Point-to-point and collision avoidance control of the motion of an autonomous bicycle

Given two points rA, rB, and a circular obstacle in the horizontal plane. Also, given a time interval [0, tf], where 0 < tf < ∞. It is shown here that by applying a kind of inverse dynamics control, the motion of the bicycle is stabilized while simultaneously controlling its speed and direction in such a manner that the point of contact between the bicycle's rear wheel and the horizontal plane will be able, during [0, tf], to move from rA to rB without hitting the obstacle.