Modeling and Validation of Free Road with Geometric Parameter Representation for wheeled mobile robots

Road geometric parameters such as turning radius, roadway width, deflection angle and direction are all the constraints when robots passing through a road. When robots know the geometric parameters of the whole road, the control input could be designed in advance and the trajectory could be planned based on the whole road. In this paper, we present an approach to mathematical formulation of a free road which contains multiple curves. We designed a construction to present a free path with the combination of three parts: straight line, spiral and circular arc. Then add the width of the transverse and construct a free road model oriented to robot. Second, we establish the relationship between the trajectory curvature and the velocity which combined the presented road model and the dynamic model of a four-wheeled differential robot. Third, simulation and actual experiments have been carried out to verify the road model and proved that the model can be used to control the robot.