Analytical procedures for determining global minimum friction requirement for a six wheeled rover negotiating hard uneven terrain

Abstract

The problem of determining wheel torques of a rover, to minimize friction requirement, has been addressed by many researchers. We address it by trying to understand the ways in which local optima can occur, and on the basis of that understanding, develop analytical and non-iterative algorithms for determining global optima. The problem is posed in two variations, with normal reaction forces on wheels bounded below by (a) zero, and (b) a positive limit. In both cases, the nature of optima is studied comprehensively, and illustrated by solving examples. Explicit expressions are used to find roots of up to a cubic polynomial. Our algorithms are on the average about an order of magnitude faster than an SQP based general optimization solver, when the latter is started from random guesses. Moreover, our algorithms were able to reach global minima without fail for all examples solved, which number more than a thousand.