Quaternion-Based Kinematic Modeling and Control for Differential Drive Mobile Robots

The paper presents a quaternion-based model of the kinematic differential equation for a differential drive mobile robot that is subject to the rolling-without-slipping constraint. The proposed kinematic differential equation differs from the commonly utilized kinematic differential equation in that it contains no trigonometric functions. The most intensive mathematical operation is a squaring operation. This trait lends the model well to use on microcontrollers possessing only multipliers. Emphasizing this computational improvement, the paper presents several numerical tests showing that this feature results in significantly faster computation times on embedded devices. Lastly, the paper presents a control law that is implemented in terms of quaternions. This control law also contains no trigonometric functions and its most intensive mathematical operation is a square root operation. Effectiveness of the control law is shown via numerical simulation.