A Decomposition Framework for the Autonomous Navigation of Agricultural Vehicles
1)
Yiannis Ampatzidis1), Stavros Vougioukas1) and Dionisis Bochtis1) Aristotle University of Thessaloniki, Department of Agricultural Engineering, 54124 Thessaloniki, Greece. E-mail:
[email protected]
Abstract All machine operations require careful – optimal - planning. Furthermore, the execution of preplanned motions should be very accurate, reliable and - above all safe for human life, for the vehicle itself and for the crops. Optimization of the entire planning and execution problem is not realistic, because of the complexity of the problem. This paper proposes a decomposition of autonomous navigation for agricultural production in four stages: field coverage planning, motion and action sequence generation, point-to-point motion planning and trajectory generation, motion and operations execution. All these stages are discussed in detail, in order to present the state of the art in their implementations and to pinpoint focus areas for future research Keywords: Automatic Guidance, Autonomous Tractor, Field Operation, Precision Agriculture Introduction The efficient, accurate and reliable autonomous navigation of agricultural vehicles in modern precision farming applications is a challenging problem. Given the expected high cost of autonomous machines, even a small improvement in efficiency can result in large cost savings. Recent studies have shown that efficiency could be improved significantly by computing optimal fieldwork patterns which minimize turning time. According to Hansen et al. (2003), optimization of the combine harvesting pattern in corn fields can increase harvesting efficiency substantially. Taylor et al. (2002) have used Differential Global Positioning System (DGPS) data obtained during yield mapping operations to evaluate the potential for improving harvest efficiency. They supported that harvest efficiency depends more upon turning time rather than unloading time. In addition, controlled traffic in the field will reduce soil compaction. Hence, all machine operations require careful – optimal – planning. Optimization of the entire motion planning and execution is not realistic, because of the complexity of the problem. This paper proposes a decomposition of autonomous navigation for agricultural production in four stages. The first three stages compute the desired motions the vehicle should perform in increasing detail, and the last one executes the vehicle’s planned motions. The four stages are shown in figure 1. Field coverage planning
Motion and action sequence generation
Figure 1: Flow chart of the problem’s stages
Point-topoint motion planning and trajectory
Motion and operations execution
1. Field coverage planning: computes lines which cover the field, based on field geometry, crop pattern, tractor/implement working width and required operation. 2. Motion and action sequence generation: computes the optimal traversal of the field lines based on tractor turning radius, tractor/implement working width, characteristics of operation, location of storage silos, etc. Also, the discrete actions that need to be performed are computed, e.g., raising an implement at a headland, start/stop spraying, etc. 3. Point-to-point motion planning and trajectory generation: computes the detailed tractor motion in the field and outside (e.g., headlands) and creates the corresponding motion trajectory at a sampling interval equal to the one required by the tractor controller. 4. Motion and operations execution: localization and trajectory tracking, execution of discrete actions. Analytically, the first stage determines an optimal field coverage pattern, i.e., a set of straight lines and curves, which cover the entire field with minimum non productive time. This set depends on the vehicle characteristics (e.g. working width, turning radius), the field geometry and the required agricultural operation to be performed. In some agricultural applications the first stage could be omitted, because the lines that the vehicle must follow in order to execute an operation are predetermined (e.g. linear cultivation, orchards). At the second stage, a vehicle motion is represented by a pair of states, i.e. an initial and a final tractor state. This stage computes a sequence of vehicle motions and actions based on task-specific optimization criteria and on the characteristics of the vehicle (e.g. vehicle turning radius, tractor/implement working width etc.). Optimization criteria for agricultural field operations planning may include the non productive time (turning time), trampling of field, etc. It should also take into account constraints, such as reduced manoeuvrability due to field geometry, obstacles and vehicle kinematics. The third stage accepts as input the sequence of pairs of initial-final tractor states and computes the detailed optimal point-to-point motion for each pair. A motion at this stage is represented be a sequence of vehicle states. Again, the optimization should take into account the vehicle kinematic and dynamic constraints, as well as the field geometry. The trajectory generator calculates – for each point-to-point motion - trajectory points at a sampling rate equal to the frequency of the digital tracking controller. In the final stage the actual motion is executed. A tracking controller keeps the vehicle’s motion on the pre-planned trajectory with the required accuracy, while avoiding any unexpected stationary or moving obstacles. Next, all stages are discussed in detail, in order to present the state of the art in their implementations and to pinpoint focus areas for future research. Field coverage planning Field coverage planning is the problem of moving a vehicle over every point in a given region based on field geometry, crop pattern, tractor/implement working width and required operation. This stage should compute a path that that minimizes some desired cost, such as time. Several coverage algorithms have been published in the robotic literature, including on-line and off-line algorithms, and single or multiple
