Modified virtual semi-circle path planning

The challenging part of path planning for an Unmanned Ground Vehicle (UGV) is to conduct a reactive navigation. Reactive navigation is implemented to the sensor based UGV. The UGV defined the environment by collecting the information to construct it path planning. The UGV in this research is known as Mobile Guard UGV-Truck for Surveillance (MG-TruckS). Modified Virtual Semi Circle (MVSC) helps the MG-TruckS to reach it predetermined goal point successfully without any collision. MVSC is divided into two phases which are obstacles detection phase and obstacles avoidance phase to compute an optimal path planning. MVSC produces shorter path length, smoothness of velocity and reach it predetermined goal point successfully

A 'snowflake' geometrical representation for optimised degree six 3-modified chordal ring networks

The performance parameters and properties of chordal rings have been researched extensively as models for parallel and distributed interconnection topology models since their founding in 1981. A chordal ring is modelled after a circulant graph, where its vertices represent processor nodes and its edges represent the links between them. Hence, its performance and properties of connectivity can be studied through graph theory. This research was aimed at the investigation of a new degree six chordal ring, the optimised degree six 3-modified chordal ring CHR6o3. A tree visualisation was constructed based on its connectivity to enable the generation of formulae for optimal diameter and average optimal path lengths. As the numbers of nodes further increased with its layers, the visualisation was found to be more accurately represented in a table where all the combinations of different links for each node were listed, compared to drawing it out. Redundant nodes were also more easily found by using this representation. Furthermore, the ‘snowflake’ geometrical representation was proposed to illustrate the connectivity of nodes in CHR6o3 as well as to aid the proving of some properties involving its Hamiltonicity. The results of this research are important in developing a routing algorithm for CHR6o3

Graph theoretical properties of degree six 3-modified chordal ring networks

Chordal rings are important models for the development of parallel and distributed interconnection networks. Hence, much research on their variations and properties had been published over the years. In this study, a new type of chordal ring network is presented, the degree six 3-modified chordal ring (CHR6m_3) which is able to accommodate both odd and even numbers of nodes so long as the network size is divisible by 3. The aim of the research was to develop relations for the theoretical diameter and average path length for CHR6m_3 as well as to present the main properties of CHR6m_3. The relations were developed based on data from the tree visualisation of CHR6m_3 while the main properties encompass Hamiltonicity, asymmetry and node colouring. Results for theoretical diameter and average path lengths for their corresponding network sizes were based on the formulae generated. Several theorems regarding the main properties were constructed and proven. Hamiltonian circuits could be constructed on the basis of certain types of chords if certain conditions were met. CHR6m_3 was proven to be asymmetric. A proper node colouring was proposed along with the conditions for its existence. A small chromatic number is important in minimising network process completion times

Path planning for mobile robot based on reactive collision avoidance method

Background: The number of research regarding local path planning of the Unmanned Ground Vehicle (UGV) is increasing widely. The Modified Virtual Semi Circle (MVSC) approach is proposed for real-time path planning. This research proposes the implementation of five ultrasonic range finder sensors with a very small blind zone existence in the sensor arrangement. The navigation of the mobile robot depends on the position of the mobile robot in the influence zone area. The formation of three layers of influence zone shows the optimized path planning without making any unnecessary obstacle avoidance presence. Objective: The purpose of this paper is to navigate a cost effective UGV known as MG-TruckS with optimal path planning. Results: The implementation of MVSC produced shortest path, smoothness of the velocity and successfully avoids collision with the obstacles to reach it predetermined target. Conclusion: MVSC propose a simple path planning that requires low computational cost and do not demand for a very large memory

Some graph properties of the optimised degree six 3-modified chordal ring network

