Analysis of Toe-In Braking in Longitudinal Motion for 4WIS4WID EV

This paper presents toe-in braking in the longitudinal motion of a four-wheel independent steering four-wheel independent drive (4WIS4WID) electric vehicle (EV) in its heading direction. The steering function in these EVs allows achieving toe-in braking without any significant modification of the hardware. It uses an established mathematical model of 4WIS4WID EV and slightly modifies an existing path-tracking control scheme to achieve toe-in braking. The toe-in algorithm uses a feed-forward scheme with two serial components: The first helps specify the required deceleration rate, while the second helps compute the toe-in angle that helps meet this deceleration rate. Analysis shows effect of varying toe-in angle on forces and slips during braking, and on stopping time. Analysis for input-to-state stability of the said modified scheme helps develop a constraint on allowable toe-in angles. It simulates two situations with toe-in braking. The first involves velocity tracking in an open-loop configuration, while the second involves path tracking using a closed-loop configuration. Simulation results agree with the above analysis.