Experimental data-tracking of the BMX SX gate start using biomechanical modeling and trajectory optimization

Introduction During Bicycle Motocross races (BMX SX), the start has been proven to be crucial for good overall performance [1]. Riders reaching the bottom of the eight meter high starting ramp in front of the pack, have a favorable position to perform the first jump and can pick the most ideal line through the first corner. The chances of getting involved in collisions with other riders are also highly reduced. Since riders start behind a gate, the anticipation and timing with respect to this gate movement are most important [2]. Most scientific research regarding the BMX SX gate start is focused on defining the performance indicators for a fast start [2] [3] [4] or using in-field experimentsto evaluate the effects of minor changes to the bicycle design [5] [6]. However, using the results of these studies to actually improve the start performance would require extensive training using these new conditions. Using predictive simulations, these adaptations can be evaluated without practicing and can thus have a huge contribution to enhancing the gate start technique. However, before these simulation models can have any impact, they must be thoroughly analyzed to prove their validity.Objective The main goal for this study was to construct a biomechanical model for the BMX SX gate start which could reproduce experimental data. The model must be able to track kinematic data with an accuracy of less than 5% while also match the main kinetic characteristics without tracking those. The kinetic profiles should show the same peak pattern as is commonly seen in cycling and must not differ more than 10% with experimental data. When these goals are reached, this model could serve as a framework for future applications within BMX SX gate start research or other cycling disciplines.Method A nine degree-of-freedom biomechanical planar model was created within the open-source software package OpenSim [7] [8]. The model consists out of the ground surface, the gate, the BMX SX bicycle, and the rider. The latter two are connected using kinematic constraints on the feet and pedals. The upper body is connected to the frame by a single arm. The model is driven by eight optimal torque actuators located at the hip, knee, ankle, shoulder, and elbow joints. The contact dynamics of the wheels to the ground and the gate are included using the Hunt-Crossley model [9]. Moco [10], a direct collocation package for OpenSim, was used to solve the kinematic tracking optimization problem. The kinematic data was taken from a prior study by Melle van Dilgt [11] who captured three-dimensional kinematics of an elite female BMX SX athlete of the Dutch National team using an Xsens suit (Xsens Technologies, Enschede, The Netherlands). This IMU data was projected on the planar model using OpenSense, a tool within OpenSim that converts experimental IMU data into the model’s generalized coordinates. Simulation outcomes were compared to kinetic data collected by Hylke van Grieken [4], who used a fully instrumented bicycle including special cranks (Axis2D, Swift Performance, Brisbane, Australia) to capture the pedal forces executed during in-field experiments with a sample rate of 100 Hz. These experiments used the same elite participant but were taken on a different day using a different bicycle.Results The optimized tracking simulation showed close agreement with experimental kinematic data, showing an average root mean squared error (RMSE) of 0.337° or 0.52% for the six leg joints. For the tracking of the crank angle and the horizontal displacement of the bicycle similar results were found (RMSEs of 0.079% and 0.6% respectively). Simulated crank torque peak values were off by 4.4%, 7.7%, and 5.1% for the first, second and third torque peak respectively. Overall the crank torque was reproduced with an RMSE of 18%.Conclusion This work shows the suitability of the designed model for future applications in predictive simulation of the BMX SX gate start. The model can be used to study a wide range of "what-if" scenarios and could lead to the improvement of gate start performance. The way the model is constructed, the main building blocks can be adjusted to more accurate, but also more complex, components if desired.