Theoretically, there is zero slip between two bodies when there is no relative motion in their contact points. In the contact between a wheel and a surface, zero slip can be obtained only in the case of a single contact point. In this case, the wheel and the surface must be rigid. The theoretical zero-slip condition can't be obtained in the contact between tire and terrain surface. In much of the scientific literature, two alternatives are suggested for a practical definition of the zero-slip condition: the point at which the gross traction force is equal to zero, or the point at which the net traction force is equal to zero. In the ASABE (2013), there is still no unique definition for the practical zero-slip condition. According to the definition of zero-slip condition, the rolling radius is not constant and depends on the slip. A detailed finite-element model using Lagrangian elements was built for each tire, taking into account the effect of all tire materials and their arrangement, lug shape, and inflation pressure. The soil model was built with Eulerian elements, which allow a large degree of deformation and flow of the soil. The initial verification experiments of the tire models were conducted by pressing the tires against a rigid plane. Each tire was examined under several different inflation pressures. Very good correlations were obtained between the experimental and model results. The verification test for the gross and net traction forces was performed in the soil-bin laboratory at the Technion. Special equipment was built, including a heavy dragging platform and a cell to hook the tire. This equipment allows control of the tire slip. The net traction force, gross traction force, and vertical load were measured in each test. Good correlations were obtained between the experimental and model results. Using the FEM model developed, some definitions for zero-slip condition were examined. The results indicate that the best criterion for zero-slip condition is definition of the point at which the gross traction force is equal to zero. (C) 2018 ISTVS. Published by Elsevier Ltd. All rights reserved.

The goal of a melon harvesting robot is to maximize the number of melons it harvests given a progressive speed. Selecting the sequence of melons that yields this maximum is an example of the orienteering problem with time windows. We present a dynamic programming-based algorithm that yields a strictly optimal solution to this problem. In contrast to similar methods, this algorithm utilizes the unique properties of the robotic harvesting task, such as uniform gain per vertex and time windows, to expand domination criteria and quicken the optimal path selection process. We prove that the complexity of this algorithm is linearithmic in the number of melons and can be implemented online if there is a bound on the density. The results of this algorithm are demonstrated to be significantly better than the standard heuristic solution for a wide range of harvesting robot scenarios.

A mobile melon robotic harvester consisting of multiple Cartesian manipulators, each with three degrees of freedom, is being developed. In order to design an optimal robot in terms of number of arms, manipulator capabilities, and robot speed, a method of allocating the fruits to be picked by each manipulator in a way that yields the maximum harvest has been developed. Such a method has already been devised for a multi-arm robot with 2DOF each. The maximum robotic harvesting problem was shown there to be an example of the maximum k-colorable subgraph problem (MKCSP) on an interval graph. However, for manipulators with 3DOF, the additional longitudinal motion results in variable intervals. To overcome this issue, we devise a new model based on the color-dependent interval graph (CDIG). This enables the harvest by multiple robotic arms to be modeled as a modified version of the MKCSP. Based on previous research, we develop a greedy algorithm that solves the problem in polynomial time, and prove its optimality using induction. As with the multi-arm 2DOF robot, when simulated numerous times on a field of randomly distributed fruits, the algorithm yields a nearly identical percentage of fruit harvested for given robot parameters. The results of the probabilistic analysis developed for the 2DOF robot was modified to yield a formula for the expected harvest ratio of the 3DOF robot. The significance of this method is that it enables selecting the most efficient actuators, number of manipulators, and robot forward velocity for maximal robotic fruit harvest.

