1,338 research outputs found

    Flow Stability of Patchy Vector Fields and Robust Feedback Stabilization

    Full text link
    The paper is concerned with patchy vector fields, a class of discontinuous, piecewise smooth vector fields that were introduced in AB to study feedback stabilization problems. We prove the stability of the corresponding solution set w.r.t. a wide class of impulsive perturbations. These results yield the robusteness of patchy feedback controls in the presence of measurement errors and external disturbances.Comment: 22 page

    Singularity-free Guiding Vector Field for Robot Navigation

    Get PDF
    Most of the existing path-following navigation algorithms cannot guarantee global convergence to desired paths or enable following self-intersected desired paths due to the existence of singular points where navigation algorithms return unreliable or even no solutions. One typical example arises in vector-field guided path-following (VF-PF) navigation algorithms. These algorithms are based on a vector field, and the singular points are exactly where the vector field diminishes. In this paper, we show that it is mathematically impossible for conventional VF-PF algorithms to achieve global convergence to desired paths that are self-intersected or even just simple closed (precisely, homeomorphic to the unit circle). Motivated by this new impossibility result, we propose a novel method to transform self-intersected or simple closed desired paths to non-self-intersected and unbounded (precisely, homeomorphic to the real line) counterparts in a higher-dimensional space. Corresponding to this new desired path, we construct a singularity-free guiding vector field on a higher-dimensional space. The integral curves of this new guiding vector field is thus exploited to enable global convergence to the higher-dimensional desired path, and therefore the projection of the integral curves on a lower-dimensional subspace converge to the physical (lower-dimensional) desired path. Rigorous theoretical analysis is carried out for the theoretical results using dynamical systems theory. In addition, we show both by theoretical analysis and numerical simulations that our proposed method is an extension combining conventional VF-PF algorithms and trajectory tracking algorithms. Finally, to show the practical value of our proposed approach for complex engineering systems, we conduct outdoor experiments with a fixed-wing airplane in windy environment to follow both 2D and 3D desired paths.Comment: Accepted for publication in IEEE Trransactions on Robotics (T-RO

    Controle híbrido para estabilização de pose usando quaternions duais

    Get PDF
    Tese (doutorado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Elétrica, 2018.Motivado tanto pelas vantagens da representação em dual quatérnios duais e por problemas relativos à obstrução topológica de se ter um equilíbrio assintótico globalmente estável, esse trabalho visa usar o formalismo de quaternion dual e as ferramentas de sistemas dinâmicos híbridos para tratar o problema de estabilização de pose de corpos rígidos. O grupo de Lie dos quatérnios duais proporciona um modo eficiente de representar a cinemática linear e rotacional de um corpo rígido sem singularidades. Algumas estratégias híbridas são propostas para lidar com o problema de “chattering” presente em todos os controladores por realimentação descontínuos enquanto ao mesmo tempo garantindo atratividade global da pose de estabilização do corpo rígido.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) e Fundação de Apoio à Pesquisa do Distrito Federal (FAP-DF).Motivated both by the advantages of the dual quaternion representation and by the problems concerning the topological obstruction to global asymptotic stability, this work addresses the rigid body pose stabilization problem using dual quaternion formalism and dynamic hybrid systems tools. The Lie group of unit dual quaternions provides a computationally efficient way to represent coupled linear and rotational kinematics without singularities. Some hybrid control strategies are proposed to overcome the chattering problem present in all discontinuous-based feedback controllers while at same time also guaranteeing global attractivity of the stabilization pose of the rigid body

    Physically Interacting With Four Dimensions

    Get PDF
    Thesis (Ph.D.) - Indiana University, Computer Sciences, 2009People have long been fascinated with understanding the fourth dimension. While making pictures of 4D objects by projecting them to 3D can help reveal basic geometric features, 3D graphics images by themselves are of limited value. For example, just as 2D shadows of 3D curves may have lines crossing one another in the shadow, 3D graphics projections of smooth 4D topological surfaces can be interrupted where one surface intersects another. The research presented here creates physically realistic models for simple interactions with objects and materials in a virtual 4D world. We provide methods for the construction, multimodal exploration, and interactive manipulation of a wide variety of 4D objects. One basic achievement of this research is to exploit the free motion of a computer-based haptic probe to support a continuous motion that follows the \emph{local continuity\/} of a 4D surface, allowing collision-free exploration in the 3D projection. In 3D, this interactive probe follows the full local continuity of the surface as though we were in fact \emph{physically touching\/} the actual static 4D object. Our next contribution is to support dynamic 4D objects that can move, deform, and collide with other objects as well as with themselves. By combining graphics, haptics, and collision-sensing physical modeling, we can thus enhance our 4D visualization experience. Since we cannot actually place interaction devices in 4D, we develop fluid methods for interacting with a 4D object in its 3D shadow image using adapted reduced-dimension 3D tools for manipulating objects embedded in 4D. By physically modeling the correct properties of 4D surfaces, their bending forces, and their collisions in the 3D interactive or haptic controller interface, we can support full-featured physical exploration of 4D mathematical objects in a manner that is otherwise far beyond the real-world experience accessible to human beings

