The Ollie: A Case Study in Trajectory Optimization with Varied Contacts

Modelling the discrete dynamics of contacts with objects and the environment is a challenging aspect of trajectory optimization. In this paper, we use the ollie, a skateboarding manoeuvre, as case study to develop formulations for a variety of contact types: the elastic collision between the skateboard tail and the ground, the inelastic collision between the wheels and a ground surface with discrete changes in height, and the interaction between the skateboarder's feet and the skateboard - an inelastic, frictional contact that can be applied anywhere on the skateboard's surface. With the exception of the tail-ground interaction, all formulations are unscheduled. The model we developed was able to replicate the key phases of the ollie motion, but comparison of the ground reaction force profiles to those in the literature indicates that further development is necessary for it to be a sufficiently accurate model for biomechanical analysis. The contact models behaved as expected, however, and they could easily be applied to other problems such as robotic motion planning.