Predictive Dynamic Simulation of Child Gait Using Direct Collocation Optimal Control

Abstract

Despite many studies in human gait analysis, human gait predictive simulation is still challenging researchers to increase the accuracy and computational efficiency for evaluative studies, including the design of wearable robotic systems, athletic training, rehabilitation, orthosis design, and orthosis tuning. Moreover, the majority of recent predictive gait simulations focused on adult and older people. In contrast, clinical centers working on child rehabilitation and treatments of child gait disorders prefer to rely more on findings from pediatric gait predictive simulations than from adult gait predictive simulations.

This thesis developed a 2-dimensional (2D) 11-degree-of-freedom (11-DOF) child model actuated by muscle torque generators and in contact with the ground through a 3-dimensional (3D) ellipsoidal volumetric foot-ground contact model. We took advantage of muscle torque generators to propose simplified but accurate and computationally-efficient musculoskeletal and neuromusculoskeletal models for children. These models predict physiologically-realistic torques, motions, ground reaction forces, muscle excitations, and metabolic energy consumption for natural, slow and fast gaits using direct collocation optimal control.

First, we highlighted the features of current skeletal, musculoskeletal, and neuromusculoskeletal human gait models. We found that symbolic programming, a fast optimal control method, an accurate volumetric foot-ground contact model, and a two-segment foot model are required to develop a computationally-efficient and accurate predictive simulation of gait. Then, to investigate the importance of these requirements, we studied a more straightforward task (vertical jump) than gait. We showed that a toe-included human model with 3D ellipsoidal volumetric foot-ground contact model would simulate this lower-extremity task more accurately than a toeless human model with a kinematically-constrained foot-ground contact model. According to the findings from the vertical jump model, we decided to develop a 2D human model for our child gait, including metatarsal joints with a 3D ellipsoidal volumetric contact model, and we identified the contact parameters using three approaches: (1) GlobalSearch trajectory optimization, (2) Direct collocation optimal control, and (3) Direct collocation optimal control along with mass-{\&}-joint-property identification. We showed that the third approach is more accurate than the other two approaches and concluded that the contact parameters should be identified along with the mass and joint properties to have a more realistic gait simulation. For all child gait simulations in the remainder of the thesis, we decided to use direct collocation optimal control in which the contact parameters and mass and joint properties are set to the identified values.

To develop the muscle model, we adapted a recently-developed muscle-torque-generator (MTG) model to our child model, and identified the MTG parameters using experimental child gait data. We used the identified muscle torque generators to generate simplified but accurate musculoskeletal and neuromusculoskeletal models that best fit child gait. The control inputs of the musculoskeletal and neuromusculoskeletal models are MTG activations and muscle excitations, respectively. Our proposed neuromusculoskeletal model enabled us to predict muscle excitations comparable with EMG data, and estimate the metabolic energy rate, metatarsal angles, and metatarsal torques consistent with the literature. We also developed 16 optimizations (8 optimizations for each musculoskeletal and neuromusculoskeletal model), ranging from fully-data-tracking to fully-predictive optimizations, to simulate a child natural-speed (1.26 m/s) gait and compare the models in terms of prediction accuracy and computational time. We illustrated that the neuromusculoskeletal model was more computationally-efficient than the musculoskeletal model, since the control inputs of the neuromusculoskeletal model are muscle excitations with a reasonable initial guess (i.e., EMG data were used as the initial guess for the muscle excitations). We also showed that the fully-predictive neuromusculoskeletal model could predict more accurate results with less computational time than the fully-predictive musculoskeletal model. Furthermore, the muscle excitations predicted by the fully-predictive neuromusculoskeletal model were more accurate than those predicted by the data-tracking gait models.

Finally, we used our proposed musculoskeletal and neuromusculoskeletal models to generate semi-predictive simulations of four different-speed gaits for children: very slow walking at 0.9 m/s, slow walking at 1.09 m/s, fast walking at 1.29 m/s, and very fast walking at 1.58 m/s. In the different-speed gait simulations, we did not track the experimental data of the slow or fast gaits since we wanted to evaluate whether our proposed musculoskeletal and neuromusculoskeletal models are able to minimze the reliance of simulations on experiments and predict dynamically-consistent and physically-realistic slow and fast gaits, without tracking the experimental data of the corresponding slow and fast gaits. We showed that the neuromusculoskeletal model was more computationally-efficient and accurate than the musculoskeletal model in simulating slow and fast gaits. We also plotted the cost of transport (COT) values with respect to the gait speeds; The plot follows the expected `U'-shaped curve, where the minimum (the most efficient COT) occurs at the natural speed (preferred speed), in agreement with experimental observations.