Related papers: The Collective Coordinate Fix
We established a fixed-point theorem for mapping satisfying a general contractive inequality of integral type depended an another function. This theorem substantially extend the theorem due to Branciari (2003) and Rhoades (2003)
Reactive control is often considered insufficient for multi-objective tasks because conflicting objectives give rise to local minima. We argue this limitation is not inherent but arises from static encodings that fail to reflect how…
In this article, we address the control problem of unicycle path following, using a rigidly attached target point. The initial path following problem has been transformed into a reference trajectory following problem, using saturated…
In semiclassical studies of systems with mixed phase space, the neighbourhood of bifurcations of co-dimension two is felt strongly even though such bifurcations are ungeneric in classical mechanics. We discuss a scenario which reveals this…
The development of vehicle-to-vehicle (V2V) communication facil-itates the study of cooperative positioning (CP) techniques for vehicular applications. The CP methods can improve the posi-tioning availability and accuracy by inter-vehicle…
A recently proposed curvature renormalization group scheme for topological phase transitions defines a generic `curvature function' as a function of the parameters of the theory and shows that topological phase transitions are signalled by…
Traffic congestion is a persistent problem in our society. Previous methods for traffic control have proven futile in alleviating current congestion levels leading researchers to explore ideas with robot vehicles given the increased…
This paper describes the construction of a canonical compactification of the space of trajectories and of the unstable/stable sets of a generic gradient like vector field on a closed manifold as well as a canonical structure of a smooth…
We develop the structure theory for transformations of weakly geometric rough paths of bounded $1 < p$-variation and their controlled paths. Our approach differs from existing approaches as it does not rely on smooth approximations. We…
Robots exhibit a rich variety of symmetries arising from their mechanical structure and the properties of their tasks. Although many robotics problems exhibit several symmetries simultaneously, existing approaches typically treat them in…
We present a general approach to the bifurcation analysis of elastic frameworks with symmetry. While group-theoretic methods for bifurcation problems with symmetry are well known, their actual implementation in the context of elastic…
This paper discusses a more general contractive condition for a class of extended cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same…
The cooperation of connected and automated vehicles (CAVs) has shown great potential in improving traffic efficiency during intersection management. Existing research mainly focuses on intersections where lane changing is prohibited, which…
In this paper, we provide a hierarchical coordination framework for connected and automated vehicles (CAVs) at two adjacent intersections. This framework consists of an upper-level scheduling problem and a low-level optimal control problem.…
In a smooth dynamical system, a homoclinic connection is a closed orbit returning to a saddle equilibrium. Under perturbation, homoclinics are associated with bifurcations of periodic orbits, and with chaos in higher dimensions. Homoclinic…
In a recent paper we have analyzed the role that a universal set of local symmetries plays in suppressing the superposition principle in classical mechanics via a path-integral formulation of classical mechanics itself. In this paper first…
Collaborative perception plays a crucial role in enhancing environmental understanding by expanding the perceptual range and improving robustness against sensor failures, which primarily involves collaborative 3D detection and tracking…
Cooperative driving at isolated intersections attracted great interest and had been well discussed in recent years. However, cooperative driving in multi-intersection road networks remains to be further investigated, because many algorithms…
The recent introduced \textit{dressed coordinates} are studied in the path-integral approach. These coordinates are defined in the context of a harmonic oscillator linearly coupled to massless scalar field and, it is shown that in this…
Matched asymptotic expansion is a useful technique in General Relativity and other fields whenever interaction takes place between physics at two different length scales. Here matched asymptotic expansion is argued to be equivalent quite…