The agricultural vehicle routing problem lies under the broad category of Stochastic Dynamic VRP

These are simplifying assumption, as it has been shown that proper row sequences reduce total turning time substantially . However, dropping this assumption would require solving a routing optimization problem inside the loop that iterates through driving orientations, and many maneuvering/turning motion planning problems inside each route optimization; this would be very expensive computationally. Furthermore, all algorithms use a swath of fixed width, implicitly assuming that the field will be covered by one machine, or many machines with the same operating width. Relaxing this assumption has not been pursued, but the problem would become much more complicated. Planning could also be extended to non-straight driving patterns using nonlinear boustrophedon decompositions based on Morse functions , with appropriate agronomic, cultivation and machine constraints. Finally, as pointed out by Black more , row cultivation was historically established because it is easier to achieve with animals and simple machines. Crops do better when each plant has equal access to light, water and nutrients. Small robots could grow crops in grid patterns with equal space all around by following arbitrary driving patterns that may be optimal for the cropping system and the terrain. Hence the boustrophedon assumption could be relaxed and approximate cellular decomposition could be used to compute optimal driving patterns, where field shape is approximated by a fine grid of square or hexagonal cells. This approach has received very little attention,custom grow rooms as field spatial planning has targeted existing large machines. An example of early work in this direction combined route planning and motion planning, with appropriate agronomic, cultivation and machine constraints .

The basic version of route planning computes an optimal traversal sequence for the field rows that cover the field, for a single auto-guided machine with no capacity constraints. This is applicable to operations in arable land, orchards and greenhouses that do not involve material transfer or, when they do, the quantities involved are smaller than the machine’s tank or storage space; hence the machine’s limited storage capacity does not affect the solution. For operations where the machine must apply or gather material in the field the maximum number of rows it can cover is restricted by its capacity; the same applies to fuel. Hence, route planning with capacity constraints is a more complicated version of the problem. When many machines operate in the same field there are two classes of operations which have different characteristics. The first class is when machines are independent of each other, i.e., they do not share any resources. In such cases, coordinated route planning is straightforward because the machines can simply work on different swaths or sub-fields of the field; possible crossings of their paths at the headlands and potential collisions can be resolved during task execution. The second class is cooperative field operations, also known as in-field logistics, which are executed by one or more primary unit/s performing the main task and one or more service unit/s supporting it/them. For example, in a harvesting operation a self propelled harvester may be supported by transport wagons used for out-of-the field removal of harvested grain . Similarly, in fertilizing or spraying operations the auto-guided spreader/sprayer may be supported by transport robots carrying the fertilizer/sprayer for the refilling of the application unit. Agricultural tasks are dynamic and stochastic in nature.

The major issues with off-line route planning are that it breaks down in case of unexpected events during operations, and it can only be performed if the “demand” of each row is known exactly in advance. For example, if a sprayer’s flow rate is constant or the crop yield is known in advance, the quantity of chemical or harvest yield of each field row can be pre-computed and optimal routing can be determined. However, yield maps are either not available before harvest or their predicted estimates based on sampling or historic data contain uncertainty. Also, robotic precision spraying and fertilizing operations are often performed “on-the go” using sensors, rather than relying on a pre-existing application map. Hence, information is often revealed in a dynamic manner during the execution of the task. Vehicle routing for agricultural vehicles is based on approaches from operations research and transportation science. Optimal row traversal for a single or multiple independent auto-guided vehicles has been modeled and solved as a Vehicle Routing Problem . This methodology was conceptually extended to include multiple identical collaborating capacity-limited machines with time-window constraints, and to nonidentical vehicles . A review of similar problems in transportation science is given in . The problem of visiting a set of known, pre-defined field locations to take measurements or samples is not an area coverage problem, and was recently modeled as an orienteering problem for non-collaborating robots, and as VRP with time windows for capacitated cooperating vehicles . Dynamic, on-line route planning has recently received attention in the agricultural robotics literature for large-scale harvesting operations because of its economic importance and the availability of auto-guided harvesters and unloading trucks. Reported approaches compute a nominal routing plan for the harvesters assuming some initial yield map, and then they route the support units based on the computed points where harvesters fill up their tanks .