robot algorithms. Huang (2001) proposed the decomposing of the coverage region into subregions, selecting a sequence of those subregions, and then generating a path that covers each subregion in turn. Choset and Pignon (1997) introduced an offline planning algorithm for polygonal worlds which based on a new type of exact cellular decomposition approach termed the boustrophedon cellular decomposition and creates a sequence of subregions (cells). Choset and Burdick (1995a, 1995b) developed the hierarchical generalized Voronoi graph (HGVG) which is a roadmap developed for sensor based path planning exploration in unknown environments. Coverage algorithms have been used for multiple robots to cover an unknown rectilinear environment (Butler et al., 2000). All the field coverage planning techniques from the robotics area must be modified in order to be applied in agricultural operations because of their special characteristics. For example, field machines need to make short turns at the ends of the field and while following crop rows planted on the contour and in curves. So, the turning radius of implements is an important factor affecting the time lost in the end travel and at corners (Tsatsarelis, 2003). Few tillage or seeding machines can make square turns. With most cutter bar mowers the turning radius is short enough to permit square corners. The succeeding raking, windrowing and baling operations, however, usually follow a rounded corner pattern (Hunt, 2001). Several farm machines have rather rigid pattern requirements because they are one-way oriented. Moldboard plows; pull-type movers, rakes and windrowers; and most pull-type harvesters require a definite operating position with respect to the unprocessed portion of the field. Most tillage implements and most self-propelled implements are more liberal in their pattern operating requirements. So, the field coverage planning mostly depends on agronomic factors. Figure 2 illustrates some common patterns for straightsided fields.
(a) (b) (c) Figure 2: Common field machine patterns for rectangular fields. (a)-(b) continuous, turn strips at each end, (c) circuitous, turn strips at corner diagonals. This stage could be omitted for some agricultural applications, because the lines that the vehicle must follow in order to execute an operation are predetermined (e.g. linear cultivation, orchards). Motion and action sequence generation The first stage defines an optimal field coverage pattern, i.e., a set of straight lines and curves. The second stage computes a sequence of vehicle motions and actions, in the given pattern (determinate from the first stage), based on task-specific optimization criteria and on the characteristics of the vehicle (e.g. vehicle turning radius, tractor/implement working width etc.).
A method for this problem which gives optimal or near optimal solutions with low computational time has proposed by Bochtis et.al (2006). In this method, the fieldwork pattern planning for a self-propelled agricultural machine operating in parallel rows in a known rectangular field is formulated as a Vehicle Routing Problem (VRP). The VRP is a generic name given to a whole class of problems in which a set of routes for a fleet of vehicles based on one, or several depots must be determined for a number of geographically dispersed destinations, or “customers” with known demands. Its computational complexity, which is a direct consequence of the large number of variables involved, prohibits the use of an exact algorithm. Therefore, an existing solution algorithm with low computational requirements which uses a combination of stochastic and heuristic techniques is adopted to compute optimal or near-optimal solutions for a number of scenarios. For small-size problems the solution’s optimality was verified via direct enumeration. Based on these preliminary results, it seems that optimal, or, near-optimal solutions can be computed reasonably fast, for a wide rage of operations and problem sizes. In this stage the tractor’s maneuvers are very important. It will specify the sequence of vehicle motions and determinate the non productive time. For example, the alternation pattern, one of the common field machine patterns for rectangular fields, is used in processing established row crops. In an alternation pattern, the trips (a half round or the travel from one end of the field to the other) may be adjacent (figure 3a; straight alternation pattern), or non-adjacent (figure 3b; overlapping alternation pattern). Non adjacent patterns provide turns that are easy for the operator to negotiate. In every case there is a standard motive which is repeated. Despite the fact that the motive repetition doesn’t lead to the optimal pattern, it is imposed by human factors constraints. For example, it is not feasible for the operator of a conventional agricultural machine to follow a row sequence 1st →8th →3rd →14th →… This can be easily understood when one realizes that the rows are not visible, like a road, but are specified by the machine’s operating width. Recently, the combination of accurate navigational systems (GPS-based) with various real-time controllers and sensors have provided the necessary technology for a driver to follow a path like the one mentioned before. For these semi-autonomous agricultural vehicles generation, the optimization of the fieldwork pattern has a practical value.
