| 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. |