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Computational prediction of 3D crutch-assisted walking patterns is a challenging problem that could be applied to study different biomechanical aspects of crutch walking in virtual subjects, to assist physiotherapists to choose the optimal crutch walking pattern for a specific subject, and to help in the design and control of exoskeletons, when crutches are needed for balance. The aim of this work is to generate a method to predict three-dimensional crutch-assisted walking motions following different patterns without tracking any experimental data. To achieve this goal, we collected gait data from a healthy subject performing a four-point non-alternating crutch walking pattern, and developed a 3D torque-driven full-body model of the subject including the crutches and foot-and crutch-ground contact models. First, we developed a predictive (i.e., no tracking of experimental data) optimal control problem formulation to predict crutch walking cycles following the same pattern as the experimental data collected, using different cost functions. To reduce errors with respect to reference data, a cost function combining minimisation terms of angular momentum, mechanical power, joint jerk and torque change was chosen. Then, the problem formulation was adapted to handle different foot-and crutch-ground conditions to make it capable of predicting three new crutch walking patterns, one of them at different speeds. A key aspect of our algorithm is that having ground reactions as additional controls allows to define phases inside the cycle without the need of formulating a multiple-phase problem, thus facilitating the definition of different crutch walking patterns.

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Background: Experimental and modeling errors can lead to dynamically inconsistent results when performing inverse dynamic analyses of human movement. Adding low-value residual pelvis actuators could deal with such a problem. However, in certain tasks, these residuals may remain quite large, and strategies based on motion or force variation must be applied. Research question: Can the dynamic inconsistency be handled by an optimal control algorithm that changes the measured kinematics in the preparatory phase of the single leg triple hop test, a relatively high-speed and torque-demanding task, so that residuals are kept within a low range? Methods: The proposed optimal control algorithm was developed as a tracking problem, in which the implicit form of dynamics was used. Equations of motion were introduced as path constraints, as well as residual forces and moments acting on the pelvis. To do so, GPOPS-II and IPOPT were employed to solve the optimization problem. Furthermore, OpenSim API was called at each iteration to solve the equations of motion through an inverse dynamic analysis. Results: Results presented a high reduction in all six components of residual actuators during the entire task. Moreover, resulting motion after the optimization showed a very similar evolution than the reference motion before the ascending phase of the task. Once the ascending phase started, some coordinates presented a more significant discrepancy compared to the reference, such as the pelvis tilt and lumbar extension. Significance: The findings suggest that the proposed algorithm can deal with dynamic inconsistency in high-speed tasks, obtaining low residual forces and moments while keeping similar kinematics. Hence, it could complement other optimal control algorithms that simulate new motions, relying on dynamically consistent data.