The Rollover Risk in Delta Tricycles: A New Rollover Index and Its Robust Mitigation by Rear Differential Braking

Although there are efforts to electrify and diversify small vehicles, active safety on motorcycles and tricycles (also known as auto rickshaw, tuk-tuk, mototaxi, etc.) has been relegated until a few years ago. For instance, the electric tricycles (even the combustion ones) marketed today do not have an active safety system that prevents or mitigates the risk of rollover, despite how prone they are to such a situation. The concern for the increase in its marketing is latent and, unfortunately, there are very few related studies. In this article, we present the obtaining and validation of a new rollover index for tricycles demonstrating its effectiveness in predicting and detecting the risk, even statically, by means of a simple quantity. In addition, a controller for the mitigation of the risk of rollover is presented which, by means of a Lyapunov type analysis, it is shown to be robust to changes in parameters, such as the center of gravity height, using a polytopic representation of the system and a differential braking strategy on the rear wheels. Numerical simulations, including video simulation captures, of the operation of the rollover mitigation system using widely recognized commercial software, are also presented. This work can be extended to vehicles with a suspension system or for trikes without autocamber.