Powerbike - Model-based optimal control for cycling
Final Report Abstract
Modern sensor technology for GPS signals, heart rate, oxygen uptake, and cycling power has made it possible to monitor and quantify road cycling performance in the lab, during training, and even in competitions. In this project we contributed to modeling, prediction, and optimization of road cycling performance by designing, calibrating, and validating mathematical physiological models that provide the means to analyze and predict cycling performance, and methods to compute optimal pacing strategies for cycling time trials based on these models. The research project was interdisciplinary including computer science and sports/exercise science, and it combined method development with implementations and validations in laboratory and field tests. A time trial in road cycling refers to a competition in which each cyclist individually races against the clock on a fixed course. A pacing strategy for such a race informs the athlete about how to expend his or her power to achieve the best result, i.e., the minimal time to reach the finish line. In the literature and in current practice, pacing is qualitative and rule-based. For example, a coach may recommend to generally ride at a certain power output and to increase the effort by 20–40 Watts on uphill road segments. The main goal of this research was a more specific pacing strategy that prescribes for any point along the track precisely the power output in Watts that the athlete should deliver for propulsion. In practice, such a strategy must be communicated to the rider during the course by an instrument like a handlebar mounted, programmable smartphone or a commercial bike computer. In order to compute such optimal pacing strategies, two mathematical models are required. The first one is a mechanical model that relates the pedal power to the speed along the entire track that must be given as a geometric model. There are numerous parameters that need to be calibrated such as rolling and aerial resistance, total system weight, and frictional loss in the drive chain. The second model is required to quantify the performance limits and remaining energy resources of the rider during the exercise, in particular the point of exhaustion. For an optimal performance, complete exhaustion must occur precisely at the finish line of the track. Again, the model must be adapted to the athlete by calibration of its parameters, among them so-called critical power and total anaerobic energy. These mathematical models must be given in a suitable form such that numerical algorithms of optimal control can be applied. This project contributed to all of these components, starting with the development of methods for parameter calibration and design and selection of the physiological model. In particular, the state-of-the-art for modeling oxygen consumption as a function of power and time was generalized from the constant work-rate case to a dynamic model allowing for variable power output. Several variations of the basic critical power model for performance were analyzed. The resulting equations do not easily lend themselves for numerical solution, and required researching suitable reparametrization and regularization methods for implementation in a number of computing packages for numerical optimal control. Besides this basic work, the optimal strategies and their visual feedback to the athlete were implemented in a custom made Android based smart phone application, as well as for application in a commercial bike computer. An adaptation of the optimal strategy was also developed based on current state-of-the-art engineering practice. Such an adaptation should be made when deviations of riding conditions from the ones used in the computation or deviations of the applied pacing from the optimal one occur. Our optimal pacing strategies were tested in severals experiments. The first one was a lab test on a simulator providing the advantage over field rides that the simulated riding conditions could be strictly controlled. We have developed a testing methodology that separates the contribution of the optimal pacing from the effect of just using a pacemaker. It clearly confirmed the potential of the optimal strategies to improve cycling performance. A second series of trials was carried out in the field using smartphones with our app for visual feedback of the pacing. The results show that our app can guide cyclists on precomputed optimal pacing strategies using adaptation algorithms and improve their finish time. For the future, we are planning to modify the technology to be applicable in a broad sense for hobby and amateur riders without requiring elaborate testing for parameter settings. This can be achieved by making use of recorded rides on a social media platform for GPS based activities for calibration, by minimizing the required energy to reach the finish line of an uphill time trial in a desired time specified by the user, and by using a common bike computer giving feedback in the form of time ahead resp. behind the optimal pacing strategy. We have applied optimization also for the cases of systems of two cooperating respectively competing riders, by modeling and incorporating the slipstream effect. The method for cooperating riders can show how often the lead position of the riders should be swapped for optimal performance of the team. The one for competing riders can show, when the drafting rider should overtake the leading one for the final sprint.
Publications
- (2019) Adaptive feedback system for optimal pacing strategies in road cycling. Sports Eng (Sports Engineering) 22 (1)
Wolf, Stefan; Biral, Francesco; Saupe, Dietmar
(See online at https://doi.org/10.1007/s12283-019-0294-5) - Visual feedback for pacing strategies in road cycling, Proceedings spinfortec, 12th Symposium of the Section of Sportinformatik und Sporttechnologie der Deutschen Vereinigung fur Sportwissenschaft (dvs), pp. 76–77
Artiga Gonzalez, A., Wolf, S., Bertschinger, R., Saupe, D.
- Modeling VO2 and VCO2 with Hammerstein-Wiener models, Proceedings of the 4th International Congress on Sport Sciences Research and Technology Support (icSPORTS 2016), pp. 134–140, Nov. 2016
Artiga Gonzalez, A., Bertschinger, R., Saupe, D.
(See online at https://doi.org/10.5220/0006086501340140) - Road cycling climbs made speedier by personalized pacing strategies, Proceedings of the 4th International Congress on Sport Sciences Research and Technology Support (icSPORTS 2016), Vol. 1, pp. 109–114, Nov. 2016
Wolf, S., Bertschinger, R., Saupe, D.
(See online at https://doi.org/10.5220/0006080001090114) - Robust computation of minimum-time pacing strategies on realistic road cycling tracks, 11. Symposium der dvs-Sektion Sportinformatik, Sportinformatik, K. Witte, N. Bandow and J. Edelmann-Nusser (eds.), pp. 96–101, Magdeburg, September 2016, Shaker Verlag
Dahmen, T., Brosda, F.
- How to accurately determine the position on a known course in road cycling, Proceedings of the 11th International Symposium on Computer Science in Sport (IACSS 2017), Advances in Intelligent Systems and Computing (AISC, Vol. 663), Springer Verlag, pp. 103–109, 2017
Wolf, S., Dobiasch, M., Artiga Gonzalez, A., Saupe, D.
(See online at https://doi.org/10.1007/978-3-319-67846-7_11) - How to stay ahead of the pack: Optimal road cycling strategies for two cooperating riders, International Journal of Computer Science in Sport, Vol. 16, No. 2, pp. 88–100, December 2017
Wolf, S., Saupe, D.
(See online at https://doi.org/10.1515/ijcss-2017-0008) - Kinetic analysis of oxygen dynamics under a variable work rate, Human Movement Science, 2017
Artiga Gonzalez, A., Bertschinger, R., Brosda, F., Dahmen, T., Thumm, P., Saupe, D.
(See online at https://doi.org/10.1016/j.humov.2017.08.020)
