New Algorithms for Navigating a Gantry Tractor Comprising a “Chorus Line” of Synchronized Modules

This paper presents two new algorithms for real-time calculation of the wheel angles and speeds of gantry tractor modules. In transport mode, the gantry tractor is, in a sense, a snakelike robot with passive joints and active wheels, with each module having autonomous four-wheel drive and four-wheel steering. The algorithms determine the wheel angles and speeds of each module with the prescription that the four wheels will have the same center of curvature, wheel speeds provide cooperative redundancy, and all hitching points follow the same path, thereby eliminating scuffing and minimizing off-tracking. Details of the analytical algorithm for a predetermined path were presented at the 2009 IEEE International Conference on Industrial Technology, together with a simulation for a single module. In this paper, we also present the results of a newly developed numerical algorithm which enables the gantry tractor to be steered online by an operator. We also show, by simulation, that this new numerical algorithm gives a good approximation to analytical solutions. The numerical algorithm is then used to calculate wheel angles and speeds for a three-module tractor with the results depicted graphically as functions of time.