The interconnection topology of a parallel or distributed network is pivotal in ensuring good system performance. It can be modelled by a graph, where its edges represent the links between processor nodes represented by vertices. One such graph model that has gained attention by researchers since its founding is the chordal ring, based on an undirected circulant graph. This paper discusses the degree six 3-modified chordal ring, CHR6o3, and presents its graph theoretical properties of symmetry and Hamiltonicity. CHR6o3 is shown to be asymmetric, and can be decomposed into similar subgraphs, each consisting of only one type of node in its class if ring links are ignored. These properties aid both the development of a routing scheme and also determining lower bounds for its chromatic number. Conditions for the existence of a Hamiltonian Circuit within CHR6o3 are also discussed. The existence of a Hamiltonian Circuit within a network simplifies parallel processing as the processors can be arranged to work on a task in a linear array. An Eulerian Circuit was shown to exist in CHR6o3. The existence of an Eulerian Circuit plays a role in routing in optical networks

Modified virtual semi-circle approach for a reactive collision avoidance of a mobile robot in an outdoor environment

There are numerous numbers of methods that have been introduced to the Unmanned Ground Vehicle (UGV) to find its optimal path. The purpose of this paper is to navigate a cost effective UGV known as MG-TruckS with optimal path planning in an outdoor environment. A Modified Virtual Semi Circle approach is proposed based on situated-activity paradigm. This approach is divided into two phase to compute a free collision path planning; detection and avoidance phase. Implementation of five ultrasonic range finder sensors with a very small blind zone created on purpose and the formation of three layers of influence zone shows the optimized path planning without making any unnecessary obstacle avoidance being computed

Chromatic numbers and indices of the optimised degree six 3-modified chordal ring network topology

Graph colouring is the labelling of the elements of a graph subject to certain constraints. It is divided into vertex and edge colouring. In both cases, the assignment of labels, traditionally called colours is such that two vertices or edges must not have the same colour. This has various applications, especially in parallel computing. This paper introduces the degree six 3-modified chordal ring, CHR6o3, a parallel network interconnection topology model, and discusses its node and link colouring. Despite its asymmetry, the chromatic number of CHR6o3 cannot be generalised and must be determined specifically based on the combination of chords in each case. Cases where the chromatic index of CHR6o3 is its degree and where it is its one colour more than its degree were generalised and proven. Chromatic numbers are important in minimising the completion times of processes in parallel processing by reducing points of synchronisation, and link colouring aids processor scheduling

Analysis of modified degree six chordal rings and traditional chordal rings degree six interconnection network

Chordal rings are attractive network interconnection due to their short diameters especially when the degree was increased. Chordal rings were related to find the shortest path in a ring structured. This paper presents an analysis of modified degree six chordal rings (CHRm6) and chordal rings degree six (CR6) or commonly known as traditional chordal rings degree six (CR6). This analysis includes the structures, tree visualization, paths, formulations and geometrical representation. The comparison of diameters was made between theoretical and ideal graphs for these two methods. We tested and compared for a large number of nodes. CHRm6 gives shortest diameters for even and odd source node

On properties of modified degree six chordal rings network

Chordal rings are circulant graphs and have deserved significant attention in the last decade. Chordal rings were used to build interconnection networks for distributed and parallel systems. There are many of publications analyzing their networks properties. In this paper, we present the main properties of the latest method of chordal rings called Modified Chordal Rings Degree Six (CHRm6). The properties are connectivity, Hamiltonian cycle and asymmetry. We prove some lemmas and theorems for every property. All of these properties are useful for further works especially in developing a routing scheme

Broadcasting communication in high degree modified chordal rings networks

The design of the interconnection network is one of the main research issues in distributed computing with regard to some specific parameters. This paper works on Modified Chordal Rings Degree Six (CHRm6) topology. Two broadcasting schemes for CHRm6 are proposed. The first scheme is for even source nodes and the second scheme is for odd source nodes. The proposed broadcasting schemes give upper and lower bound of broadcasting in CHRm6 depends on total number of nodes. We prove the lower bound on the broadcast time is d+2 where d is the diameter of the CHRm6