Figure 3: Field machine alternation patterns for rectangular fields: (a) straight alternation pattern (b) overlapping alternation pattern. A scenario for the “motion and action sequence generation problem” was presented by Bochtis et.al (2006). In this scenario an agricultural machine with effective operating width w=5m, minimum turning radius R=5m and capacity equal to the
half of the field total demand, must cover a rectangular field with sort edge length equal to 20w=100m (i.e., 20 rows). In this case the relation between operating width and turning radius ( w ≤ R < 2 w ) necessitates the use of the loop turn for the headland-motion of the machine between two adjacent rows. The corresponding fieldwork patterns for the above scenario are illustrated in Figure 4. The algorithm was used in this paper was the Clarke-Wright savings algorithm, a well-known algorithm in vehicle routing (Clarke et al., 1964).
Figure 4: Solutions of fieldwork pattern for two problem instances. Point-to-point motion planning and trajectory generation In the context of precision farming, research in the area of autonomous tractor navigation has focused mainly on the accurate tracking of predetermined paths. The problem of automatically computing such paths has not received as much attention, mainly because, in many applications, the work paths are defined by the crop rows. For such operations, the paths consist of long line segments connected by curves at the headland turns. However, not all agricultural applications involve row-following and headland turning. For example, autonomous agricultural vehicles may have to move from one field to another, avoiding known obstacles such as trees, fences, barns etc., or may operate inside nonempty structures such as greenhouses. The generic path planning problem for agricultural vehicles deals mainly with point-topoint motion of nonholonomic tractor-trailer type vehicles (Laumond et al., 1998). Path planning for agricultural applications typically involves few and sparsely located obstacles, but requires optimal paths on possibly non-flat terrain. A path planning algorithm is said to be complete if it always finds a feasible path in a finite number of steps, if such a path exists; otherwise it terminates with an empty path. The computational complexity of path planning has been investigated for motion amidst polyhedral obstacles and has been shown to be at least polynomial in the dimension of the state and the number of obstacles. Hence, complete planners are restricted to solving relatively simple problems, and are not practical for complex real-world applications. In an effort to overcome the complexity problem, various randomized, or stochastic path-planning schemes have been developed (Kavraki et al., 1996; LaValle and Kuffner 2001) which trade completeness for performance. In juxtaposition to deterministic planners, which perform a systematic search of the robot’s configuration space based on some optimality or heuristic criteria, randomized planners rely on random sampling of the robot’s configuration space in order to construct a feasible path. In the agricultural domain, such planners have been implemented by using genetic algorithms (Noguchi & Terao, 1997) and random trees (Vougioukas, 2004). A common problem pertaining to randomized planners is that the convergence to the
final suboptimal path can be slow, and very often the resulting paths are not “smooth” because of the randomness involved in their generation. In (Vougioukas et. al, 2005) a two-stage route planning algorithm which can compute low cost paths for autonomous agricultural vehicles, given an arbitrary cost function defined over the entire path (e.g., shortest path, maximum clearance etc). The machine’s motion is modeled by a discrete state equation of the form x k +1 = f (x k , u k ) , k ≥ 0 , where x k ∈ n and u k ∈ m . For example, for a tractor the state could be its easting, northing and orientation and the input could be the tractor rear-wheel speed and front-wheel steering angle. The state and control vectors are subject to constraints of the form x min ≤ x k ≤ x max , u min ≤ u k ≤ u max . In the first stage, the algorithm utilizes randomized planning to compute a feasible suboptimal control sequence uˆ of length N-1, which results in a collision-free suboptimal path xˆ of length N. We should note that the solution of the planner is actually a trajectory, since each node carries time information. Usually this trajectory contains jagged segments created by the randomization in the first stage. In the second stage, trajectory optimization is formulated within the optimal control framework and numerical gradient descent is used to minimize the cost of the entire motion. The cost function is of the form N −1
J = θ (x N ) + ∑ φ (x k , u k ) , where θ is a cost function associated with the final state k =0
and φ is a cost function evaluated at every point of the trajectory. These cost functions encode the desirable optimization criteria, but may also contain penaltyterms which enforce the problem constraints. An example of the first and second stage motions for a small-sized vehicle is given in Figure 5a, whereas the simulated motion is presented in Figure 5b.
