The development of computationally efficient and validated single-track vehicle-rider models has traditionally required handcrafted one-off models. Here we introduce BRiM, a software package that facilitates building these models in a modular fashion while retaining access to the mathematical elements for handcrafted modeling when desired. We demonstrate the flexibility of the software by constructing the Carvallo-Whipple bicycle model with different numerical parameters representing different bicycles, modifying it with a front fork suspension travel model, and extending it with moving rider arms driven by joint torques at the elbows. Using these models we solve a lane-change optimal control problem for six different model variations which solve in mere seconds on a modern personal computer. Our tool enables flexible and rapid modeling of single-track vehicle-rider models that give precise results at high computational efficiency.@en

The ollie is the base aerial human–board maneuver, foundational to most modern skateboarding tricks. We formulate and solve an optimal control problem of a two-dimensional simplified human model and a rigid body skateboard with the objective of maximizing the height of the ollie. Our solution simultaneously discovers realistic human-applied force trajectories and optimal board geometry. We accomplish this with a direct collocation formulation using a null seed initial guess by carefully modeling the discontinuous aspects of board–ground impact and foot–board friction. This leads to efficient and robust solutions that are 10 times more computationally efficient than prior work on similar problems. The solutions show that ollie height can increase 3% by decreasing the wheelbase and that a smaller board with a back-foot-dominated force strategy can give 12% higher ollies. Our model can be used to inform jump strategy and the effects of changes to the essential board geometry.

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