Abstract Stability of rider-controlled bicycles is related to the appropriate coupling between leaning and steering. Inspired by this driving experience, we propose a linear control law between steer and lean angles to balance motion of an unmanned bicycle. The selection of the control parameters is based on stability analysis for the controlled bicycle dynamics, in which the control law and the constant rear-wheel velocity ω0 serve as servo-constraints imposed to the bicycle system. To facilitate the stability analysis of the controlled motion, we use tools from geometric mechanics to reduce the bicycle's dynamics, leading to a two-dimensional dynamic system. We thereafter study its relative equilibria and related stability. Theoretical results show that there is a critical value of ωc, above which the bicycle can move in a stable uniform straight forward motion, and below which a pair of relative equilibria related to stable uniform circular motion exist. The driving rule of steering toward a fall (STF) and counter-steering (CST) can also be explained theoretically. Finally, we fabricate a powered autonomous bicycle and propose an error correction algorithm to eliminate the drift error of the gyroscope sensor. Our experimental results are in good agreement with the theoretical predictions. Generally, this paper presents the mathematical basis for designing the more advanced and intelligent autonomous bicycles, and may find potential applications in other vehicle systems.

Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics falls under a branch of physics known as classical mechanics. Bike motions of interest include balancing, steering, braking, accelerating, suspension activation, and vibration. The study of these motions began in the late 19th century and continu Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics falls under a branch of physics known as classical mechanics. Bike motions of interest include balancing, steering, braking, accelerating, suspension activation, and vibration. The study of these motions began in the late 19th century and continues today. Bicycles and motorcycles are both single-track vehicles and so their motions have many fundamental attributes in common and are fundamentally different from and more difficult to study than other wheeled vehicles such as dicycles, tricycles, and quadracycles. As with unicycles, bikes lack lateral stability when stationary, and under most circumstances can only remain upright when moving forward. Experimentation and mathematical analysis have shown that a bike stays upright when it is steered to keep its center of mass over its wheels, that is in line with the resultant force of gravity and centrifugal force. This steering is usually supplied by a rider, or in certain circumstances, by the bike itself. Several factors, including geometry, mass distribution, and gyroscopic effect all contribute in varying degrees to this self-stability, but long-standing hypotheses and claims that any single effect, such as gyroscopic or trail (the distance between steering axis and ground contact of the front tire), is solely responsible for the stabilizing force have been discredited. While remaining upright may be the primary goal of beginning riders, a bike must lean in order to maintain balance in a turn: the higher the speed or smaller the turn radius, the more lean is required. This balances the roll torque about the wheel contact patches generated by centrifugal force due to the turn with that of the gravitational force. This lean is usually produced by a momentary steering in the opposite direction, called countersteering. Unlike other wheeled vehicles, the primary control input on bikes is steering torque, not position. Although longitudinally stable when stationary, bikes often have a high enough center of mass and a short enough wheelbase to lift a wheel off the… The…