Figure 5: a) Planned paths among trees, b) tractor simulated motion (Vougioukas et. al, 2005) It seems that two-stage motion planners, which combine the search power of randomization with numerical optimization for path refinement, can offer a practical tool for planning point-to-point motions in agricultural applications. For long paths though, the computational requirements of numerical optimization may become prohibitive and thus powerful numerical techniques should be used.
Motion and operations execution In the final stage the actual motion is executed. This includes the next interrelated procedures (figure 6): accurate estimation of the vehicle’s location, path tracking (trajectory tracking) and detection of - and reaction to - obstacles. Path tracking /trajectory tracking
Estimation of the vehicle’s location
Obstacle avoidance
Figure 6: Motion and operations interrelated procedures Estimation of the vehicle’s location Location estimation and correction of path deviations are necessary to prevent robot drifts from the planned path over long distances. Usually, a continuous determination of robot location is obtained by dead reckoning systems. Frohlich et al. (1991) used a multisonar system for selflocalization of the robot with respect to natural landmarks. The University of Illinois (Stombaugh 1997, Stombaugh et al. 1998) utilized a 5 Hz real-time kinematic (RTK) GPS for agricultural vehicle guidance. Hague et al. (2000) proposed the separation of the ground based (as opposed to satellite based) sensors for automated systems into two categories. In the first group are the motion measurement sensors, which measure the internal stage of the system, e.g. odometers, accelerometers, gyroscopes, geomagnetic compass. The second group are the external observations sensors, which offer observations of local environment features, e.g. laser, sonar, radar, machine vision. Also, a review of sensing methods applicable to agricultural vehicle position fixing is available in Tillett (1991a, 1991b) and Reid (1998). Due to individual sensor’s errors the availability of data from multiple sensors provides opportunities to better integrate the data to give a result superior to the use of individual sensor. Noguchi et al. (1998) developed a guidance system by the sensor fusion integration with a machine vision, a RTK-GPS and a geometric direction sensor (GDS). Sensor fusion can also be used to improve lower quality sensors to higher precision. Will et al. (1998) tested a commercially available system that integrates basic GPS with inertial guidance and vehicle radar to provide a high precision DGPS system through use of an extended Kalman filter (EKF). The Kalman filter is a well-established technique to combine data from different sensors, in order to improve the availability and precision of the overall localization system. Last years this filter has been used in modern precision farming applications to achieve an accurate and unfailing estimation of vehicle positioning (Ampatzidis, 2005), (Han et al., 2002), (Sasiadek and Wang, 1999). Obstacle avoidance Real-time obstacle avoidance is a very important issue to successful applications of mobile robot systems. An autonomous vehicle should be able to detect obstacles and estimate their dimensions interfering with the tractor path, in order to avoid a collision. The environment, mainly in agricultural applications, contains known and unknown obstacles. Hence, it is necessary that the off-line motion planning algorithm computes vehicle motions which are collision-free among the known
obstacles, and that a real-time obstacle avoidance algorithm is used during execution in the field, for unexpected and moving obstacles. In indoor environments real-time obstacle avoidance can be solved by the wallfollowing method (Bauzil et al., 1981), (Giralt, 1984). With this approach the vehicle navigation is based on moving alongside walls at a predefined distance. If an obstacle is detected, the robot regards the obstacle as just another wall, following the obstacle’s contour until avoiding it and then keeps moving in the desired direction. Other more general and commonly method for obstacle avoidance is based on edge detection. The algorithm determines the position of the vertical edges of the obstacles and therefore attempts to guide the vehicle around either edge (Borenstein and Koren, 1988), (Weisbin et al., 1986), (Cooke, 1983). A drawback, in this method, is that the vehicle should stop in front of obstacles for more accurate measurements. Another method is the Certainty Grid method which was used by Elfes (1985) and Moravec (1986). It allows adding and retrieving data on the fly and permits integration of multiple sensors. In addition, Borenstein and Koren (1989) described the virtual force field (VFF) method for obstacle avoidance, which combines the Certain Grids method for obstacle representation with the Potential Field method (Khatib, 1985) for real-time path planning. Vougioukas et al. (2005) introduced a formal task-implementation framework for autonomous agricultural vehicle that was implemented for obstacle avoidance algorithm based on the VFF method. Still, the reliable detection, characterization and avoidance of obstacles in real-world farming applications, constitutes