To automate the harvesting of melons, a mobile Cartesian robot is developed that traverses at a constant velocity over a row of precut melons whose global coordinates are known. The motion planner is programmed to have the robot harvest as many melons as possible. Numerous simulations of the robot over a field with different sets of randomly distributed melons resulted in nearly identical percentages of melons harvested. This result holds true over a wide range of robot dimensions, motor capabilities, velocities and melon distributions. Using probabilistic methods, we derive these results by modelling the robotic harvesting procedure as a stochastic process. In this simplified model, a harvest ratio is predicted analytically using Poisson and geometric distributions. Further analysis demonstrates that this model of robotic harvesting is an example of an infinite length Markov chain. Applying the mathematical tools of Markov processes to our model yields a formula for the harvest percentage that is in strong agreement with the results of the simulation. The significance of the approach is demonstrated in two of its applications: to select the most efficient actuators for maximal melon harvesting and determine the set of optimal velocities along a row of melons of varying densities.

This paper describes an analytical procedure to calculate the time-optimal trajectory for a mobile Cartesian manipulator to traverse between any two fruits it picks up it. The goal is to minimize the time required from the retrieval of one fruit to that of the next while adhering to velocity, acceleration, location, and endpoint constraints. This is accomplished using a six stage procedure, based on Bellman's Principle of Optimality and nonsmooth optimization that is completely analytical and requires no numerical computations. The procedure sequentially calculates all relevant parameters, from which side of the mobile platform to place the fruit on to the velocity profile and drop-off point, that yield a minimum time trajectory. In addition, it provides a time window under which the mobile manipulator can traverse from any fruit to any other, which can be used for a globally optimal retrieving sequence algorithm.

A 3DOF mobile Cartesian robotic harvester for two-dimensionally distributed crops such as melons is being developed. A two-step procedure to calculate the trajectory of its manipulator that will result in the maximum number of melons harvested is described in this article. The goal of the first step is to calculate the minimum-time trajectory required to traverse between any two melons while adhering to velocity, acceleration, location, and endpoint constraints. This step is accomplished in a hierarchal manner by solving several subproblems involving optimal control and nonconvex optimization, enabling optimal (maximum) melon harvesting to be formulated as an orienteering problem with time windows. In the second step, the orienteering problem is solved using the moving branch and prune method, based on dynamic programming. This enables suboptimal sequences of melons (out of all options) to be eliminated on the fly without the need to solve the entire problem at once. An example is shown to demonstrate the efficacy of the algorithm.

A multiarm robotic harvester is being developed for two-dimensional crops such as melons. A number of Cartesian manipulators, mounted in parallel on a rectangular frame, traverse laterally across the crop bed as the frame moves along it. The robotic arms reach down to pick melons and place them on adjacent lateral conveyors. The coordinates of the fruits to be harvested are assumed to be known prior to harvest so that the robot gets a bank of targets in local coordinates. In this paper, we describe the algorithms developed and used to plan the assignment of melons to be harvested by each of a number of arms in a collaborative way so that the maximum number of fruits will be harvested by a given number of arms. Under practical kinematic conditions, the fruits and the manipulators’ capabilities can be modeled as a task of coloring an interval graph, and a greedy algorithm known to produce an optimal solution for a k colorable sub-graph problem is used. Under faster manipulator performance, an approximation algorithm based on heuristics and a local search was shown to produce near-optimal harvest assignments. The algorithms are used to facilitate the design of the robot using simulations of the effects of robot speed, number of arms, manipulator’s lateral acceleration and fruit handling time on the harvest. The simulations enable economic optimization of the design of such robotic harvesters, taking into account the costs of robotic arms, labor and operation time and the value of the crop.

This paper describes a two step procedure to calculate the trajectory of a melon harvesting Cartesian mobile manipulator that results in the maximum number of melons harvested. The goal of the first step is to calculate the minimum-time trajectory required to traverse between any two melons while adhering to velocity, acceleration, location, and endpoint constraints. This is accomplished in a hierarchal manner by solving several sub problems involving optimal control and nonconvex optimization, enabling maximum melon harvesting to be formulated as the orienteering problem with time windows. In the second step, the orienteering problem is solved using the moving branch and prune method, based on dynamic programming. This allows sub-optimal sequences of melons to be eliminated on the fly without the need to solve the entire problem at once, enabling online implementation. An example is shown to demonstrate the efficacy of the algorithm.

