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A multibody model for riderless bicycle dynamics considering tire characteristics is presented. A riderless bicycle is regarded as a multibody system consisting of four rigid bodies: rear wheel, frame, front fork, and front wheel. Every two bodies are connected with a revolute joint. The mass center coordinates and Euler angles of the rigid bodies are used as the generalized coordinates to describe their positions and orientations. The system equations of motion are obtained using Lagrange equations of the first kind. Due to the existence of the three revolute constraints and the use of dependent generalized coordinates, the Lagrange multipliers are employed to account for revolute reaction forces. As for the contact between the wheel and the ground, many studies regarded the wheel as a rigid body with a knife edge, which lead to the nonholonomic constraints between the wheel and the ground.

The present study introduces a novel approach for achieving path tracking of an unmanned bicycle in its local body-fixed coordinate frame. A bicycle is generally recognized as a multibody system consisting of four distinct rigid bodies, namely the front wheel, the front fork, the body frame, and the rear wheel. In contrast to most previous studies, the relationship between a tire and the road is now considered in terms of tire forces rather than nonholonomic constraints. The body frame has six degrees of freedom, while the rear wheel and front fork each have one degree of freedom relative to the body frame. The front wheel exhibits a single degree of freedom relative to the front fork. A bicycle has a total of nine degrees of freedom.