201,864 research outputs found
Safe and Quasi-Optimal Autonomous Navigation in Environments with Convex Obstacles
We propose a continuous feedback control strategy that steers a point-mass
vehicle safely to a destination, in a quasi-optimal manner, in sphere worlds.
The main idea consists in avoiding each obstacle via the shortest path within
the cone enclosing the obstacle and moving straight toward the target when the
vehicle has a clear line of sight to the target location. In particular, almost
global asymptotic stability of the target location is achieved in
two-dimensional (2D) environments under a particular assumption on the
obstacles configuration. We also propose a reactive (sensor-based) approach,
suitable for real-time implementations in a priori unknown 2D environments with
sufficiently curved convex obstacles, guaranteeing almost global asymptotic
stability of the target location. Simulation results are presented to
illustrate the effectiveness of the proposed approach.Comment: arXiv admin note: substantial text overlap with arXiv:2302.1230
Attractive and repulsive polymer-mediated forces between scale-free surfaces
We consider forces acting on objects immersed in, or attached to, long
fluctuating polymers. The confinement of the polymer by the obstacles results
in polymer-mediated forces that can be repulsive (due to loss of entropy) or
attractive (if some or all surfaces are covered by adsorbing layers). The
strength and sign of the force in general depends on the detailed shape and
adsorption properties of the obstacles, but assumes simple universal forms if
characteristic length scales associated with the objects are large. This occurs
for scale-free shapes (such as a flat plate, straight wire, or cone), when the
polymer is repelled by the obstacles, or is marginally attracted to it (close
to the depinning transition where the absorption length is infinite). In such
cases, the separation between obstacles is the only relevant macroscopic
length scale, and the polymer mediated force equals ,
where is temperature. The amplitude is akin to a critical
exponent, depending only on geometry and universality of the polymer system.
The value of , which we compute for simple geometries and ideal
polymers, can be positive or negative. Remarkably, we find for
ideal polymers at the adsorption transition point, irrespective of shapes of
the obstacles, i.e. at this special point there is no polymer-mediated force
between obstacles (scale-free or not).Comment: RevTeX, 10 pages, 10 figure
Vehicle Motion Planning Using Stream Functions
Borrowing a concept from hydrodynamic analysis, this paper presents stream functions which satisfy Laplace's equation as a local-minima free method for producing potential-field based navigation functions in two dimensions. These functions generate smoother paths (i.e. more suited to aircraft-like vehicles) than previous methods. A method is developed for constructing analytic stream functions to produce arbitrary vehicle behaviors while avoiding obstacles, and an exact solution for the case of a single uniformly moving obstacle is presented. The effects of introducing multiple obstacles are discussed and current work in this direction is detailed. Experimental results generated on the Cornell RoboFlag testbed are presented and discussed, as well as related work applying these methods to path planning for unmanned air vehicles
Polymers with self-avoiding interaction in random media: a localization-delocalization transition
In this paper we investigate the problem of a long self-avoiding polymer
chain immersed in a random medium. We find that in the limit of a very long
chain and when the self-avoiding interaction is weak, the conformation of the
chain consists of many ``blobs'' with connecting segments. The blobs are
sections of the molecule curled up in regions of low potential in the case of a
Gaussian distributed random potential or in regions of relatively low density
of obstacles in the case of randomly distributed hard obstacles. We find that
as the strength of the self-avoiding interaction is increased the chain
undergoes a delocalization transition in the sense that the appropriate free
energy per monomer is no longer negative. The chain is then no longer bound to
a particular location in the medium but can easily wander around under the
influence of a small perturbation. For a localized chain we estimate
quantitatively the expected number of monomers in the ``blobs'' and in the
connecting segments.Comment: 20 pages, 2 figures, revtex
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