A three step procedure is presented to calculate the cost-optimal actuator capabilities of a melon harvesting mobile Cartesian robot. In the first step, the minimum-time trajectory required to traverse between any two melons that adheres to motion constraints is calculated. This is accomplished in a hierarchal manner by solving several sub-problems involving optimal control and optimization, allowing maximum melon harvesting to be formulated as the orienteering problem with time windows. In the second step, the solution to the orienteering problem - the sequence of melons for the robot to pick up that result in the maximum number harvested - is solved. A novel solution method based on dynamic programming, the moving branch and prune method, is devised. This allows optimal melons sequences to be computed without need to solve the entire problem at once, accommodating online implementation. In the third step, the costs and revenues are modeled as a function of actuator capabilities and platform velocity and then factored into a cost function. Optimization of this function results in the most cost optimal actuators of the robot. Examples demonstrate the efficacy of the algorithm.

Israel recently instituted new safety regulations requiring the use of a harness on agricultural high-altitude platforms. The benefit of these regulations is controversial, since although these platforms frequently roll over, there is often no severe damage to the worker. Farmers claim that the regulation requiring workers to fasten themselves to the platform with a harness will prevent operators from jumping from the rolling platform to protect themselves. This paper describes the advantages of a multi-body dynamic man-machine interaction model in investigating the benefit of harnessing the operator to the platform cell. Different working scenarios caused by the Afron three-wheeled platform and human reactions to rollover were simulated. A model of ground contact force during impact between soil and man was defined according to experiments on different surfaces. Simulation results show that the use of the harness did not improve the worker's safety conditions or decrease the severity of human injury significantly in comparison with the human injury incurred without the use of a harness. In fact, the operator may be protected by escaping from the platform cell and the harness prevents such an option during rollover. Thus the use of a harness on these agricultural platforms in conditions that may cause rollover does not reduce potential injury in comparison to that of unbelted operators.

The underlying similarity between soils, grains, fertilizers, concentrated animal feed, pellets, and mixtures is that they are all granular materials used in agriculture. Modeling such materials is a complex process due to the spatial variability of such media, the origin of the material (natural or biological), the nonlinearity of these materials, the contact phenomenon and flow that occur at the interface zone and between these granular materials, as well as the dynamic effect of the interaction process. The lack of a tool for studying such materials has limited the understanding of the phenomena relevant to them, which in turn has led to energy loss and poor quality products. The objective of this study was to develop a reliable prediction simulation tool for cohesive agricultural particle materials using Discrete Element Modeling (DEM). The specific objectives of this study were (1) to develop and verify a 3D cohesionless agricultural soil-tillage tool interaction model that enables the prediction of displacement and flow in the soil media, as well as forces acting on various tillage tools, using the discrete element method; (2) to develop a micro model for the DEM formulation by creating a cohesive contact model based on liquid bridge forces for various agriculture materials; (3) to extend the model to include both plastic and cohesive behavior of various materials, such as grain and soil structures (e.g., compaction level), textures (e.g., clay, loam, several grains), and moisture contents; (4) to develop a method to obtain the parameters for the cohesion contact model to represent specific materials. A DEM model was developed that can represent both plastic and cohesive behavior of soil. Soil cohesive behavior was achieved by considering tensile force between elements. The developed DEM model well represented the effect of wedge shape on soil behavior and reaction force. Laboratory test results showed that wedge penetration resistance in highly compacted soil was two times greater than that in low compacted soil, whereas DEM simulation with parameters obtained from the test of low compacted soil could not simply be extended to that of high compacted soil. The modified model took into account soil failure strength that could be changed with soil compaction. A three dimensional representation composed of normal displacement, shear failure strength and tensile failure strength was proposed to design mechanical properties between elements. The model based on the liquid bridge theory. An inter particle tension force measurement tool was developed and calibrated A comprehensive study of the parameters of the contact model for the DEM taking into account the cohesive/water-bridge was performed on various agricultural grains using this measurement tool. The modified DEM model was compared and validated against the test results. With the newly developed model and procedure for determination of DEM parameters, we could reproduce the high compacted soil behavior and reaction forces both qualitatively and quantitatively for the soil conditions and wedge shapes used in this study. Moreover, the effect of wedge shape on soil behavior and reaction force was well represented with the same parameters. During the research we made use of the commercial PFC3D to analyze soil tillage implements. An investigation was made of three different head drillers. A comparison of three commonly used soil tillage systems was completed, such as moldboard plow, disc plow and chisel plow. It can be concluded that the soil condition after plowing by the specific implement can be predicted by the DEM model. The chisel plow is the most economic tool for increasing soil porosity. The moldboard is the best tool for soil manipulation. It can be concluded that the discrete element simulation can be used as a reliable engineering tool for soil-implement interaction quantitatively and qualitatively.

