Terrain mobility performance optimization: Fundamentals for autonomous vehicle applications. Part I. New mobility indices: Optimization and analysis

Based on an analysis of vehicle mobility performance indices in use, it is shown that an index for the optimization of autonomous vehicle mobility performance should be constituted as a set of technical parameters that result directly from the interactive dynamics of tires and terrain and should be measurable and controllable in real-time. In addition, the combination of the parameters should characterize the vehicle’s technical productivity/efficiency (not energy efficiency), and thus, enable the estimation and control of vehicle mobility performance. If such requirements are satisfied, the index can be optimized and optimization results can facilitate autonomous control design. This article provides results of a study to address the above-formulated requirements in the proposed mobility performance index.

In Part I of this article, wheel mobility performance is characterized first by the wheel circumferential force and the actual linear velocity. The proposed wheel mobility performance (WMP) index mathematically relates the wheel circumferential force and velocity to the theoretical maximum performance. Thus, the actual performance can be evaluated in terms of the theoretical maximum performance in a similar manner that the actual energy efficiency is compared to its theoretical maximum, i.e., to unity. The WMP-index is then extended to multi-wheel vehicles. The proposed vehicle mobility performance (VMP) index relates the traction and velocity characteristics of all wheels to a theoretical maximum performance.

Founded on the circumferential force and velocity characteristics of the wheels, the VMP-index mathematically reflects the influence of the power distribution among the wheels on the vehicle mobility performance. Hence, the VMP-optimization is formulated as an examination for the optimal tire slippages. Essentially, their combination characterizes the optimal wheel power split, and consequently, the best set of the wheel circumferential forces and the vehicle actual velocity for the maximum mobility performance in a given terrain condition. The tire slippages are subject to lower and upper bound constraints. The lower bound ensures positive tire slippages, and thus, positive traction of the wheels. The upper bound is imposed in the form of characteristic slippages such that exceeding them drives the wheels into an extremely nonlinear zone of the traction characteristic. In this zone, the wheel mobility margins drop significantly and some or all wheels can easily be immobilized. Further, the optimization is subject to the vehicle longitudinal dynamics, which sets the summation of the wheel circumferential forces equal to the motion resistance forces.

By applying Lagrange Multipliers (LMs) to the objective function, a system of equations is arranged to compute the optimal tire slippages that correspond to the necessary conditions of an extremum of the objective function. The strict monotonicity property of the LM-based equations is then examined and the uniqueness of the solution is exhibited. Finally, the Hessian theory for a constrained optimal problem is used to prove that the solution is globally minimum.

Part II discusses the computational results of mobility performance optimization for a 4x4 vehicle simulated on three homogeneous terrains and split terrains on flat surface and on slopes, with and without drawbar pull. Additionally, the vehicle with three conventional driveline systems is simulated in the same terrain conditions, and a detailed analysis establishes dependences between the optimal tire slippages and optimal circumferential forces of the wheels and their correlation to those provided by the driveline systems. Advantages of the mobility optimization for control design are explained and discussed. It is also concluded that the use of energy efficiency indices in mobility performance assessment can be considered as a supplementary, but not the primary subject-heading of the vehicle mobility performance.

The mobility performance optimization directly contributes to mobility design that is illustrated by conceptual implementation of the optimization results in two driveline systems of the 4x4 vehicle: a driveline with positive engagement of the power-dividing units and a virtual driveline that serves for fully electric vehicles with in-wheel motors.

Finally, a verification of the mobility optimization results and validation of the proposed mobility performance index is conducted through statistics-based assessment against experimental wheel circumferential forces and tire slippages.