8,433 research outputs found
Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff
In this article we provide global subelliptic estimates for the linearized
inhomogeneous Boltzmann equation without angular cutoff, and show that some
global gain in the spatial direction is available although the corresponding
operator is not elliptic in this direction. The proof is based on a multiplier
method and the so-called Wick quantization, together with a careful analysis of
the symbolic properties of the Weyl symbol of the Boltzmann collision operator
Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation
Many algorithms for control, optimization and estimation in robotics depend
on derivatives of the underlying system dynamics, e.g. to compute
linearizations, sensitivities or gradient directions. However, we show that
when dealing with Rigid Body Dynamics, these derivatives are difficult to
derive analytically and to implement efficiently. To overcome this issue, we
extend the modelling tool `RobCoGen' to be compatible with Automatic
Differentiation. Additionally, we propose how to automatically obtain the
derivatives and generate highly efficient source code. We highlight the
flexibility and performance of the approach in two application examples. First,
we show a Trajectory Optimization example for the quadrupedal robot HyQ, which
employs auto-differentiation on the dynamics including a contact model. Second,
we present a hardware experiment in which a 6 DoF robotic arm avoids a randomly
moving obstacle in a go-to task by fast, dynamic replanning
Bounded decomposition in the Brieskorn lattice and Pfaffian Picard--Fuchs systems for Abelian integrals
We suggest an algorithm for derivation of the Picard--Fuchs system of
Pfaffian equations for Abelian integrals corresponding to semiquasihomogeneous
Hamiltonians. It is based on an effective decomposition of polynomial forms in
the Brieskorn lattice. The construction allows for an explicit upper bound on
the norms of the polynomial coefficients, an important ingredient in studying
zeros of these integrals.Comment: 17 pages in LaTeX2
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