Optimal Coverage Path Research Articles

Development of a Path Generation and Tracking Algorithm for a Korean Auto-guidance Tillage Tractor

Purpose: Path planning and tracking algorithms applicable to various agricultural operations, such as tillage, planting, and spraying, are needed to generate steering angles for auto-guidance tractors to track a point ahead on the path. An optimal coverage path algorithm can enable a vehicle to effectively travel across a field by following a sequence of parallel paths with fixed spacing. This study proposes a path generation and tracking algorithm for an auto-guided Korean tractor with a tillage implement that generates a path with C-type turns and follows the generated path in a paddy field. A mathematical model was developed to generate a waypoint path for a tractor in a fi eld. This waypoint path generation model was based on minimum tractor turning radius, waypoint intervals and LBOs (Limit of Boundary Offsets). At each location, the steering angle was calculated by comparing the waypoint angle and headin g angle of the tractor. A path following program was developed with Labview-CVI to automatically read the waypoints and generate steering angles for the tractor to proceed to the next waypoint. A feasibility test of the developed program for real-time path tracking was performed with a mobile platform traveling on flat ground. The test results showed that the developed algorithm generated the desired path and steering angles with acceptable accuracy.

Optimal Coverage Path Planning for Arable Farming on 2D Surfaces

With the rapid adoption of automatic guidance systems in agriculture, automated path planning has great potential to further optimize field operations. Field operations should be done in a manner that minimizes time and travel over field surfaces and should be coordinated with specific field operation requirements, machine characteristics, and topographical features of arable lands. To reach this goal, an intelligent coverage path planning algorithm is the key. To determine the full coverage pattern of a given field by using boustrophedon paths, it is necessary to know whether to and how to decompose a field into sub-regions and how to determine the travel direction within each sub-region. A geometric model was developed to represent this coverage path planning problem, and a path planning algorithm was developed based on this geometric model. The search mechanism of the algorithm was guided by a customized cost function resulting from the analysis of different headland turning types and implemented with a divide-and-conquer strategy. The complexity of the algorithm was analyzed, and methods for reducing the computational time are discussed. Field examples with complexity ranging from a simple convex shape to an irregular polygonal shape that has multiple obstacles within its interior were tested with this algorithm. The results were compared with other reported approaches or farmers' recorded patterns. These results indicate that the proposed algorithm was effective in producing optimal field decomposition and coverage path direction in each sub-region.

Optimal Hamiltonian completions and path covers for trees, and a reduction to maximum flow

A minimum Hamiltonian completion of a graph G is a minimum-size set of edges that, when added to G, guarantee a Hamiltonian path. Finding a Hamiltonian completion has applications to frequency assignment as well as distributed computing. If the new edges are deleted from the Hamiltonian path, one is left with a minimum path cover, a minimum-size set of vertex-disjoint paths that cover the vertices of G. For arbitrary graphs, constructing a minimum Hamiltonian completion or path cover is clearly NP-hard, but there exists a linear-time algorithm for trees. In this paper we first give a description and proof of correctness for this linear-time algorithm that is simpler and more intuitive than those given previously. We show that the algorithm extends also to unicyclic graphs. We then give a new method for finding an optimal path cover or Hamiltonian completion for a tree that uses a reduction to a maximum flow problem. In addition, we show how to extend the reduction to construct, if possible, a covering of the vertices of a bipartite graph with vertex-disjoint cycles, that is, a 2-factor.

Deferred‐query: An efficient approach for some problems on interval graphs

This paper introduces the idea of a deferred-query approach to design O(n) algorithms for the domatic partition, optimal path cover, Hamiltonian path, Hamiltonian circuit, and maximum matching problems on interval graphs given n endpoint-sorted intervals. The previous best-known algorithms run in O(n log log n) or O(n +m) time, where m is the number of edges in the corresponding interval graphs. © 1999 John Wiley & Sons, Inc. Networks 34: 1–10, 1999

Optimal path cover problem on block graphs

Let G = ( V, E) be a block graph. First we show that an algorithm for finding the path partition number p( G) by J.H. Yan and G.J. Chang gives wrong answers to some block graphs. Then we present an efficient algorithm for finding a minimum path partition of G (not just the path partition number p( G)). The complexity of this algorithm is O( m), where m = ¦E¦.

