Similarity conditions for comparing closed-loop vehicle roll and pitch dynamics

Previous work has demonstrated that dynamic matching and similitude between controllers can be achieved for planar dynamic motion by careful construction of the test vehicle and testing under conditions that match selected parameters. Central to this analysis was the use of the Buckingham Pi theorem as applied to the planar vehicle dynamics. Increasingly, scale vehicle testbeds are being used to investigate non-planar dynamics such as roll, pitch, and jackknifing for tractor-trailer systems, but little investigation has been given to conditions of dynamic similarity in these cases. Additionally, some authors have questioned how to scale non-kinematic dynamics that also influence chassis behavior, for instance ABS subsystems or actuator dynamics. This work presents solutions to these questions by presenting methods to derive conditions for similitude for non-planar and non-kinematic dynamic motion.