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.

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.

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 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.

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.

This paper offers a unified measure for dynamic stability of off-road vehicles that accounts for the tendency to tipover, slide, or loose contact with ground during static equilibrium and in motion. The contacts between the vehicle and ground are assumed rigid, and all wheels are assumed active. The dynamic stability measure is determined by computing the range of velocity and acceleration of the vehicle's center of mass that satisfies a set of dynamics constraints. The upper velocity limit serves as a dynamic stability measure, whereas the acceleration limit at zero speed serves as a static stability measure. In this paper, we demonstrate the approach for a four-wheel drive planar vehicle.

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 constraints and the geometric path constraints. This paper presents a geometric procedure for computing the set of admissible speeds and accelerations of a planar all-wheel drive vehicle. It first determines the boundaries of the set of resultant forces at the center of mass that satisfy the ground force constraints and the equations of motion along the path. This set is then mapped to the set of feasible speeds and accelerations along the path, from which the dynamic stability margin (DSM) is determined. A byproduct of this procedure is a static stability margin (SSM) that reflects the vehicle's ability to accelerate, or decelerate, at zero speed. Both stability margins are useful as cost measures for physics-based motion planning over rough terrain. The approach is demonstrated for a planar vehicle moving on a sinusoidal track.

This paper describes a unified measure of stability of a Rocker Bogie vehicle that accounts for the tendency to slide, tipover, or lose contact with the ground considering both static equilibrium and dynamic effects. The measure of stability is computed by solving for the range of acceptable velocities and accelerations that satisfy a set of dynamic constraints. The maximum acceptable velocity serves as a dynamic stability measure, whereas the maximum acceptable acceleration at zero velocity serves as a static stability measure. The utility of the static and dynamic stability margins are demonstrated for both two dimensional and longitudinal quasi-3D motion in several examples.