Several of the existing models of soilblade interaction are based on very basic relations known from soil mechanics. The best-known model, developed by McKyes (1989), is used to calculate the vertical and horizontal forces applied on the blade during quasistatic bulldozer operation. McKeys's approach does not consider the effect of the build-up heap in front of the blade on the forces applied on the blade. In addition, the McKyes approach assumes a constant sinkage of the blade, and consequently the penetration force is not taken into the account, either. The literature includes no models based on classic soil mechanics theories that predict the process of blade penetration into soil and the build-up heap in front of the blade. The forces that are created by the penetration and the heap are very significant and cannot be ignored. The goal of the present research is to develop models to predict the effect of the penetration and the build-up heap in front of the blade on the forces applied to the blade, by using classic soil mechanics theories.

[First paragraph]: Soil-machine interactions present a continuous challenge for researchers, developers, and manufacturers. Modeling field machines for earthmoving and farming operations is an important engineering task. However, modeling soil-machine interactions is a complex process due to the spatial variability of the soil media, the nonlinear behavior of soil, the contact phenomena and flow that occur at the interface zone between the soil and the tool, and the dynamic effects. In this chapter we present a novel approach--the Discrete Element Method (DEM)--to model soil-machine interactions.

Currently available models for dynamic simulation of tracked vehicles do not include the necessary detail required of a high-fidelity model of crawlers. The rapid increase in computing speed enables the utilization of more complex models, which may include many bodies and force elements. A three-dimensional multi-body simulation model for simulating the dynamic behavior of a crawler was developed using the LMS-DADS simulation program. The model incorporates detailed description of the track, the suspension system, and the dynamic interaction among its components. Three-dimensional contact force elements are used to describe the interaction of the track links with the vehicle’s rollers, sprocket, and idler. User-defined force elements are used to describe the interaction between each track link and the soil. The normal and tangential forces are calculated using classic soil mechanics equations, such as Bekker and Janosi correlations. The grousers, which are a significant part of any crawler track link, were modeled using McKeys’ approach. The model includes new elements, such as the plasticity and viscosity properties of the soil. Sinkage and slip are calculated separately for each track link. Simulation results were compared with the experimental results. In some ride conditions, the simulation results indicate forward motion of a track link while in contact with the soil. The existing theories consider backward motion of a track link when the vehicle moves forward and the link is in contact with the soil. This phenomenon was verified in the experimental work. It was concluded that the influence of the track dynamics and the soil-link interaction on the vehicle dynamics can be better predicted with the newly developed model.

Modeling soil-tillage interaction is a complex process due to dynamic soil-implement interaction which includes a high rate of plastic deformation and soil failure, characterized by the flow of soil particles. The need for a sound modeling technique for soil-implement interaction is the motivation for the present work.The discrete element method (DEM) seems to be a promising approach for constructing a high-fidelity model to describe the soil-implement interaction and can serve as a predicting simulation tool in the process of designing the implement shape.The wide cutting-blade interaction was modeled using a 2D discrete element code-PFC2D and the soil particles by clumps of two disks with a cohesion force contact model between the particles. Four different blade shapes were analyzed by the discrete element model and experimentally by a soil box filled with sand. A very good correlation was obtained between the discrete element simulation and the experimental results. The simulations indicate an increasing horizontal force applied on the blades during motion, as a result of the piling effect of the soil in front of the blade. It was found that the soil flow beneath the blade tip can affect the vertical force applied on the blade.The simulation results were also compared with classical soil mechanics theories for straight blades (the McKyes approach). A good correlation was obtained between the simulation results and McKyes approach for the horizontal force applied on the blade. Weaker correlations were obtained in the vertical direction. This finding can be explained by the soil particle flow beneath the blade tip, which the McKyes approach, does not take into consideration. Observation of the simulation revealed that the failure curve could be reasonably described by a straight line, as assumed in the classical theories. (c) 2007 Elsevier B.V. All rights reserved.

