493 research outputs found
Decentralized Collision-Free Control of Multiple Robots in 2D and 3D Spaces
Decentralized control of robots has attracted huge research interests.
However, some of the research used unrealistic assumptions without collision
avoidance. This report focuses on the collision-free control for multiple
robots in both complete coverage and search tasks in 2D and 3D areas which are
arbitrary unknown. All algorithms are decentralized as robots have limited
abilities and they are mathematically proved.
The report starts with the grid selection in the two tasks. Grid patterns
simplify the representation of the area and robots only need to move straightly
between neighbor vertices. For the 100% complete 2D coverage, the equilateral
triangular grid is proposed. For the complete coverage ignoring the boundary
effect, the grid with the fewest vertices is calculated in every situation for
both 2D and 3D areas.
The second part is for the complete coverage in 2D and 3D areas. A
decentralized collision-free algorithm with the above selected grid is
presented driving robots to sections which are furthest from the reference
point. The area can be static or expanding, and the algorithm is simulated in
MATLAB.
Thirdly, three grid-based decentralized random algorithms with collision
avoidance are provided to search targets in 2D or 3D areas. The number of
targets can be known or unknown. In the first algorithm, robots choose vacant
neighbors randomly with priorities on unvisited ones while the second one adds
the repulsive force to disperse robots if they are close. In the third
algorithm, if surrounded by visited vertices, the robot will use the
breadth-first search algorithm to go to one of the nearest unvisited vertices
via the grid. The second search algorithm is verified on Pioneer 3-DX robots.
The general way to generate the formula to estimate the search time is
demonstrated. Algorithms are compared with five other algorithms in MATLAB to
show their effectiveness
Small polaron with generic open boundary conditions revisit: exact solution via the off-diagonal Bethe ansatz
The small polaron, an one-dimensional lattice model of interacting spinless
fermions, with generic non-diagonal boundary terms is studied by the
off-diagonal Bethe ansatz method. The presence of the Grassmann valued
non-diagonal boundary fields gives rise to a typical -symmetry-broken
fermionic model. The exact spectra of the Hamiltonian and the associated Bethe
ansatz equations are derived by constructing an inhomogeneous relation.Comment: 12 pages, no figure, published versio
A second-order length-preserving and unconditionally energy stable rotational discrete gradient method for Oseen-Frank gradient flows
We present a second-order strictly length-preserving and unconditionally
energy-stable rotational discrete gradient (Rdg) scheme for the numerical
approximation of the Oseen-Frank gradient flows with anisotropic elastic energy
functional. Two essential ingredients of the Rdg method are reformulation of
the length constrained gradient flow into an unconstrained rotational form and
discrete gradient discretization for the energy variation. Besides the
well-known mean-value and Gonzalez discrete gradients, we propose a novel
Oseen-Frank discrete gradient, specifically designed for the solution of
Oseen-Frank gradient flow. We prove that the proposed Oseen-Frank discrete
gradient satisfies the energy difference relation, thus the resultant Rdg
scheme is energy stable. Numerical experiments demonstrate the efficiency and
accuracy of the proposed Rdg method and its capability for providing reliable
simulation results with highly disparate elastic coefficients
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