Predictive simulation of human motion could provide insight into optimal techniques. In repetitive or long-duration tasks, these simulations must predict fatigue-induced adaptation. However, most studies minimize cost function terms related to actuator activations, assuming it minimizes fatigue. An additional modeling layer is needed to consider the previous use of muscles to reveal adaptive strategies to the decreased force production capability. Here, we propose interfacing Xia's three-compartment fatigue dynamics model with rigid-body dynamics. A stabilization invariant was added to Xia's model. We simulated the maximum repetition of dumbbell biceps curls as an optimal control problem (OCP) using direct multiple shooting. We explored three cost functions (minimizing minimum torque, fatigue, or both) and two OCP formulations (full-horizon and sliding-horizon approaches). We found that Xia's model modified with the stabilization invariant (10 or 5) was adapted to direct multiple shooting. Sliding-horizon OCPs achieved 20 to 21 repetitions. The kinematic strategy slowly deviated from a plausible dumbbell lifting task to a swinging strategy as fatigue onset increasingly compromised the ability to keep the arm vertical. In full-horizon OCPs, the latter kinematic strategy was used over the whole motion, resulting in 32 repetitions. We showed that sliding-horizon OCPs revealed a reactive strategy to fatigue when only torque was included in the cost function, whereas an anticipatory strategy was revealed when the fatigue term was included in the cost function. Overall, the proposed approach has the potential to be a valuable tool in optimizing performance and helping reduce fatigue-related injuries in a variety of fields.

翻译：人体运动的预测仿真能够为最优技术提供深刻见解。在重复性或长期任务中，这些仿真必须预测由疲劳引起的适应性变化。然而，大多数研究通过最小化与执行器激活相关的成本函数项来假定其可减少疲劳，但这种方法仍需要额外的建模层来考虑肌肉的既往使用情况，以揭示针对力量产生能力下降的适应策略。本文提出将Xia三室疲劳动力学模型与刚体动力学相结合，并在Xia模型中增加了稳定性不变性约束。我们采用直接多重打靶法，将哑铃肱二头肌弯举的最大重复次数建模为最优控制问题（OCP）。我们探索了三种成本函数（最小化最小扭矩、最小化疲劳、或两者兼顾）和两种OCP形式（全视界方法和滑窗方法）。研究发现：加入稳定性不变性约束（取值为10或5）后的Xia模型能够适配直接多重打靶法；滑窗OCP方法实现了20至21次重复；随着疲劳加剧导致手臂无法维持垂直姿态，运动学策略从合理的哑铃提举任务逐渐偏离为摆动策略；而在全视界OCP方法中，整个运动均采用后一种运动学策略，最终实现了32次重复。研究结果表明：当成本函数仅包含扭矩项时，滑窗OCP方法揭示了针对疲劳的反应性策略；而当成本函数包含疲劳项时，则揭示了预期性策略。总体而言，所提出的方法有望成为优化运动表现、减少各领域疲劳相关损伤的重要工具。