Investigation of optimal descent trajectories using feedback control for the Olympic sport of bob-skeleton

In the Olympic sport of Bob-Skeleton, the athletes compete to achieve the fastest possible descent of an ice track lying prone on a sled in contact with the ice via two circular section steel runners. Their elapsed time of descent is influenced by their speed after the initial sprint phase, aerodynamics and ice friction and critically their skill as a slider in being able to steer down the ‘best’ trajectory. Minimising the number and magnitude of steering control interventions is seen as key to minimising energy loss and hence achieving a fast time. Tracks typically have 12 to 14 corners, descend about 150 m vertically over a track length of 1500 m or so. A physics based simulation developed by the University of Southampton was used as a test environment to investigate the fastest route of descent for a three dimensionally accurate bobskeleton track. This simulation captures the inertial, gravitational, centripetal, friction and aerodynamic forces and moment acting on the slider and their sled. As the descent time is so short, 50 - 60 seconds, sliders prepare for events by walking the track and ‘learning’ the best route under the guidance of their experienced coaches. The simulation analysis was limited to computing the descent time for the coach specified trajectory. The aim of this research was to investigate how the optimum trajectory down a track can be determined. In order to do this it was necessary to develop a suitable control method to evaluate whether a potential trajectory was feasible. A series of control algorithms were investigated and simulation times compared to those achieved in competitions to verify the approach. This thesis has established that control laws can be used to ensure path following during descent. The control law used, in the main, was of the proportional plus derivative form but promising initial results were also obtained for model based control laws, such as model predictive control