A metabolic energy expenditure model with a continuous first derivative and its application to predictive simulations of gait

Koelewijn, Anne D.; Dorschky, Eva; Bogert, Antonie J. van den

doi:10.1080/10255842.2018.1490954

Cited by 39 publications

(70 citation statements)

References 27 publications

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“…This gait pattern requires smaller knee extension torques. Biomechanics researchers have suggested that gait with near-zero joint torques is unstable and that taking uncertainty into account would lead to more optimal movements with larger knee flexion during stance and larger knee extension torques as consequence [Koelewijn et al 2018]. Figure 7 visualizes the learned torque limits for different states.…”

Section: Runningmentioning

confidence: 99%

Synthesis of biologically realistic human motion using joint torque actuation

et al. 2019

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Using joint actuators to drive the skeletal movements is a common practice in character animation, but the resultant torque patterns are often unnatural or infeasible for real humans to achieve. On the other hand, physiologicallybased models explicitly simulate muscles and tendons and thus produce more human-like movements and torque patterns. This paper introduces a technique to transform an optimal control problem formulated in the muscleactuation space to an equivalent problem in the joint-actuation space, such that the solutions to both problems have the same optimal value. By solving the equivalent problem in the joint-actuation space, we can generate humanlike motions comparable to those generated by musculotendon models, while retaining the benefit of simple modeling and fast computation offered by joint-actuation models. Our method transforms constant bounds on muscle activations to nonlinear, state-dependent torque limits in the joint-actuation space. In addition, the metabolic energy function on muscle activations is transformed to a nonlinear function of joint torques, joint configuration and joint velocity. Our technique can also benefit policy optimization using deep reinforcement learning approach, by providing a more anatomically realistic action space for the agent to explore during the learning process. We take the advantage of the physiologically-based simulator, OpenSim, to provide training data for learning the torque limits and the metabolic energy function. Once trained, the same torque limits and the energy function can be applied to drastically different motor tasks formulated as either trajectory optimization or policy learning.

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Section: Runningmentioning

confidence: 99%

Synthesis of biologically realistic human motion using joint torque actuation

et al. 2019

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“…As an illustration, we added a term representing the metabolic energy rate [30] to the objective function of the 2D predictive simulations. Minimizing metabolic energy rate is common in predictive studies of walking [4,6,24]. Solving the resulting optimal control problem was about 60 times faster with AD-Recorder than with FD (although FD required fewer iterations), whereas AD-Recorder was only about 10 times faster than FD without incorporating the metabolic energy rate in the objective function.…”

Section: Discussionmentioning

confidence: 99%

“…Solving the resulting optimal control problem was about 60 times faster with AD-Recorder than with FD (although FD required fewer iterations), whereas AD-Recorder was only about 10 times faster than FD without incorporating the metabolic energy rate in the objective function. This increased time difference can be explained by our use of computationally expensive hyperbolic tangent functions to make the metabolic energy rate model twice continuously differentiable, as required when using second-order gradient-based optimization algorithms [24]. Overall, AD reduces the number of function evaluations, which has an even larger effect if these functions are expensive to compute.…”

Section: Discussionmentioning

confidence: 99%

“…In these examples, we modeled pendulum/skeletal movement with Newtonian rigid body dynamics and, for the walking simulations, compliant Hunt-Crossley foot-ground contact [15,17]. We created a continuous approximation of a contact model from Simbody to provide twice continuously differentiable contact forces, which are required when using second-order gradient-based optimization algorithms [24]. We performed the approximations of conditional if-tests using hyperbolic tangent functions.…”

Section: Methodsmentioning

confidence: 99%

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Algorithmic differentiation improves the computational efficiency of OpenSim-based optimal control simulations of movement

Falisse

Serrancolí

et al. 2019

Preprint

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AbstractAlgorithmic differentiation (AD) is an alternative to finite differences (FD) for evaluating function derivatives. The primarily aim of this study was to demonstrate the computational benefits of using AD instead of FD in OpenSim-based optimal control simulations. The secondary aim was to evaluate computational choices including different AD tools, different linear solvers, and the use of first- or second-order derivatives. First, we enabled the use of AD in OpenSim through a custom source code transformation tool and through the operator overloading tool ADOL-C. Second, we developed an interface between OpenSim and CasADi to perform optimal control simulations. Third, we evaluated computational choices through simulations of perturbed balance, two-dimensional predictive simulations of walking, and three-dimensional tracking simulations of walking. We performed all simulations using direct collocation and implicit differential equations. Using AD through our custom tool was between 1.8 ± 0.1 and 17.8 ± 4.9 times faster than using FD, and between 3.6 ± 0.3 and 12.3 ± 1.3 times faster than using AD through ADOL-C. The linear solver efficiency was problem-dependent and no solver was consistently more efficient. Using second-order derivatives was more efficient for balance simulations but less efficient for walking simulations. The walking simulations were physiologically realistic. These results highlight how the use of AD drastically decreases computational time of optimal control simulations as compared to more common FD. Overall, combining AD with direct collocation and implicit differential equations decreases the computational burden of optimal control simulations, which will facilitate their use for biomechanical applications.

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“…The advantages of direct collocation have led biomechanists to use the method for tracking motions [16,23], predicting motions [24][25][26][27][28][29][30][31][32][33], fitting muscle properties [34], and optimizing design parameters [35]. Researchers have made key methodological advances, including efficiently handling multibody and muscle dynamics via implicit formulations [36,37], minimizing energy consumption [38,39], and employing algorithmic differentiation to simulate complex models more rapidly compared to using finite differences [40]. Along with these methodological advances, researchers have discovered that minimizing an energy-related cost produces non-physiological motions during walking [24], skipping is the most efficient gait on our moon [41], and unilateral amputees can improve gait symmetry with only a minor increase in effort [42].…”

Section: Introductionmentioning

confidence: 99%

OpenSim Moco: Musculoskeletal optimal control

Dembia

Bianco

Falisse

et al. 2019

Preprint

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Musculoskeletal simulations of movement can provide insights needed to help humans regain mobility after injuries and design robots that interact with humans. Here, we introduce OpenSim Moco, a software toolkit for optimizing the motion and control of musculoskeletal models built in the OpenSim modeling and simulation package. Open-Sim Moco uses the direct collocation method, which is often faster and can handle more diverse problems than other methods for musculoskeletal simulation but requires extensive technical expertise to implement. Moco frees researchers from implementing direct collocation themselves, allowing them to focus on their scientific questions. The software can handle the wide range of problems that interest biomechanists, including motion tracking, motion prediction, parameter optimization, model fitting, electromyographydriven simulation, and device design. Moco is the first musculoskeletal direct collocation tool to handle kinematic constraints, which are common in musculoskeletal models. To show Moco's abilities, we first solve for muscle activity that produces an observed walking motion while minimizing muscle excitations and knee joint loading. Then, we predict a squat-to-stand motion and optimize the stiffness of a passive assistive knee device. We designed Moco to be easy to use, customizable, and extensible, thereby accelerating the use of simulations to understand human and animal movement.

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A metabolic energy expenditure model with a continuous first derivative and its application to predictive simulations of gait

Cited by 39 publications

References 27 publications

Synthesis of biologically realistic human motion using joint torque actuation

Synthesis of biologically realistic human motion using joint torque actuation

Algorithmic differentiation improves the computational efficiency of OpenSim-based optimal control simulations of movement

OpenSim Moco: Musculoskeletal optimal control

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