Coupled lateral-longitudinal vehicle dynamics and control design with three-dimensional state portraits

The dynamics of vehicles with pneumatic tyres are well-known to be non-holonomic, nonlinear, and subject to state bounds in order to remain on defined roadways. As such, it can be challenging to apply many of the tools typically used to analyse nonlinear dynamics and synthesise control strategies. Furthermore, the use of traditional stability analyses is often insufficient for vehicle control design since adherence to the roadway geometry implies a constrained space that dictates stricter conditions on the states than provable stability. A two-state phase portrait approach has been used to analyse vehicle dynamics and provides an illustrative view of the state trajectories at constant speed. This paper extends the phase portrait to three states to represent the nonlinear vehicle dynamics with steering and longitudinal tyre force inputs and consideration of the longitudinal vehicle dynamics. The concept of a fixed point in the phase plane is extended to a stable curve and example controllers are examined and synthesised using the three-dimensional vector space.