Research Paper: AEdAutomation and Emerging Technologies Minimising the non-working distance travelled by machines operating in a headland field pattern D.D. Bochtis*, S.G. Vougioukas Aristotle University of Thessaloniki, Faculty of Agriculture, Department of Agricultural Engineering, Box 275, 54124 Thessaloniki, Greece article info Article history: Received 29 November 2007 Received in revised form 6 June 2008 Accepted 18 June 2008 Published online 6 August 2008 When treating an area of field using agricultural equipment, the field is usually traversed by a series of parallel tracks using a pattern established by the experience of the operator. At the end of each track the process is constrained by the ability of the operator to distin- guish the next track to be followed. The introduction of commercially available auto- steering or navigation-aid systems for agricultural machines has made it possible to upload arbitrary field pattern sequences into programmable navigational computers and for the machines to follow them with precision. This new technology also offers a new perspective for improving machine field efficiency, since not all field traversal sequences are similar in terms of total non-working distance travelled. This paper presents an algorithmic approach towards computing traversal sequences for parallel field tracks, which improve the field efficiency of machines by minimising the total non-working distance travelled. Field coverage is expressed as the traversal of a weighted graph and the problem of finding an optimum traversing sequence is shown to be equiva- lent to finding the shortest route in the graph. The optimisation is formulated and solved as a binary integer programming problem. Experimental results show that by using optimum sequences, the total non-working distance can, depending on operation, be reduced by up to 50%. ª 2008 IAgrE. Published by Elsevier Ltd. All rights reserved. 1. Introduction Modern agricultural machines are, in theory, capable of achieving very high performance in terms of work rate and quality. A measure of machine performance during field oper- ations is its field efficiency, E f , which is defined (ASAE, 2005) as the ratio between the productivity of the machine under field conditions and the theoretical maximum productivity. Field efficiency is not a constant for a particular machine, but varies with the size and shape of the field, pattern of field operation, crop yield, crop moisture, and other conditions. In particular, the pattern of field operation affects very much the time lost in the field due to non-working travel (Hunt, 2001). A large por- tion of the non-working time occurs during turning and the strong negative influence of turning time on field efficiency has been verified experimentally in grain harvesting opera- tions (Taylor et al., 2002; Hansen et al., 2003), as well as by using simulation tools (Benson et al., 2002). When turning on the headland non-working time depends on the distance travelled during turning (i.e., the length of the manoeuvre), and the mean turning speed. Some types of ma- noeuvre are easily executed and consequently can be executed at high speed, while other types demand skilful driving, or even reversing, resulting in lower mean speeds and requiring * Corresponding author. E-mail address: dionmpo@agro.auth.gr (D.D. Bochtis). Available at www.sciencedirect.com journal homepage: www.elsevier.com/locate/issn/15375110 1537-5110/$ – see front matter ª 2008 IAgrE. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.biosystemseng.2008.06.008 biosystems engineering 101 (2008) 1–12