Dynamic Modelling of a 4WD/4WS Ground Vehicle by Using Gibbs-Appell Approach

Abstract

Although most wheeled robotic ground vehicles are either skid steered or differentially steered, there has been an increased interest in four independently driven all-wheel steering systems because of their torque density and maneuverability in tight turns. Controlling these vehicles requires coordination of the steering angles and wheel speeds such that the basic rigid body kinematic constraint on the instantaneous center of rotation (ICR) is satisfied. This makes them difficult to control except for simple cases where either the center of curvature for all turns is constrained to be along the perpendicular bisector to the longitudinal centerline of the vehicle or considerable wheel slippage is allowed to happen. Several efforts have been reported to address this problem, most of which tend to simplify the problem by extending the well-known bicycle model to these vehicles. This paper uses the Gibbs-Appel formulation to develop the equations of motion of a 4WD/4WS vehicle in the quasi-coordinate space while enforcing both the ICR and no slip constraints. Unlike the Lagrange-Euler and the Newton-Euler formulations that use Lagrange multipliers to handle constraints, which increases the dimension of the system, the Gibbs-Appell formulation results in a model of a relatively lower dimension. This model is not only easy to use in control design but also captures the dynamics of the vehicle by constraining the wheels to remain on the path. Simulation results using a simple feedback linearization controller showed the vehicle tracking the path more accurately without wheel slip where the wheels remained on the path all times.