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When organizing robots into formations, the interplay between the underlying network topology of the team and the sensing and communication modalities available to the individual robots has a fundamental effect on what types of formations are possible. The purpose of this article is to characterize the available motions of formations in which relative angles between robots equipped with bearing-only sensors are maintained. First, infinitesimal shape-similarity, a property of frameworks for which maintaining certain angles between robots ensures that the formation is invariant to translation, rotation, and uniform scaling, is examined; the shape-similarity matrix is redeveloped, and results on its nullspace are presented. Second, triangulations, a class of frameworks, are shown to be infinitesimally shape-similar. Finally, the coupling between network topology and robot capabilities is examined through the design of a decentralized heterogeneous formation-control strategy for a class of triangulations in which all robots are equipped with bearing-only sensors and a single robot can measure distances; the formation-control strategy is demonstrated on a team of differential-drive robots. [ABSTRACT FROM AUTHOR]

Positioning is a fundamental issue in mobile robot applications, and it can be achieved in multiple ways. Among these methods, triangulation based on angle measurements is widely used, robust, accurate, and flexible. This paper presents BeAMS, which is a new active beacon-based angle measurement system used for mobile robot positioning. BeAMS introduces several major innovations. One innovation is the use of a unique unsynchronized channel with on–off keying modulated infrared signals to measure angles and to identify the beacons. We also introduce a new mechanism to measure angles: Our system detects a beacon when it enters and leaves an angular window. We show that the estimator resulting from the center of this angular window provides an unbiased estimate of the beacon angle. A theoretical framework for a thorough performance analysis of BeAMS is provided. We establish the upper bound of the variance and validate this bound through experiments and simulations; the overall error measure of BeAMS is lower than \0.24^\circ for an acquisition rate of 10\,\Hz. In conclusion, BeAMS is a low-power, flexible, and robust solution for angle measurement and a reliable component for robot positioning. [ABSTRACT FROM PUBLISHER]

Positioning is a fundamental issue in mobile robot applications. It can be achieved in many ways. Among them, triangulation based on angles measured with the help of beacons is a proven technique. Most of the many triangulation algorithms proposed so far have major limitations. For example, some of them need a particular beacon ordering, have blind spots, or only work within the triangle defined by the three beacons. More reliable methods exist; however, they have an increasing complexity, or they require to handle certain spatial arrangements separately. In this paper, we present a simple and new three object triangulation algorithm, known as ToTal, that natively works in the whole plane and for any beacon ordering. We also provide a comprehensive comparison between many algorithms and show that our algorithm is faster and simpler than comparable algorithms. In addition to its inherent efficiency, our algorithm provides a very useful and unique reliability measure that is assessable anywhere in the plane, which can be used to identify pathological cases, or as a validation gate in Kalman filters. [ABSTRACT FROM PUBLISHER]

In this paper, we present a computational framework for automatic generation of provably correct control laws for planar robots in polygonal environments. Using polygon triangulation and discrete abstractions, we map continuous motion planning and control problems, specified in terms of triangles, to computationally inexpensive problems on finite-state-transition systems. In this framework, discrete planning algorithms in complex environments can be seamlessly linked to automatic generation of feedback control laws for robots with underactuation constraints and control bounds. We focus on fully actuated kinematic robots with velocity bounds and (underactuated) unicycles with forward and turning speed bounds. [ABSTRACT FROM AUTHOR]

Many generic position-estimation algorithms are vulnerable to ambiguity introduced by nonunique landmarks. Also, the available high-dimensional image data is not fully used when these techniques are extended to vision-based localization. This paper presents the landmark matching, triangulation, reconstruction, and comparison (LTRC) global localization algorithm, which is reasonably immune to ambiguous landmark matches. It extracts natural landmarks for the (rough) matching stage before generating the list of possible position estimates through triangulation. Reconstruction and comparison then rank the possible estimates. The LTRC algorithm has been implemented using an interpreted language, onto a robot equipped with a panoramic vision system. Empirical data shows remarkable improvement in accuracy when compared with the established random sample consensus method. LTRC is also robust against inaccurate map data. [ABSTRACT FROM AUTHOR]