Navigation function

Abstract: Map-matching algorithms integrate positioning data with spatial road network data (roadway centrelines) to identify the correct link on which a vehicle is travelling and to determine the location of a vehicle on a link. A map-matching algorithm could be used as a key component to improve the performance of systems that support the navigation function of intelligent transport systems (ITS). The required horizontal positioning accuracy of such ITS applications is in the range of 1 m to 40 m (95%) with relatively stringent requirements placed on integrity (quality), continuity and system availability. A number of map-matching algorithms have been developed by researchers around the world using different techniques such as topological analysis of spatial road network data, probabilistic theory, Kalman filter, fuzzy logic, and belief theory. The performances of these algorithms have improved over the years due to the application of advanced techniques in the map matching processes and improvements in the quality of both positioning and spatial road network data. However, these algorithms are not always capable of supporting ITS applications with high required navigation performance, especially in difficult and complex environments such as dense urban areas. This suggests that research should be directed at identifying any constraints and limitations of existing map matching algorithms as a prerequisite for the formulation of algorithm improvements. The objectives of this paper are thus to uncover the constraints and limitations by an in-depth literature review and to recommend ideas to address them. This paper also highlights the potential impacts of the forthcoming European Galileo system and the European Geostationary Overlay Service (EGNOS) on the performance of map matching algorithms. Although not addressed in detail, the paper also presents some ideas for monitoring the integrity of map-matching algorithms. The map-matching algorithms considered in this paper are generic and do not assume knowledge of ‘future’ information (i.e. based on either cost or time). Clearly, such data would result in relatively simple map-matching algorithms.

Abstract: This paper presents the first motion planning methodology applicable to articulated, nonpoint nonholonomic robots with guaranteed collision avoidance and convergence properties. It is based on a new class of nonsmooth Lyapunov functions and a novel extension of the navigation function method to account for nonpoint articulated robots. The dipolar inverse Lyapunov functions introduced are appropriate for nonholonomic control and offer superior performance characteristics compared to existing tools. The new potential field technique uses diffeomorphic transformations and exploits the resulting point-world topology. The combined approach is applied to the problem of handling deformable material by multiple nonholonomic mobile manipulators in an obstacle environment to yield a centralized coordinating control law. Simulation results verify asymptotic convergence of the robots, obstacle avoidance, boundedness of object deformations, and singularity avoidance for the manipulators.

Abstract: Examination of total energy shows that the global limit behavior of a dissipative mechanical system is essentially equivalent to that of its constituent gradient vector field. The class of “navigation functions” is introduced and shown to result in “almost global” asymptotic stability for closed loop mechanical control systems upon which a navigation function has been imposed as an artifical potential energy. Two examples from the engineering literature satellite attitude tracking and robot obstacle avoidance are provided to demonstrate the utility of these observations. For more information: Kod*Lab Disciplines Electrical and Computer Engineering | Engineering | Systems Engineering Comments Preprint version. First published in Control Theory and Multibody Systems , in Volume 97, 1989, pages 131-158, published by the American Mathematical Society in the Contemporary Mathematics series. NOTE: At the time of publication, author Daniel Koditschek was affiliated with Yale University. Currently, he is a faculty member in the Department of Electrical and Systems Engineering at the University of Pennsylvania. This journal article is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/672