Planned Trajectory Classification for Wheeled Mobile Robots to Prevent Rollover and Slip

In this paper, a novel planned trajectory classification method (PTCM) is proposed to evaluate the safety of the car- like four-wheeled mobile robots (4-WMRs) with Ackermann steering and high-stiffness suspensions. To classify a planned trajectory to be safe or unsafe before the 4-WMR actually follows it, the conditions of the wheel forces (WFs: longitudinal, lateral, and normal forces for each wheel) necessary to execute the planned trajectory without rollover and slip are calculated using the passive decomposition of the WMR dynamics with the Pfaffian constraints of the no-rollover and no-slip conditions. Similar to the case of Navier's table problem, only nine-dimensional WFs projected onto the constrained space are identifiable among the twelve-dimensional WFs. This indeterminacy turns out not to affect the rollover prediction, yet does so for the slip prediction. For this, we propose novel optimistic and pessimistic methods, together upper and lower bounding the exact slip prediction. The proposed PTCM classifies the planned trajectory as safe if rollover and slip are not predicted and unsafe otherwise. The proposed PTCM is demonstrated and validated by simulations and outdoor experiments.