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Differential flatness-based distributed control of underactuated robot swarms
This paper proposes a distributed control method based on the differential flatness (DF) property of robot swarms. The swarm DF map** is...
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Trajectory Tracking Control for Under-Actuated Hovercraft Using Differential Flatness and Reinforcement Learning-Based Active Disturbance Rejection Control
This paper proposes a scheme of trajectory tracking control for the hovercraft. Since the model of the hovercraft is under-actuated, nonlinear, and...
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K-flatness and orthogonality in homotopy categories
K-flatness for unbounded complexes of modules over a ring R was introduced by Spaltenstein [27], as an analogue of the classical notion of flatness...
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Interactions Between Differential Geometry and Production Theory
The use of differential geometry in the theory of production is an interesting topic that has attracted the attention of many researchers in the last...
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Safe Interval Path Planning and Flatness-Based Control for Navigation of a Mobile Robot among Static and Dynamic Obstacles
AbstractIn this work we study a navigation problem for a nonholonomic differential drive robot operating in the environment with static and dynamic...
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Differential equations and Lie group representations
We discuss the role of differential equations in Lie group representation theory. We use Kashiwara’s pentagon as a reference frame for the real...
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The cube axiom and resolutions in homotopy theory
We show that a version of the cube axiom holds in cosimplicial unstable coalgebras and cosimplicial spaces equipped with a resolution model...
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Differential Structures of Frölicher Spaces on Tangent Curves
Differential-geometric structures of Frölicher spaces for a singular manifold consisting of two tangent curves are considered. Calculations for two...
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The Cayley Cubic and Differential Equations
We define Cayley structures as a field of Cayley’s ruled cubic surfaces over a four dimensional manifold and motivate their study by showing their...
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Simplicial Chern–Weil theory for coherent analytic sheaves, part II
In the previous part of this diptych, we defined the notion of an admissible simplicial connection , as well as explaining how H.I. Green constructed...
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Quantum parameters of the geometric Langlands theory
Fix a smooth, complete algebraic curve X over an algebraically closed field k of characteristic zero. To a reductive group G over k , we associate an...
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Applications of Differential Graded Algebra Techniques in Commutative Algebra
Differential graded (DG) algebras are powerful tools from rational homotopy theory. We survey some recent applications of these in the realm of...
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Regularized mean curvature flow for invariant hypersurfaces in a Hilbert space and its application to gauge theory
In this paper, we investigate a regularized mean curvature flow starting from an invariant hypersurface in a Hilbert space equipped with an isometric...
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Minimal Rational Curves and 1-Flat Irreducible G-Structures
1-Flat irreducible G-structures, equivalently, irreducible G-structures admitting torsion-free affine connections, have been studied extensively in...
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Norm Estimates and Invertibility Results for SIO’s on Unbounded Boundaries
One of the main goals in this chapter is to estimate singular integral operators of “chord-dot-normal” type, associated with Ahlfors regular domains...
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Boundary Value Problems for Elliptic Systems in Rough Domains
As a culmination of the work in Volumes I-V, here we shall formulate and solve boundary value problems for elliptic systems in a multitude of...
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Relevant Differential Topology in Statistical Manifolds
The author agrees and assumes that this paper is a mixture of several subjects and ongoing perspectives but he emphasizes that their unifying...