    Situational Awareness Enhancement for Connected and Automated Vehicle Systems

    Get PDF
    Recent developments in the area of Connected and Automated Vehicles (CAVs) have boosted the interest in Intelligent Transportation Systems (ITSs). While ITS is intended to resolve and mitigate serious traffic issues such as passenger and pedestrian fatalities, accidents, and traffic congestion; these goals are only achievable by vehicles that are fully aware of their situation and surroundings in real-time. Therefore, connected and automated vehicle systems heavily rely on communication technologies to create a real-time map of their surrounding environment and extend their range of situational awareness. In this dissertation, we propose novel approaches to enhance situational awareness, its applications, and effective sharing of information among vehicles.;The communication technology for CAVs is known as vehicle-to-everything (V2x) communication, in which vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) have been targeted for the first round of deployment based on dedicated short-range communication (DSRC) devices for vehicles and road-side transportation infrastructures. Wireless communication among these entities creates self-organizing networks, known as Vehicular Ad-hoc Networks (VANETs). Due to the mobile, rapidly changing, and intrinsically error-prone nature of VANETs, traditional network architectures are generally unsatisfactory to address VANETs fundamental performance requirements. Therefore, we first investigate imperfections of the vehicular communication channel and propose a new modeling scheme for large-scale and small-scale components of the communication channel in dense vehicular networks. Subsequently, we introduce an innovative method for a joint modeling of the situational awareness and networking components of CAVs in a single framework. Based on these two models, we propose a novel network-aware broadcast protocol for fast broadcasting of information over multiple hops to extend the range of situational awareness. Afterward, motivated by the most common and injury-prone pedestrian crash scenarios, we extend our work by proposing an end-to-end Vehicle-to-Pedestrian (V2P) framework to provide situational awareness and hazard detection for vulnerable road users. Finally, as humans are the most spontaneous and influential entity for transportation systems, we design a learning-based driver behavior model and integrate it into our situational awareness component. Consequently, higher accuracy of situational awareness and overall system performance are achieved by exchange of more useful information

    Pedestrian flows in bounded domains with obstacles

    Full text link
    In this paper we systematically apply the mathematical structures by time-evolving measures developed in a previous work to the macroscopic modeling of pedestrian flows. We propose a discrete-time Eulerian model, in which the space occupancy by pedestrians is described via a sequence of Radon positive measures generated by a push-forward recursive relation. We assume that two fundamental aspects of pedestrian behavior rule the dynamics of the system: On the one hand, the will to reach specific targets, which determines the main direction of motion of the walkers; on the other hand, the tendency to avoid crowding, which introduces interactions among the individuals. The resulting model is able to reproduce several experimental evidences of pedestrian flows pointed out in the specialized literature, being at the same time much easier to handle, from both the analytical and the numerical point of view, than other models relying on nonlinear hyperbolic conservation laws. This makes it suitable to address two-dimensional applications of practical interest, chiefly the motion of pedestrians in complex domains scattered with obstacles.Comment: 25 pages, 9 figure

    The geometry of dynamical triangulations

    Full text link
    We discuss the geometry of dynamical triangulations associated with 3-dimensional and 4-dimensional simplicial quantum gravity. We provide analytical expressions for the canonical partition function in both cases, and study its large volume behavior. In the space of the coupling constants of the theory, we characterize the infinite volume line and the associated critical points. The results of this analysis are found to be in excellent agreement with the MonteCarlo simulations of simplicial quantum gravity. In particular, we provide an analytical proof that simply-connected dynamically triangulated 4-manifolds undergo a higher order phase transition at a value of the inverse gravitational coupling given by 1.387, and that the nature of this transition can be concealed by a bystable behavior. A similar analysis in the 3-dimensional case characterizes a value of the critical coupling (3.845) at which hysteresis effects are present.Comment: 166 pages, Revtex (latex) fil

    Dynamical Modularity in Automata Models of Biochemical Networks

    Full text link
    Given the large size and complexity of most biochemical regulation and signaling networks, there is a non-trivial relationship between the micro-level logic of component interactions and the observed macro-dynamics. Here we address this issue by formalizing the existing concept of pathway modules, which are sequences of state updates that are guaranteed to occur (barring outside interference) in the dynamics of automata networks after the perturbation of a subset of driver nodes. We present a novel algorithm to automatically extract pathway modules from networks and we characterize the interactions that may take place between modules. This methodology uses only the causal logic of individual node variables (micro-dynamics) without the need to compute the dynamical landscape of the networks (macro-dynamics). Specifically, we identify complex modules, which maximize pathway length and require synergy between their components. This allows us to propose a new take on dynamical modularity that partitions complex networks into causal pathways of variables that are guaranteed to transition to specific states given a perturbation to a set of driver nodes. Thus, the same node variable can take part in distinct modules depending on the state it takes. Our measure of dynamical modularity of a network is then inversely proportional to the overlap among complex modules and maximal when complex modules are completely decouplable from one another in the network dynamics. We estimate dynamical modularity for several genetic regulatory networks, including the Drosophila melanogaster segment-polarity network. We discuss how identifying complex modules and the dynamical modularity portrait of networks explains the macro-dynamics of biological networks, such as uncovering the (more or less) decouplable building blocks of emergent computation (or collective behavior) in biochemical regulation and signaling.Comment: 42 pages, 7 figure
    corecore