Differential geometric structures in vehicle lane keeping and roll mitigation

This paper uses a geometric framework to create a control scheme designed to prevent road departure and vehicle roll-over. The system is based on making the closed-loop dynamics analogous to a dissipative mechanical system with a degenerate kinetic energy (a kinetic energy that is zero for some nonzero velocities), using the concept of metric compatible affine connections. Some propositions are given concerning the possibility of implementing the desired closed loop dynamics when the system is underactuated. They are applied to the task of preventing vehicle roll-over and road departure, where the system is underactuated due to the lack of direct actuation of the roll mode. An example from simulation is presented for illustration.