Applications of Optimal Control to Road Cycling

Abstract

This thesis describes theoretical as well as practical applications of optimal control to road cycling. Its main concern is the optimization of pacing strategies and their transfer to the field. Based on mathematical models, optimal control problems are defined to calculate pacing strategies that minimize the time that is needed to finish a race. Besides physical conditions, the physiological properties of the rider are the limiting factor for the optimal time. While several theoretical studies have been recently carried out to optimize pacing strategies for individual time trials based on optimal control theory, none has considered more than one rider or the practical validity and relevance of those strategies. These two topics are tackled by this thesis. In the first part, the optimal control problem for pacing strategies for individual time trials is extended to two riders. A break-away of two riders from the peloton is simulated, where they are forced to work together and complete the remaining course as quickly as possible in order to stay ahead of the peloton. This approach could also be extended to team time trials, in which normally six athletes ride together. In the second, major part, the focus is a practical evaluation of the optimal pacing strategies. In cooperation with the sports science department of the University of Konstanz, a laboratory study was carried out to evaluate time gains during rides with optimal strategy feedback compared to self paced rides. The tests were performed on a simulated real world course on a cycling ergometer. Since the results were promising and even for experienced riders a time improvement was achieved, a similar experiment will be conducted in the field in the future. Therefore, a mobile application is currently being developed in order to provide feedback during the ride. In this thesis, the backend functionality for this application, e.g., the evaluation of the position during the ride, is provided. In contrast to the simulated environment in the laboratory, in the field the underlying physical processes are not known exactly. Therefore, the perturbations induced by the slope estimate of the course and the model parameters for rolling resistance, air resistance, and chain efficiency are evaluated and minimized. Additionally, a strategy adaptation based on model predictive control as well as a PID-controller is presented to handle remaining inaccuracies in the model and changing wind conditions. In the end, simulations of the whole process are provided to evaluate the performance of the system under various conditions.