Muscular co-contraction of antagonistic muscle pairs is often observed in human movement, but it is considered inefficient and it can currently not be predicted in simulations where muscular effort or metabolic energy is minimized. Here, we investigated the relationship between minimizing effort and muscular co-contraction in systems with random uncertainty to see if muscular co-contraction can minimize effort in such system. We also investigated the effect of time delay in the muscle, by varying the time delay in the neural control as well as the activation time constant. We solved optimal control problems for a one-degree-of-freedom pendulum actuated by two identical antagonistic muscles, using forward shooting, to find controller parameters that minimized muscular effort while the pendulum remained upright in the presence of noise added to the moment at the base of the pendulum. We compared a controller with and without feedforward control. Task precision was defined by bounding the root mean square deviation from the upright position, while different perturbation levels defined task difficulty. We found that effort was minimized when the feedforward control was nonzero, even when feedforward control was not necessary to perform the task, which indicates that co-contraction can minimize effort in systems with uncertainty. We also found that the optimal level of co-contraction increased with time delay, both when the activation time constant was increased and when neural time delay was added. Furthermore, we found that for controllers with a neural time delay, a different trajectory was optimal for a controller with feedforward control than for one without, which indicates that simulation trajectories are dependent on the controller architecture. Future movement predictions should therefore account for uncertainty in dynamics and control, and carefully choose the controller architecture. The ability of models to predict co-contraction from effort or energy minimization has important clinical and sports applications. If co-contraction is undesirable, one should aim to remove the cause of co-contraction rather than the co-contraction itself.

中文翻译：

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拮抗性共同收缩可以最大限度地减少不确定性系统中的肌肉努力

在人类运动中经常观察到拮抗肌对的肌肉共同收缩，但它被认为是低效的，目前无法在肌肉努力或代谢能量最小化的模拟中预测。在这里，我们研究了具有随机不确定性的系统中最小化努力和肌肉协同收缩之间的关系，以了解肌肉协同收缩是否可以最大限度地减少这种系统中的努力。我们还通过改变神经控制中的时间延迟以及激活时间常数来研究肌肉中时间延迟的影响。我们解决了由两个相同的拮抗肌驱动的单自由度摆的最佳控制问题，使用向前射击，找到控制器参数，使肌肉力量最小化，同时钟摆在存在噪音的情况下保持直立在钟摆底部的时刻。我们比较了有和没有前馈控制的控制器。任务精度是通过限制与直立位置的均方根偏差来定义的，而不同的扰动水平定义了任务难度。我们发现，当前馈控制不为零时，即使前馈控制不是执行任务所必需的，工作量也会最小化，这表明协同收缩可以最小化具有不确定性的系统中的工作量。我们还发现，当激活时间常数增加和添加神经时间延迟时，最佳协同收缩水平会随着时间延迟而增加。此外，我们发现，对于具有神经时间延迟的控制器，具有前馈控制的控制器与没有前馈控制的控制器相比，不同的轨迹是最佳的，这表明仿真轨迹取决于控制器架构。因此，未来的运动预测应考虑动力学和控制的不确定性，并仔细选择控制器架构。模型预测来自努力或能量最小化的共同收缩的能力具有重要的临床和运动应用。如果共收缩是不可取的，那么应该以消除共收缩的原因而不是共收缩本身为目标。因此，未来的运动预测应考虑动力学和控制的不确定性，并仔细选择控制器架构。模型预测来自努力或能量最小化的共同收缩的能力具有重要的临床和运动应用。如果共收缩是不可取的，那么应该以消除共收缩的原因而不是共收缩本身为目标。因此，未来的运动预测应考虑动力学和控制的不确定性，并仔细选择控制器架构。模型预测来自努力或能量最小化的共同收缩的能力具有重要的临床和运动应用。如果共收缩是不可取的，那么应该以消除共收缩的原因而不是共收缩本身为目标。