Optimal control of a Two-Mass Skate bicycle without steering

Until recently it was believed that the ability of riderless bicycles to remain upright derives from a combination of the gyroscopic precession of the front wheel and the trail designed into the steering geometry. As it turns out neither influence is necessary for straight-running stability. It is also believed that rider steering torque and/or a roll moment applied to the main frame are required for steering. We show that this long-standing belief is also untrue. All the optimal-control calculations presented are computed off-line.