Powerbike - Model-based optimal control for cycling

我们的项目将体育中的计算机科学(SportInformation Atik)与数学建模、数值和体育科学联系起来。作为耐力运动的一个例子，我们通过设计、校准和验证数学生理模型来分析和预测自行车性能，并基于这些模型推导出计算自行车计时赛最佳起搏策略的方法，从而为耐力运动的建模和预测做出贡献。公路自行车性能分析的建模是双重的。首先，自行车的机械方面包括自行车推进的物理方面。其次，需要一个运动员个体的生理模型，它应该在任何时间点提供可用的力量和能量来源。这样的模型比物理模型更难实现。准确地模拟所有相关的生理方面是不可能的，因为人类有机体的巨大复杂性包括许多从细胞级别到尺度的子系统。因此，必须在模型的细节级别和必要的抽象之间做出妥协。对于这项任务，我们将使用半物理系统建模。系统结构的基本要素将由当前最先进的生理模型驱动，而内部系统的一些细节将留给系统识别。此外，这些生理模型的参数需要为个别运动员进行估计。这种校准是困难的，可能会使一个可能准确但过于复杂的模型在实践中毫无用处。系统辨识和参数估计可以很好地基于输入-输出对。输入是适当选择的测功机测试中的负荷分布。输出是呼吸气体交换、心率或变异性，以及乳酸水平。有了手头的模型，我们就可以通过求解某些数学最优控制问题来计算最小时间起搏策略。物理和生理模型为约束微分方程组提供了一种控制，这就是起搏策略。最近，为了有效地解决一般最优控制问题而设计的改进的数值算法是可用的，部分原因是开发了良好的开源软件。然而，具体的问题仍然包含一些特征，需要额外的方法来保证可靠的收敛。首先，必须制定测试协议来确定生理模型的参数，以评估这些模型的有效性和准确性。其次，我们将首先在我们的自行车模拟器上测试最佳起搏策略，然后还将在需要GPS功能的反馈设备的现场进行测试，该设备可以为骑车者实时提供关于最佳起搏的信息。理想情况下，该设备应该在路上在线更新最佳起搏策略。

Our project connects Computer Science in Sport (Sportinformatik) with mathematical modeling, numerics, and sport science. We contribute to modeling and prediction for cycling as an example of endurance sports by- designing, calibrating, and validating mathematical physiological models that provide the means to analyze and predict cycling performance, and by- deriving methods to compute optimal pacing strategies for cycling time trials based on these models.The modeling for performance analysis in road cycling is twofold. Firstly, the mechanical aspects of cycling include the physics of the bicycle propulsion. Secondly, a physiological model of the individual athlete is required which should provide available power and energy resources at any point in time. Such a model is much more difficult to achieve than the physical one. It is impossible to accurately simulate all relevant physiological aspects because of the vast complexity of the human organism encompassing numerous subsystems with scales down to the cellular level. Thus, a compromise between the level-of-detail and the necessary abstraction of the model must be made. For this task we will use semi-physical system modeling. Basic elements of the structure of the system will be motivated by current state-of-the-art physiological models while some of the internal system details will be left for the system identification. Moreover, the parameters of such physiological models need to be estimated for individual athletes. This calibration is difficult and may render a possibly accurate but too complex model useless in practice. System identification and parameter estimation can be based best on input-output pairs. Input is a load profile in a suitably chosen ergometer test. Output is respiratory gas exchange, heart rate or variability, and lactate blood level. With models on hand we can compute minimum-time pacing strategies by solving certain mathematical optimal control problems. The physical and physiological models provide a system of constrained differential equations with a control which is the pacing strategy. Recently improved numerical algorithms designed to solve general optimal control problems efficiently are available, partly as well developed open-source software. However, the specific problem still contains some features that require additional methods to guarantee reliable convergence.Our proposed work includes an evaluation. Firstly, testing protocols must be developed to determine the parameters for physiological models to evaluate the validity and accuracy of these models. Secondly, optimal pacing strategies will be tested first on our cycling simulator, and then also in the field which requires a gps-enabled feedback device that provides the cyclist with the information about the optimal pacing in real-time. Ideally, the device should update online the optimal pacing strategy while on the road.