncertainties related to experimental data, add further challenges to this process (Valente et al, 2014 ). Due to the mentioned assumptions and challenges, the simulation results in estimated muscle activations that may not be correct (Norman-Gerum and McPhee, 2018 ).…”

Simulation of Stand-to-Sit Biomechanics for Design of Lower-Limb Exoskeletons and Prostheses with Energy Regeneration

“…Each participant performed 20 sitting and standing movements, using self-selected rates, while lower-limb kinematics and ground reaction forces were measured with optical motion capture cameras and synchronized force plates, respectively (see Figure 3). The seat height resembled that from previous research (i.e., approximately 46 cm) [43][44]. Prior to experimental data collection, the imaging system was calibrated, and the global…”

“…Sitting and standing movement durations were defined when the smoothed pelvis translational velocities exceeded some subject-specific percentage of their maximum values; optimal percentages were approximated through trial-and-error simulations for consistent results. Other investigations have used changes in vertical ground reaction forces [36,44] and knee and hip joint kinematics [40][41] for defining the sitting and standing movement durations. The force plate measurements were filtered using 10thorder low-pass Butterworth filters with 30 Hz cut-off frequencies and zero-phase digital filtering [12].…”

“…The biomechanical model comprised a two-dimensional (sagittal-plane) inverted triple-pendulum with shank, thigh, and HAT rigid body segments (see Figure 4). The foot segment was fixed to the inertial ground frame [43][44]. The ankle, knee, and hip joints were modelled as revolute kinematic pairs.…”