Moshe P. Mann

Dynamic stability of off-road vehicles

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 vehicles 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 of a Rocker Bogie Vehicle: Longitudinal Motion

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.

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.

Dynamic stability of off-road vehicles: a geometric approach

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 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 vehicles 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

Dynamic stability of off-road vehicles: Quasi-3D analysis

This paper presents a method to determine the stability of off-road vehicles moving on rough terrain. The measures of stability are defined as the maximum speed and acceleration under which the vehicle does not slide or tip over. To compute these stability measures, we propose a quasi 3D analysis by decomposing the vehicle dynamics into three separate planes: the yaw, pitch, and roll planes. In each plane, we compute the set of admissible speeds and acceleration for the planar vehicle model, contact model, and ground force constraints. The intersection of the admissible sets provides the total range of feasible speeds and accelerations along the vehicles path, from which we obtain the stability margins. Numerical results for a vehicle traversing a simulated terrain demonstrate the effectiveness of the approach.

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.

On the Dynamic Stability of Off-Road Vehicles

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 an analytical method for computing the stability margins of a planar all-wheel drive vehicle. 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 determines the static and dynamic stability margins, used to gauge 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.