The plan is adjusted during operations based on updated predictions of when and where harvester tanks will be full. A recent application that falls in this category is robot-aided harvesting of manually harvested fruits , where a team of robotic carts transports the harvested crops from pickers to unloading stations, so that pickers spend less time walking. Overall, the increasing deployment of commercially available auto-guided harvesters and unloading trucks, and the emerging paradigm of replacing large, heavy machines with teams of smaller agricultural autonomous vehicles drive the need for practical on-line route planning software.Primary units and support autonomous vehicles form a ‘closed-loop’ system: the delays introduced by the support vehicles affect the primary units’ temporal and spatial distributions of future service requests. Reactive policies are not efficient enough, because support trucks/robots must traverse large distances to reach the primary units in the field, thus introducing large waiting times.The incorporation of predictions about future service requests has been shown to improve scheduling for SDVRP . However, most SDVRP applications are characterized by requests that are stochastic and dynamic in time, but fixed and known in terms of location . In contrast, service requests from primary units in agriculture are stochastic and dynamic, both temporally and spatially . Also, the real-time and dynamic nature of agricultural operations means that very few established requests are available to the planner/scheduler, which has to rely much more on predicted requests. In addition, the optimization objective also varies depending on the situation. For example, it can be minimizing waiting time, maximizing served requests and so on,montel grow rack while VRP mainly focuses on minimizing travel distance. Therefore, existing SDVRP predictive scheduling approaches are not well suited for agriculture and more research is needed to incorporate uncertainty in on-line route planning for teams of cooperating autonomous agricultural machines. Agricultural robots will typically execute computed motions for a very large number of times . Therefore particular focus has been on computing paths and trajectories that are optimal in some economic or agronomic sense. Also, in most cases vehicles are non-holonomic. The general problem of moving a vehicle from one point/pose to another lies in the area of general motion planning and is covered adequately in the robotics literature . The focus of this section is on motion planning inside field or orchard blocks. When several machines operate independently of each other in the field they do not share resources, other than the physical area they work in. Furthermore, independent robots will typically operate in different field or orchard rows and their paths may only intersect in headland areas, which are used for maneuvering from one row to the next. Therefore, motion planning is restricted to headland turning and involves: a) planning of independent geometrical paths for turning, and b) computing appropriate velocity profiles for these paths so that collision avoidance is achieved, when two or more robot paths intersect. Problem is a coordinated trajectory planning problem and has been addressed in the robotics literature . In headlands, optimal motion planning is of particular interest, as turning maneuvers are non-productive and require time and fuel. Auto-guided agricultural vehicles must be able to perform two basic navigation tasks: follow a row, and maneuver to enter another row. The latter requires detection of the end of the current row and the beginning of the next row.

The route planning layer specifies the sequence of row traversal and the motion planning layer computes the nominal paths. During row following, precision crop cultivation requires precise and repeatable control of the vehicle’s pose with respect to the crop. Inside rows, agricultural vehicles travel at various ground speeds, depending on the task. For example, self-propelled orchard harvesting platforms move as slow as 1-2 cm/s; tractors performing tillage operations with their implement attached and their power take off engaged may travel at 1 Km/h up to 5 Km/h. Sprayers may travel at speeds ranging from 8 Km/h up to 25 Km/h. Vehicle working speeds in orchards are typically less than 10 Km/h. The above speeds are for straight or slightly curved paths; during turning maneuvers much slower ground speeds are used. Wheel slippage is common during travel, especially in uneven or muddy terrain. Also, agricultural vehicles will often carry a trailer or pull an implement, which can introduce significant disturbance forces. There are two basic auto-guidance modes: absolute and crop-relative . Absolute auto-guidance relies exclusively on absolute robot localization, i.e., real-time access to the geographical coordinates of the vehicle’s location, its absolute roll, pitch and yaw/heading, and time derivatives of them. These components of the vehicle’s state are estimated based on GNSS and Inertial Navigation System . Tractor GPS based absolute auto-guidance was first reported in 1996 , after Carrier Phase Differential GPS technology became available. Since then, auto-guidance for farming using Global Navigation Satellite Systems has matured into commercial technology that can guide tractors – and their large drawn implements – with centimeter-level accuracy, on 3D terrain, when Real Time Kinematic corrections are used. Absolute guidance can be used for precision operations when there is an accurate geo referenced map of the field and crop rows that is valid during operations, and the vehicle knows its exact position and heading in this map, in real-time. Essentially, establishing accurate vehicle positioning with respect to the crop is achieved by achieving absolute machine positioning on the map. The first step towards this approach is to use RTK GPS guided machines to establish the crop rows – and their map , transplanting . After crop establishment, as long as crop growth does not interfere with driving, vehicles can use the established map to repeatedly drive on the furrows between rows using RTK GPS . Accurate, robust and repeatable path tracking control is needed for precision guidance. The topic has received significant attention in the literature with emphasis given on slip compensation and control of tractor-trailer systems. Approaches reported in the literature include pure-pursuit , side-slip estimation and compensation with model based Liapunov control , back stepping predictive control , fuzzy neural control , sliding mode control , and others. Model-based approaches have also been proposed, such as nonlinear model predictive control , and robust nonlinear model predictive control . Absolute auto-guidance is an established commercially available technology that has acted as enabler for many precision agriculture technologies for row crops, such as variable rate application of seeds and chemicals. It has also led to recent advances in field automation, including the development of remotely supervised autonomous tractors without cabin and master-slave operation of grain carts with combines for autonomous harvesting systems . Absolute auto-guidance is not practical in row crops or orchards where one or more of the following are true: a) no accurate crop rows map is available to be used for guidance because crop establishment was performed with machines without RTK GPS; b) such a map exists but changes in the environment or crop geometries may render pre-planned paths non collision-free ; c) GNSS is inaccurate, unreliable or unavailable .