The focus of this study is on the design of feedback control laws for swarms of robots that are based on models from fluid dynamics. We apply an incompressible fluid model to solve a pattern generation task. Possible applications of an efficient solution to this task are surveillance and the cordoning off of hazardous areas. More specifically, we use the smoothed-particle hydrodynamics (SPH) technique to devise decentralized controllers that force the robots to behave in a similar manner to fluid particles. Our approach deals with static and dynamic obstacles. Considerations such as finite size and nonholonomic constraints are also addressed. In the absence of obstacles, we prove the stability and convergence of controllers that are based on the SPH method. Computer simulations and actual robot experiments are shown to validate the proposed approach.

We present a multiobjective hybrid technique for automatic orthogonal graph drawing. The new methodology combines the classical approach to automatic orthogonal graph drawings,the topology-shape-metric approach, and a multiobjective genetic algorithm based on the NSGA-II method. In the topology-shape-metric method, a fixed planar embedding is obtained in the planarization step and submitted to the orthogonalization and compaction steps, in this order. In the hybrid approach, a greater number of planar embeddings is explored by varying the order of edges insertion that forms the planar embedding in the planarization step. The problem is then formulated as a multiobjective permutationbased combinatorial optimization problem, considering the minimization of the number of crossings, the number of bends and the area of the drawing. Solutions on the estimated Pareto front represent different drawings, that can be stored and selected by the user in real-time. We illustrate a possible multicriteria decision making based on fuzzy decision. The results show that the hybrid methodology using NSGA-II is able to find good and diverse solutions, when compared to the traditional topology-shape-metric method.

This paper presents a new approach for automatic graph drawing based on Genetic algorithms. The classical topology-shape-metric approach for orthogonal graph drawing keeps a fixed planar embedding obtained in its first step (planarization), using it for the next two steps (orthogonalization and compaction). However, each step is itself an NP-hard problem, and the choices made and heuristics used on previous stages have a direct impact on subsequent ones.

We address the problem of pattern generation in obstacle-filled environments by a swarm of mobile robots. Decentralized controllers are devised by using the Smoothed Particle Hydrodynamics (SPH) method. The swarm is modelled as an incompressible fluid subjected to external forces. Actual robot issues such as finite size and nonholonomic constraints are also addressed. Collision avoidance guarantees are discussed. Finally, in the absence of obstacles, we prove for the first time stability and convergence of controllers based on the SPH.

Several recent works have combined discrete and continuous motion planning methods for robot navigation and control. The basic idea of some of these works is to plan a path, by determining a sequence of neighboring discrete regions of the configuration space, and to assign a vector field that drives the robots through these regions. This paper addresses the problem of efficiently computing vector fields over a sequence of consecutive triangles. Differently from previous numerical approaches, which were not able to compute fully continuous fields in triangulated spaces, this paper presents an algorithm that is able to compute guaranteed continuous vector fields over a sequence of adjacent triangles.

This article presents a simple efficient algorithm for the subdivision of a d -dimensional simplex in k d simplices, where k is any positive integer number. The algorithm is an extension of Freudenthal's subdivision method. The proposed algorithm deals with the more general case of k d subdivision, and is considerably simpler than the RedRefinementND algorithm for implementation of Freudenthal's strategy. The proposed simplex subdivision algorithm is motivated by a problem in the field of robust control theory: the computation of a tight upper bound of a dynamical system performance index by means of a branch-and-bound algorithm.

This paper addresses the problem of efficiently computing robot navigation functions. Navigation functions are potential functions free of spurious local minima that present an exact solution to the robot motion planning and control problem. Although some methodologies were found in the literature, none of them are easy to implement and generalize for complex shaped workspaces and robots. We discuss some of the difficulties encountered in the current methodologies and propose a novel approach using a Finite Element method for potential field computation.