Deferred-query: An efficient approach for some problems on interval graphs

This paper introduces the idea of a deferred-query approach to design O(n) algorithms for the domatic partition, optimal path cover, Hamiltonian path, Hamiltonian circuit, and maximum matching problems on interval graphs given n endpoint-sorted intervals. The previous best-known algorithms run in O(n log log n) or O(n + m) time, where m is the number of edges in the corresponding interval graphs.

COMBINATORIAL APPROACHES FOR HARD PROBLEMS IN MANPOWER SCHEDULING

Manpower scheduling is concerned with the construction of a workers' schedule which meets demands while satisfying given constraints. We consider a manpower scheduling problem, called the Change Shift Assignment Problem(CSAP). In previous work, we proved that CSAP is NP-hard and presented greedy methods to solve some restricted versions. In this paper, we present ~ombinat~orial algorithms to solve more general and realistic versions of CSAP which are unlikely solvable by greedy methods. First, we model CSAP as a fixed-charge network and show that a feasible schedule can be obtained by finding disjoint paths in the network, which can be derived from a minimum-cost flow. Next, we show that if the schedule is tableau-shaped, then such disjoint paths can be derived from an optimal path cover, which can be found by a polynomial-time algorithm. Finally, we show that if all constraints are monotonzc, then CSAP may be solved by a pseudo-polynomial backtracking algorithm which has a good run-time performance for random CSAP instances.

An optimal path cover algorithm for cographs

The class of cographs, or complement-reducible graphs, arises naturally in many different areas of applied mathematics and computer science. In this paper, we present an optimal algorithm for determining a minimum path cover for a cograph G. In case G has a Hamiltonian path (cycle) our algorithm exhibits the path (cycle) as well.

Optimal path cover problem on block graphs and bipartite permutation graphs

The optimal path cover problem is to find a minimum number of vertex disjoint paths which together cover all the vertices of the graph. In this paper, we present linear-time algorithms for the optimal path cover problem for the class of block graphs and bipartite permutation graphs.

Linear algorithm for optimal path cover problem on interval graphs

A path cover of a graph G is a set of vertex-disjoint paths that cover all the vertices of G. An optimal path cover of G is a path cover of minimum cardinality. This problem is known to be NP-complete for arbitrary graphs. We present a linear algorithm for this problem on interval graphs. Given the adjacency lists of an interval graph with n vertices and m edges, our algorithm runs in O( m+ n) time.

On mapping processes to processors in distributed systems

This paper is concerned with the implementation of parallel programs on networks of processors. In particular, we study the use of the network augmenting approach as an implementation tool. According to this approach, the capabilities of a given network of processors can be increased by adding some auxiliary links among the processors. We prove that the minimum set of edges needed to augment a line-like network so that it can accommodate a parallel program is determined by an optimal path cover of the graph representation of the program. Anoptimal path cover of a simple graphG is a set of vertex-disjoint paths that cover all the vertices ofG and has the maximum possible number of edges. We present a linear time optimal path covering algorithm for a class of sparse graphs. This algorithm is of special interest since the optimal path covering problem is NP-complete for general graphs. Our results suggest that a “cover and augment” scheme can be used for optimal implementation of parallel programs in line-like networks.

Covering Points of a Digraph with Point-Disjoint Paths and Its Application to Code Optimization

A point-disjoint path cover of a directed graph is a collection of point-disjoint paths (some paths possibly having zero length) which covers all the points. A path cover which minimizes the number of paths corresponds to an optimal sequence of the steps of a computer program for efficient coding and documentation. The minimization problem for the general directed graph is hard in the sense of being NP-complete. In the case of cycle-free digraphs, however, the problem is polynomial, for it is shown that it can be reduced to the maximum-matching problem. A heuristic given here for finding a near optimal path cover for the general case is based upon applying the maximum-matching algorithm to the subgraphs of an interval decomposition.