Dynamic stability reflects the vehicle's ability to traverse uneven terrain at high speeds. It is determined from the set of admissible speeds and tangential accelerations of the center of mass along the path, subject to the ground force and geometric path constraints. This paper presents an analytical method for computing the stability margins of a planar all-wheel drive vehicle that accounts for soil parameters. It consists of mapping the ground force constraints to constraints on the vehicle's speeds and accelerations along the path. The boundaries of the set of admissible speeds and accelerations determine the static and dynamic stability margins, used to gage the traversability of the vehicle along the path. The first is the maximum feasible acceleration at zero speed, whereas the second is the maximum feasible speed. Both stability margins are demonstrated for a planar vehicle moving on a sinusoidal path.

The dynamic interaction that occurs in the soil tillage process includes a high rate of plastic deformation and soil failure, characterized by flow of the soil particles. The discrete element method (DEM) seems to be a promising approach for constructing a high-fidelity model to describe soil–implement interaction. Proper prediction of this interaction using DEM depends upon the model parameters. However, there is no robust method for determining the parameters for discrete element models. In this study, the determination of parameters was based on in situ field tests, which consisted of sinkage tests performed with different penetration tools. Based on each test, a plot of force versus displacement, or a so-called “real curve,” was drawn. Discrete element models were built in correspondence with the field tests. “Simulation curve” plots were obtained from the results of the simulation of force versus displacement. In order to minimize the area difference between the real and simulation curves, an inverse solution technique using the Nelder–Mead algorithm of optimization was employed. The optimization results of this particular problem are sensitive to the initial estimate of the parameters. In order to achieve a unique solution, the initial estimate must be close enough to the proper value of the parameters. An energy method and elastic–plastic rule were developed to determine the initial estimation for the optimization process. The described methodology was verified experimentally and numerically; good correlation was achieved between the soil mechanical behavior obtained by experiments and the discrete element simulations.

Modeling the interaction between soil and a tillage implement, such as a bulldozer blade, is a complex task, involving many factors, such as ground layout, soil strength, soil buildup in front of the tool, soil flow, and cracks that may occur in the soil during blade work. The discrete element method (DEM) is a numerical tool designed to model granular materials. Soil, and particularly sandy soil, may be described as a granular material. Therefore, DEM seems to be a promising tool for modeling the interaction between a blade and soil. The model parameters are usually set using a trial-and-error process, as there is no robust theory for determining the soil parameters of the model. This article suggests a method for determining the parameters for the DEM model and simulates the soil-blade interaction of cohesionless soil, as a case study, using a 2D DEM program (PFC2D). The method is based on the interlocking property of the particles. The maximum error of the parameters obtained by the method compared with the actual soil parameters was 22.8%. Selecting the optimum spring constant between the particles may reduce the error. Two-dimensional simulations were performed of a bulldozer blade moving in a particle medium, working at different blade angles and depths, and in different soil parameters. Comparing the simulations with the prediction results using McKyes's calculation model, the DEM model predicted an average draft force 7.2% greater than, and an average vertical force 1.7% less than, the forces predicted by McKyes's approach. The failure line was defined in the simulation according to the differences in particle velocities; the results fit the prediction of the failure line according to McKyes's approach. The contribution of this article lies in the use of DEM as a qualitative and quantitative predictive simulation tool.