SLICOT Drives Tractors !

We describe the successful application of a SLICOT subroutine in a control engineering problem. Based on GPS data it is possible to automatically steer farm vehicles along a prescribed trajectory. The bottleneck for the successful on-line implementation of a LQG regulator is the numerical solution of a discrete-time algebraic Riccati equation in real-time and at high accuracy. This is achieved employing a For-tran 77 subroutine from the Subroutine Library in Control Theory | SLICOT. 1 Motivation In control engineering applications, the numerical solution of one of the fundamental matrix equations of linear control theory often causes a bottleneck for its successful realization. Here we will describe one such application, the automatic steering of a farm tractor, in which this situation occurs. By using a SLICOT subroutine, the problem is resolved, i.e., the used subroutine yields a numerical solution with suucient accuracy and in due time. Through the development of ever more cheap and reliable GPS (Global Positioning System) receivers, automatic steering of ground vehicles along prescribed trajectories has become an attractive research topic for several reasons: hazardous operations can be performed without risking human life, cars may be automatically piloted to the desired destination (\smart highways" { an ongoing research project for several decades), maneuvering at high precision, etc. One of the rst elds of application are vehicles used for farming on the large elds of Northern America. As farm vehicles usually move at moderate speed and agricultural elds usually are ideal in order to operate GPS properly as nothing blocks the GPS signals, they are among the rst ones for which such a technology becomes feasible for industrial application.