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We present a novel approach called Optimized Directed Roadmap Graph (ODRM). It is a method to build a directed roadmap graph that allows for collision avoidance in multi-robot navigation. This is a highly relevant problem, for example for industrial autonomous guided vehicles. The core idea of ODRM is, that a directed roadmap can encode inherent pr...

## Citations

... For example, the boundary is simple and smooth to allow the equilateral triangle grid to stay inside the border. In this report, complete coverage without exceeding the board is considered by either providing some assumptions about the shape of the area [225,222,226] or employing the assumption for the boundary effect [221,224]. ...

... However, in the simulation of those papers, that relation was not always used. In fact, when considering collision avoidance, the volume of the robot and the obstacle sensing range, the T grid could not always contain the fewest vertices in different conditions and could only guarantee the complete coverage with the assumption of the boundary effect [222,225]. ...

... However, [129] did not provide the ratio and all these paper ignore collisions. In this report, to guarantee a strict 100% 2D complete coverage of the task area, only the T grid could be used with assumptions about the passage, the relations between different parameters and the curvature of the boundaries based on [222,225]. When a complete coverage is not required and the assumption of the boundary effect is used, the way to choose the suitable grid under different situations for both 2D and 3D areas is discussed. ...

Decentralized control of robots has attracted huge research interests. However, some of the research used unrealistic assumptions without collision avoidance. This report focuses on the collision-free control for multiple robots in both complete coverage and search tasks in 2D and 3D areas which are arbitrary unknown. All algorithms are decentralized as robots have limited abilities and they are mathematically proved. The report starts with the grid selection in the two tasks. Grid patterns simplify the representation of the area and robots only need to move straightly between neighbor vertices. For the 100% complete 2D coverage, the equilateral triangular grid is proposed. For the complete coverage ignoring the boundary effect, the grid with the fewest vertices is calculated in every situation for both 2D and 3D areas. The second part is for the complete coverage in 2D and 3D areas. A decentralized collision-free algorithm with the above selected grid is presented driving robots to sections which are furthest from the reference point. The area can be static or expanding, and the algorithm is simulated in MATLAB. Thirdly, three grid-based decentralized random algorithms with collision avoidance are provided to search targets in 2D or 3D areas. The number of targets can be known or unknown. In the first algorithm, robots choose vacant neighbors randomly with priorities on unvisited ones while the second one adds the repulsive force to disperse robots if they are close. In the third algorithm, if surrounded by visited vertices, the robot will use the breadth-first search algorithm to go to one of the nearest unvisited vertices via the grid. The second search algorithm is verified on Pioneer 3-DX robots. The general way to generate the formula to estimate the search time is demonstrated. Algorithms are compared with five other algorithms in MATLAB to show their effectiveness.

The ability of mobile robots to work as a team in hard and hazardous environments and consequently their widespread use in various industries is a strong incentive for researchers to develop practical algorithm and methods for increasing the performance of mobile robots. The ability of autonomous decision-making for navigation and path planning is the important problem, which has been investigated by researchers to improve the performance of a team of mobile robots in a certain mission. The contribution of this study is classified as follows; In the first stage, we propose a decentralised motion control algorithm for the mobile robots to intercept an intruder entering (k-intercepting) or escaping (e-intercepting) a protected region. In continue, we propose a decentralized navigation strategy (dynamic-intercepting) for a multi-robot team known as predators to intercept the intruders or in the other words, preys, from escaping a siege ring which is created by the predators. A necessary and sufficient condition for the existence of a solution of this problem is obtained. At the second stage, we propose an intelligent game-based decision-making algorithm (IGD) for a fleet of mobile robots to maximize the probability of detection in a bounded region. We prove that the proposed decentralised cooperative and non-cooperative game-based decision-making algorithm enables each robot to make the best decision to choose the shortest path with minimum local information. Third, we propose a leader-follower based collision-free navigation control method for a fleet of mobile robots to traverse an unknown cluttered environment. Fourth, we propose a decentralised navigation algorithm for a team of multi-robot to traverse an area where occupied by multiple obstacles to trap a target. We prove that each individual team 3 member is able to traverse safely in the region, which is cluttered by many obstacles with any shapes to trap the target while using the sensors in some indefinite switching points and not continuously, which leads to saving energy consumption and increasing the battery life of the robots consequently. And finally, we propose a novel navigation strategy for a unicycle mobile robot in a cluttered area with moving obstacles based on virtual field force algorithm. The mathematical proof of the navigation laws and the computer simulations are provided to confirm the validity, robustness, and reliability of the proposed methods. 4

In this report, we propose a decentralised motion control algorithm for the mobile robots to intercept an intruder entering (k-intercepting) or escaping (e-intercepting) a protected region. In continuation, we propose a decentralized navigation strategy (dynamic-intercepting) for a multi-robot team known as predators to intercept the intruders or in the other words, preys, from escaping a siege ring which is created by the predators. A necessary and sufficient condition for the existence of a solution of this problem is obtained. Furthermore, we propose an intelligent game-based decision-making algorithm (IGD) for a fleet of mobile robots to maximize the probability of detection in a bounded region. We prove that the proposed decentralised cooperative and non-cooperative game-based decision-making algorithm enables each robot to make the best decision to choose the shortest path with minimum local information. Then we propose a leader-follower based collision-free navigation control method for a fleet of mobile robots to traverse an unknown cluttered environment where is occupied by multiple obstacles to trap a target. We prove that each individual team member is able to traverse safely in the region, which is cluttered by many obstacles with any shapes to trap the target while using the sensors in some indefinite switching points and not continuously, which leads to saving energy consumption and increasing the battery life of the robots consequently. And finally, we propose a novel navigation strategy for a unicycle mobile robot in a cluttered area with moving obstacles based on virtual field force algorithm. The mathematical proof of the navigation laws and the computer simulations are provided to confirm the validity, robustness, and reliability of the proposed methods.