an open problem which requires further research. Path tracking This stage tries to solve the problem of driving an autonomous vehicle along a given path. A sequence of straight or curved lines defines a path and the goal of automatic path tracking is to minimize the average and maximum deviation between a tractor’s traveled path and the desired path. Various approaches have been proposed for path tracking, such as pure-pursuit (Amidi, 1990), dynamic path search control (Zhang and Qiu, 2004), and vector pursuit (Witt, et al., 2004). Modern auto-steering systems can provide accurate and repeatable path tracking of consistently straight or curved rows at an operator-set speed. It is expected that in the near future, precision farming operations will increasingly rely on more complex automatic steering and navigation capabilities of agricultural vehicles. Such capabilities include for example, sharp turns and reverse motions during headland turns, variable speed control, and eventually navigation among field obstacles. This problem is referred to as trajectory tracking and a desired trajectory point must be available to the tractor digital controller at every sample. The tracking error is defined at each controller sample as the difference between the desired and actual trajectory points. Various trajectory tracking controllers have been developed for industrial robots, with PID control being the most widely used technique. A well known theoretical result (Brockett, 1983) for under-actuated non holonomic systems, such as wheeled vehicles under the no-slip constraint, is that linear controllers cannot offer good tracking performance for complex maneuvers, sharp turns and reverse motions. Various control techniques have been proposed for trajectory tracking for car-like robots, such as time-varying LQR (Divelbiss and Wen, 1997), sliding mode control (Balluchi, et al., 1996), and iterative model predictive control (Wen and Jung, 2004). In (Vougioukas, 2006), a nonlinear model predictive tracking (NMPT) controller
was presented for tractor automatic guidance. The basic idea is to use a motion model for the vehicle and compute in real-time, at every time step k, an optimal Mstep-ahead control sequence, which minimizes the total M-step tracking error of the projected motion. In the presence of obstacles, the controller deviates from reference trajectories safely and robustly, by incorporating into the optimization obstacledistance information from range sensors (e.g., laser scanner, ultrasound). Hence, such an approach combines trajectory tracking and real-time obstacle avoidance. Such optimizing tracking controllers are very promising; however real-world implementations with extensive experimental data are required before they can be safely incorporated into commercial agricultural vehicles. Conclusions In this paper a decomposition of autonomous navigation for agricultural production in four stages is proposed. The first three stages compute the desired motions the vehicle should perform in increasing detail, and the last one executes the vehicle’s planned motions. Given the expected high cost of autonomous machines, even a small improvement in each stage can result in large cost savings. In some agricultural applications some stages could be omitted (e.g. field coverage planning). The adoption and modification of existed methods from other scientific areas (e.g. robotics) seems to be very promising, but they must be modified in order to be applied in agricultural operations because of their special characteristics. References Amidi O., (1990). Integrated Mobile Robot Control. Masters Thesis, Dept. Of Electrical and Computer Engineering, CMU, Pittsburgh, PA. Ampatzidis Y., (2005). Precise and Unfailing Positioning of Autonomous Agricultural Vehicles Using Kalman Filtering. MSc Thesis, in Greek, Aristotle University of Tsessaloniki, Greece. Balluchi A., Bicchi, A., Balestrino, A. and Casalino G., (1996). Path Tracking Control for Dubin’s Car. Proceedings of the 1996 IEEE Intl Conference on Robotics and Automation, Minneapolis, MN, 3123-3128. Bauzil G., Briot M. and Ribes P., (1981). A navigation sub-system using ultrasonic sensors for the mobile robot HILARE. 1st International Conference on Robot Vision and Sensory Controls, Stratford-upon-Avon, UK., pp. 47-58 and pp. 681-698. Bocthis D., Vougioukas S and Tsatsarelis C., (2006). Fieldwork operations planning for row crop agricultural production. Proceedings of the 18th Hellenic Conference on Operations Research, pp 629-639. Borenstein J. and Koren Y., (1988). Obstacle avoidance with ultrasonic sensors. IEEE Journal of Robotics and Automation, Vol. RA-4, No. 2, pp. 213-218. Borenstein J. and Koren Y., (1989). Real-time obstacle avoidance for fast mobile robots. IEEE Transactions on Systems, Man, and Cybernetics, Vol. 19, No. 5, pp. 1179-1187. Brockett R., (1983). Asymptotic stability and feedback stabilization. In Differential Geometric Control Theory (R. Brockett R. Millman and J. Sussmann. (Ed.)). Birkhauser. 27,181-208. Butler Z., Rizzi A. and Hollis R., (2000). Complete distributed coverage of rectilinear environments. In Fourth International Workshop on the Algorithmic Foundations of Robotics.
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