Implicit methods for efficient musculoskeletal simulation and optimal control.
Implicit methods for efficient musculoskeletal simulation and optimal control.
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DOI：
10.1016/j.piutam.2011.04.027
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发表时间：
2011-01-01
期刊：
影响因子：
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通讯作者：
Heinrich, Dieter
中科院分区：
文献类型：
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作者：
van den Bogert, Antonie J;Blana, Dimitra;Heinrich, Dieter
肌肉骨骼动力学的常微分方程组往往具有较强的数值刚性和高度的非线性。因此，仿真需要较小的时间步长，最优控制问题求解缓慢且收敛较差。在这篇文章中，我们提出了肌肉骨骼动力学的隐式公式，这导致了新的数值方法的模拟和最优控制，以期我们可以缓解其中的一些问题。利用隐式格式建立了求解正动力学问题的一阶Rosenbrock方法。用它对具有极大动态刚度的复杂肩臂系统进行了实时动力学仿真。当以实时速度运行时，仿真在关节角度上的均方根误差仅为0.11度。为了实现肌肉骨骼系统的最优控制，提出了一种隐式模型的直接配置法。该方法被应用于假足和踝关节的步态预测。在不到一个小时的计算时间内就得到了解决方案，并展示了患者如何调整他们的步态来补偿特定假肢设计的局限性。最优控制方法还被应用于运动生物力学中的状态估计问题，其中滑雪过程中的力是根据噪声和不完整的运动学数据来估计的。使用完整的肌肉骨骼动力学模型进行状态估计还有一个额外的优势，即可以用相同的隐式模型进行正向动力学模拟，以模拟损伤和扰动反应。虽然这些方法很强大，可以解决以前难以解决的问题，但仍然存在相当大的数值挑战，特别是与基于梯度的求解器的收敛有关。
The ordinary differential equations for musculoskeletal dynamics are often numerically stiff and highly nonlinear. Consequently, simulations require small time steps, and optimal control problems are slow to solve and have poor convergence. In this paper, we present an implicit formulation of musculoskeletal dynamics, which leads to new numerical methods for simulation and optimal control, with the expectation that we can mitigate some of these problems. A first order Rosenbrock method was developed for solving forward dynamic problems using the implicit formulation. It was used to perform real-time dynamic simulation of a complex shoulder arm system with extreme dynamic stiffness. Simulations had an RMS error of only 0.11 degrees in joint angles when running at real-time speed. For optimal control of musculoskeletal systems, a direct collocation method was developed for implicitly formulated models. The method was applied to predict gait with a prosthetic foot and ankle. Solutions were obtained in well under one hour of computation time and demonstrated how patients may adapt their gait to compensate for limitations of a specific prosthetic limb design. The optimal control method was also applied to a state estimation problem in sports biomechanics, where forces during skiing were estimated from noisy and incomplete kinematic data. Using a full musculoskeletal dynamics model for state estimation had the additional advantage that forward dynamic simulations, could be done with the same implicitly formulated model to simulate injuries and perturbation responses. While these methods are powerful and allow solution of previously intractable problems, there are still considerable numerical challenges, especially related to the convergence of gradient-based solvers.