DARP: Divide Areas Algorithm for Optimal Multi-Robot Coverage Path Planning

This paper deals with the path planning problem of a team of mobile robots, in order to cover an area of interest, with prior-defined obstacles. For the single robot case, also known as single robot coverage path planning (CPP), an (n) optimal methodology has already been proposed and evaluated in the literature, where n is the grid size. The majority of existing algorithms for the multi-robot case (mCPP), utilize the aforementioned algorithm. Due to the complexity, however, of the mCPP, the best the existing mCPP algorithms can perform is at most 16 times the optimal solution, in terms of time needed for the robot team to accomplish the coverage task, while the time required for calculating the solution is polynomial. In the present paper, we propose a new algorithm which converges to the optimal solution, at least in cases where one exists. The proposed technique transforms the original integer programming problem (mCPP) into several single-robot problems (CPP), the solutions of which constitute the optimal mCPP solution, alleviating the original mCPP explosive combinatorial complexity. Although it is not possible to analytically derive bounds regarding the complexity of the proposed algorithm, extensive numerical analysis indicates that the complexity is bounded by polynomial curves for practically sized inputs. In the heart of the proposed approach lies the DARP algorithm, which divides the terrain into a number of equal areas each corresponding to a specific robot, so as to guarantee complete coverage, non-backtracking solution, minimum coverage path, while at the same time does not need any preparatory stage (video demonstration and standalone application are available on-line http://tinyurl.com/DARP-app)

Autonomous trajectory design system for mapping of unknown sea-floors using a team of AUVs

This research develops a new on-line trajectory planning algorithm for a team of Autonomous Underwater Vehicles (AUVs). The goal of the AUVs is to cooperatively explore and map the ocean seafloor. As the morphology of the seabed is unknown and complex, standard non-convex algorithms perform insufficiently. To tackle this, a new simulationbased approach is proposed and numerically evaluated. This approach adapts the Parametrized Cognitive-based Adaptive Optimization (PCAO) algorithm. The algorithm transforms the exploration problem to a parametrized decision-making mechanism whose real-time implementation is feasible. Upon that transformation, this scheme calculates off-line a set of decision making mechanism’s parameters that approximate the - nonpractically feasible - optimal solution. The advantages of the algorithm are significant computational simplicity, scalability, and the fact that it can straightforwardly embed any type of physical constraints and system limitations. In order to train the PCAO controller, two morphologically different seafloors are used. During this training, the algorithm outperforms an unrealistic optimal-one-step-ahead search algorithm. To demonstrate the universality of the controller, the most effective controller is used to map three new morphologically different seafloors. During the latter mapping experiment, the PCAO algorithm outperforms several gradient-descent-like approaches

Translation from Classical Two-Way Automata to Pebble Two-Way Automata

We study the relation between the standard two-way automata and more powerful devices, namely, two-way finite automata with an additional "pebble" movable along the input tape. Similarly as in the case of the classical two-way machines, it is not known whether there exists a polynomial trade-off, in the number of states, between the nondeterministic and deterministic pebble two-way automata. However, we show that these two machine models are not independent: if there exists a polynomial trade-off for the classical two-way automata, then there must also exist a polynomial trade-off for the pebble two-way automata. Thus, we have an upward collapse (or a downward separation) from the classical two-way automata to more powerful pebble automata, still staying within the class of regular languages. The same upward collapse holds for complementation of nondeterministic two-way machines. These results are obtained by showing that each pebble machine can be, by using suitable inputs, simulated by a classical two-way automaton with a linear number of states (and vice versa), despite the existing exponential blow-up between the classical and pebble two-way machines

On Measuring Non-Recursive Trade-Offs

We investigate the phenomenon of non-recursive trade-offs between descriptional systems in an abstract fashion. We aim at categorizing non-recursive trade-offs by bounds on their growth rate, and show how to deduce such bounds in general. We also identify criteria which, in the spirit of abstract language theory, allow us to deduce non-recursive tradeoffs from effective closure properties of language families on the one hand, and differences in the decidability status of basic decision problems on the other. We develop a qualitative classification of non-recursive trade-offs in order to obtain a better understanding of this very fundamental behaviour of descriptional systems

Systematically Improving the Efficiency of Grid-Based Coverage Path Planning Methodologies in Real-World UAVs’ Operations

This work focuses on the efficiency improvement of grid-based Coverage Path Planning (CPP) methodologies in real-world applications with UAVs. While several sophisticated approaches are met in literature, grid-based methods are not commonly used in real-life operations. This happens mostly due to the error that is introduced during the region’s representation on the grid, a step mandatory for such methods, that can have a great negative impact on their overall coverage efficiency. A previous work on UAVs’ coverage operations for remote sensing, has introduced a novel optimization procedure for finding the optimal relative placement between the region of interest and the grid, improving the coverage and resource utilization efficiency of the generated trajectories, but still, incorporating flaws that can affect certain aspects of the method’s effectiveness. This work goes one step forward and introduces a CPP method, that provides three different ad-hoc coverage modes: the Geo-fenced Coverage Mode, the Better Coverage Mode and the Complete Coverage Mode, each incorporating features suitable for specific types of vehicles and real-world applications. For the design of the coverage trajectories, user-defined percentages of overlap (sidelap and frontlap) are taken into consideration, so that the collected data will be appropriate for applications like orthomosaicing and 3D mapping. The newly introduced modes are evaluated through simulations, using 20 publicly available benchmark regions as testbed, demonstrating their stenghts and weaknesses in terms of coverage and efficiency. The proposed method with its ad-hoc modes can handle even the most complex-shaped, concave regions with obstacles, ensuring complete coverage, no-sharp-turns, non-overlapping trajectories and strict geo-fencing. The achieved results demonstrate that the common issues encountered in grid-based methods can be overcome by considering the appropriate parameters, so that such methods can provide robust solutions in the CPP domain