Biking Without Pedaling

It is well known that skilled bicycle riders can balance and propel themselves forward using motions of the handlebar. We present the complete nonlinear dynamics and control of such a pedal-less bicycle with a rider. Propulsion is achieved not by pedaling but by a cyclic motion of the steering axis of the bicycle. It is shown that this kind of actuation results in net forward motion of the bicycle and a building up of momentum. The dynamics of the bicycle and rider in a transverse plane are similar to that of a two link underactuated system where only the second link is actuated. A linear analysis of the bicycle is used to derive a control law for the rider to stabilize the bicycle about its upright position while the periodic motion of the steering axis drives the bicycle forward. After the bicycle attains a higher speed, it is easily stabilizable.