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Falls during sit-to-stand are a common cause of injury. The ability to perform this movement with ease is itself correlated with a lower likelihood of falling. However, a rigorous mathematical understanding of stability during sit-to-stand does not currently exist, particularly in different environments and under different movement control strategies. Having the means to isolate the different factors contributing to instability during sit-to-stand could have great clinical utility, guiding the treatment of fall-prone individuals. In this work, we show that the region of stable human movement during sit-to-stand can be formulated as the backward reachable set of a controlled invariant target, even under state-dependent input constraints representing variability in the environment. This region represents the ‘best-case’ boundaries of stable sit-to-stand motion. We call this the stabilizable region and show that it can be easily computed using existing backward reachability tools. Using a dataset of humans performing sit-to-stand under perturbations, we also demonstrate that the controlled invariance and backward reachability approach is better able to differentiate between a true loss of stability versus a change in control strategy, as compared with other methods. 

Musculoskeletal modeling is a powerful approach for studying the biomechanics and energetics of locomotion.Australopithecus (A.) afarensisis among the best represented fossil hominins and provides critical information about the evolution of musculoskeletal design and locomotion in the hominin lineage. Here, we develop and evaluate a three‐dimensional (3‐D) musculoskeletal model of the pelvis and lower limb ofA. afarensisfor predicting muscle‐tendon moment arms and moment‐generating capacities across lower limb joint positions encompassing a range of locomotor behaviors.

A 3‐D musculoskeletal model of an adultA. afarensispelvis and lower limb was developed based primarily on the A.L. 288‐1 partial skeleton. The model includes geometric representations of bones, joints and 35 muscle‐tendon units represented using 43 Hill‐type muscle models. Two muscle parameter datasets were created from human and chimpanzee sources. 3‐D muscle‐tendon moment arms and isometric joint moments were predicted over a wide range of joint positions.

Predicted muscle‐tendon moment arms generally agreed with skeletal metrics, and corresponded with human and chimpanzee models. Human and chimpanzee‐based muscle parameterizations were similar, with some differences in maximum isometric force‐producing capabilities. The model is amenable to size scaling from A.L. 288‐1 to the larger KSD‐VP‐1/1, which subsumes a wide range of size variation inA. afarensis.

This model represents an important tool for studying the integrated function of the neuromusculoskeletal systems inA. afarensis. It is similar to current human and chimpanzee models in musculoskeletal detail, and will permit direct, comparative 3‐D simulation studies.

 

Computer modeling, simulation and optimization are powerful tools that have seen increased use in biomechanics research. Dynamic optimizations can be categorized as either data-tracking or predictive problems. The data-tracking approach has been used extensively to address human movement problems of clinical relevance. The predictive approach also holds great promise, but has seen limited use in clinical applications. Enhanced software tools would facilitate the application of predictive musculoskeletal simulations to clinically-relevant research. The open-source software OpenSim provides tools for generating tracking simulations but not predictive simulations. However, OpenSim includes an extensive application programming interface that permits extending its capabilities with scripting languages such as MATLAB. In the work presented here, we combine the computational tools provided by MATLAB with the musculoskeletal modeling capabilities of OpenSim to create a framework for generating predictive simulations of musculoskeletal movement based on direct collocation optimal control techniques. In many cases, the direct collocation approach can be used to solve optimal control problems considerably faster than traditional shooting methods. Cyclical and discrete movement problems were solved using a simple 1 degree of freedom musculoskeletal model and a model of the human lower limb, respectively. The problems could be solved in reasonable amounts of time (several seconds to 1–2 hours) using the open-source IPOPT solver. The problems could also be solved using the fmincon solver that is included with MATLAB, but the computation times were excessively long for all but the smallest of problems. The performance advantage for IPOPT was derived primarily by exploiting sparsity in the constraints Jacobian. The framework presented here provides a powerful and flexible approach for generating optimal control simulations of musculoskeletal movement using OpenSim and MATLAB. This should allow researchers to more readily use predictive simulation as a tool to address clinical conditions that limit human mobility.

 

Simulation of musculoskeletal systems using dynamic optimization is a powerful approach for studying the biomechanics of human movements and can be applied to human‐robot interactions. The simulation results of human movements augmented by robotic devices may be used to evaluate and optimize the device design and controller. However, simulations are limited by the accuracy of the models which are usually simplified for computation efficiency. Typically, the powered robotic devices are often modeled as massless, ideal torque actuators that is without mass and internal dynamics, which may have significant impacts on the simulation results. This article investigates the effects of including the mass and internal dynamics of the device in simulations of assisted human movement. The device actuator was modeled in various ways with different detail levels. Dynamic optimization was used to find the muscle activations and actuator commands in motion tracking and predictive simulations. The results showed that while the effects of device mass and inertia can be small, the electrical dynamics of the motor can significantly impact the results. This outcome suggests the importance of using an accurate actuator model in simulations of human movement augmented by assistive devices.

Demonstrating the effects of including mass and internal dynamics of the actuator in simulations of assisted human movement

A new OpenSim electric motor actuator class to capture the electromechanical dynamics for use in simulation of human movement assisted by powered robotic devices

 

Marker‐based motion capture techniques are commonly used to measure human body kinematics. These techniques require an accurate mapping from physical marker position to model marker position. Traditional methods utilize a manual process to achieve marker positions that result in accurate tracking. In this work, we present an optimization algorithm for model marker placement to minimize marker tracking error during inverse kinematics analysis of dynamic human motion. The algorithm sequentially adjusts model marker locations in 3‐D relative to the underlying rigid segment. Inverse kinematics is performed for a dynamic motion capture trial to calculate the tracking error each time a marker position is changed. The increase or decrease of the tracking error determines the search direction and number of increments for each marker coordinate. A final marker placement for the model is reached when the total search interval size for every coordinate falls below a user‐defined threshold. Individual marker coordinates can be locked in place to prevent the algorithm from overcorrecting for data artifacts such as soft tissue artifact. This approach was used to refine model marker placements for eight able‐bodied subjects performing walking trials at three stride frequencies. Across all subjects and stride frequencies, root mean square (RMS) tracking error decreased by 38.4% and RMS tracking error variance decreased by 53.7% on average. The resulting joint kinematics were in agreement with expected values from the literature. This approach results in realistic kinematics with marker tracking errors well below accepted thresholds while removing variance in the model‐building procedure introduced by individual human tendencies.