Observations on the controllability of motion of two-wheelers

This paper presents an investigation into the motion of two-wheelers: Everyday motorcycles and bicycles. The emphasis is on controllability of the system for small lateral deviations from straight running under idealized rider control. After introduction, a discussion of the kinematics, assumptions and geometry of a rider-vehicle system is presented, followed by a statement of the equations of motion. The control systems analogy is briefly reviewed, and state space methods formalize the concept of controllability. The difficulty in steered riding is quantified by the ratio of maximum to minimum singular values of the controllability Grammian and rideability is investigated for different designs of (a) a motorcycle from a well-known study and (b) a bicycle from a recent investigation. New insight into controlled two-wheeler behaviour is shown, compared with traditional methods, and can provide another means to design for a safety of vehicle performance.