Dror Rubinstein

PREDICTING SOIL-RIGID WHEEL PERFORMANCE USING DISTINCT ELEMENT METHODS

A two-dimensional discrete element model (DEM) for the interaction between a rigid wheel and soil is presented using PFC2D code. The soil particles are modeled by clumps of two discs. The contact model between the particles includes cohesion by a so-called softening model. The parameters of the model represent soil having a cone index (CI) of 200 kPa or 400 kPa. The model of the wheel is based on 30 grousers, spaced equally around a drum 200 mm in diameter and 100 mm in width. Dynamic simulations were performed with different combinations of drawbar force, vertical load, and soil conditions. The traction performance of the wheel was calculated, and the results were compared with known theories and reported test results. The simulation results show reasonably good correlation, quantitatively and qualitatively, with previously reported results and theories, and emphasize the ability of the DEM to simulate soil-wheel interaction for design purposes. Prediction of wheel performance as a function of slip for driven, self-propelled, and towed wheels is presented for different combinations of soil conditions and vertical loads. The ability to investigate soil deformation, stress distribution beneath the wheel, and the influence of slip on sinkage is shown. Contrary to the prediction of empirical theories, the simulations suggest that vertical load and soil CI have different influences on tractive performance; this point warrants further investigation. The model also predicts a different behavior of motion resistance and net traction at high slip rates compared with empirical and semi-empirical methods.

REKEM—A design-oriented simulation program for off-road track vehicle

Abstract A design-oriented computer program, called REKEM, was developed for off-road track vehicle simulation. The equations of motion were formulated using the Lagrange approach and created automatically by a symbolic program. The model includes the detailed design and features of all suspension components, track tension, soil-track interaction, rolling resistance and soil energy dissipation. A sixth-order Runge-Kutta integration method and variable time steps were used for the solution. The output of the program includes numerical and graphical options, as well as animation of ride simulation. The simulation program is oriented for detailed design and analysis of the suspension system and for ride comfort evaluation. One of the main features of the program is the easy implementation of new suspension elements and track-soil-wheel interaction models. The source code of the model is concise in shape and size, and can be operated on work stations and personal computers with a mathematical co-processor as well. An example of ride simulation demonstrates some of the design features of the simulation model.

Dynamic Stability of Off-Road Vehicles Considering a Longitudinal Terramechanics Model

Dynamic stability reflects the vehicles 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 vehicles 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.

Prediction of Soil-Bulldozer Blade Interaction Using Discrete Element Method

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 McKyess 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 McKyess 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 McKyess approach. The contribution of this article lies in the use of DEM as a qualitative and quantitative predictive simulation tool.

Determination of robotic melon harvesting efficiency: a probabilistic approach

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.

Minimum Time Kinematic Motions of a Cartesian Mobile Manipulator for a Fruit Harvesting Robot

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 Bellmans 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.

The Orienteering Problem with Time Windows Applied to Robotic Melon Harvesting

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.

Combinatorial Optimization and Performance Analysis of a Multi-arm Cartesian Robotic Fruit Harvester--Extensions of Graph Coloring

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.

Cost effective development of a mobile conveying melon harvesting robot

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.

Prediction of the forces of blade penetration and build-up heap in front of the blade during bulldozer operation

Several of the existing models of soil–blade 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. McKeyss 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.