Adaptive feedback system for optimal pacing strategies in road cycling

Abstract

In road cycling, the pacing strategy plays an important role, especially in solo events like individual time trials. Nevertheless, not much is known about pacing under varying conditions. Based on mathematical models, optimal pacing strategies were derived for courses with varying slope or wind, but rarely tested for their practical validity. In this paper, we present a framework for feedback during rides in the field based on optimal pacing strategies and methods to update the strategy if conditions are different than expected in the optimal pacing strategy. To update the strategy, two solutions based on model predictive control and proportional-integral-derivative control, respectively, are presented. Real rides are simulated inducing perturbations like unexpected wind or errors in the model parameter estimates, e.g., rolling resistance. It is shown that the performance drops below the best achievable one taking into account the perturbations when the strategy is not updated. This is mainly due to premature exhaustion or unused energy resources at the end of the ride. Both the proposed strategy updates handle those problems and ensure that a performance close to the best under the given conditions is delivered.

Prediction of pacing and cornering strategies during cycling individual time trials with optimal control

“…In spite of the limitations, this work represents a stepforward in the current literature: it follows and extends the work of Maroński [15], Swain [61], Gordon [16], and Wolf et al [20], and takes the problem of pacing strategy calculation during ITT races to a next level of complexity and potential. This framework currently represents one of the few published tools (other examples are [43] or [62]) that can be used to evaluate the interplay between the physical/ physiological characteristics, the 3D road geometry, the race-day conditions, the pacing/cornering strategies, and the overall ITT performance.…”

“…(2) the coordinate n (m) defines the lateral displacement; and (3) the heading (rad) defines the orientation of the bicycle with reference to the heading of the road. The equations of motion were written in terms of space coordinate s [20,37]. Equation 1 describes the dynamics of the heading of the bicycle (s):…”

“…The calculation of the pacing strategy requires the combination of a cycling model with a dynamic optimisation tools. For example, an optimal control problem can be formulated [15][16][17][18][19][20], where the objective is to minimise the arrival time by appropriate selection of the power output distribution. In these optimal control problems, the physiological constraints such as the anaerobic sources depletion are typically included by means of the critical power model [21,22].…”

“…Given that the experimental velocity and power distributions are stereotypical between different cyclists, the model simulations were compared with the mean of all the riders in the sample. Additionally, a 1D model was used to represent the current state-of-the-art in the literature [20] and web-based tools (e.g., https ://www.bestb ikesp lit.com/bestb ikesp lit.com).…”

Influence of corners and road conditions on cycling individual time trial performance and ‘optimal’ pacing strategy: A simulation study

“…A virtual rider with the characteristics of an average professional cyclist 18 was included in the model. A modified critical power model 19 was used to describe the depletion of the rider’s anaerobic sources. 20 Maximal power output level was 1870 W, critical power was 386 W and initially available anaerobic sources were set to 27,000 J.…”