A Path Tracking Method for an Unmanned Bicycle Based on the Body-Fixed Coordinate Frame 2024-01-2303

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. The expression of the kinetic energy of a bike is formulated using quasi-coordinates in the local body-fixed coordinate frame, which provides a more simplified representation compared to the utilization of absolute coordinates in the global coordinate frame. The acquisition of the dynamic model involves the substitution of the expression of kinetic energy into the Lagrange equation. The application of the Lagrange equation of the second kind is computationally efficient but the derivation is difficult. The derivation using the Lagrange equation of the first kind is relatively simple, but its computational efficiency is poor. The present study combines two methods by dividing the bicycle from the steering pivot into two rigid body groups, applying the Lagrange equation of the second kind in each group, and then applying the Lagrange equation of the first kind to both groups. This method is simple to derive and has good computational efficiency. The path is strategically organized in the body coordinate frame to circumvent possible singularity issues in the global coordinate frame. A dual-loop PID controller is implemented to achieve path tracking where the inner loop controller is responsible for maintaining the stability of the bicycle, while the outer loop controller ensures that the bicycle follows the desired path.