A statistical approach for uncertain stability analysis of mobile robots

Stability prediction is an important concern for mobile robots operating in rough environments. Having the capacity to predict areas of instability means pro-actively being able to plan safer traversable paths. The most influential tip-over stability measures are based on two criteria, the robot´s center of mass (CM) and the supporting polygon (SP) defined by the convex area spanned between the ground contact-points. However, there is significant uncertainty associated with many parameters in the planning pipe-line: the actual robot kino-dynamic model, its localisation in the ground, and the terrain models, particularly in uneven terrain. This article proposes a statistical analysis of stability prediction to account for some of the uncertainties. This is accomplished using the force angle (FA) stability measure for a reconfigurable multi-tracked vehicle fitted with flippers, a manipulator arm and a sensor head. Probability density function (PDF) of contact-points, CM and the FA stability measure are numerically estimated, with simulation results performed on the open dynamics engine (ODE) simulator based on uncertain parameters. Two techniques are presented: a conventional Monte Carlo scheme, and a structured unscented transform (UT) which results in significant improvement in computational efficiency. Experimental results on maps obtained from a range camera fitted on the sensor head while the robot traverses over a ramp and a series of steps are presented that confirms the validity of the proposed probabilistic stability prediction method.