104 research outputs found
Attitude Estimation and Control Using Linear-Like Complementary Filters: Theory and Experiment
This paper proposes new algorithms for attitude estimation and control based
on fused inertial vector measurements using linear complementary filters
principle. First, n-order direct and passive complementary filters combined
with TRIAD algorithm are proposed to give attitude estimation solutions. These
solutions which are efficient with respect to noise include the gyro bias
estimation. Thereafter, the same principle of data fusion is used to address
the problem of attitude tracking based on inertial vector measurements. Thus,
instead of using noisy raw measurements in the control law a new solution of
control that includes a linear-like complementary filter to deal with the noise
is proposed. The stability analysis of the tracking error dynamics based on
LaSalle's invariance theorem proved that almost all trajectories converge
asymptotically to the desired equilibrium. Experimental results, obtained with
DIY Quad equipped with the APM2.6 auto-pilot, show the effectiveness and the
performance of the proposed solutions.Comment: Submitted for Journal publication on March 09, 2015. Partial results
related to this work have been presented in IEEE-ROBIO-201
Path following for a target point attached to a unicycle type vehicle
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
control laws and a geometric characterization hypothesis, which links the
curvature of the path to be followed with the target point. The proposed
controller allows global stabilization without restrictions on initial
conditions. The effectiveness of this controller is illustrated through
simulations
Mass Transportation on Sub-Riemannian Manifolds
We study the optimal transport problem in sub-Riemannian manifolds where the
cost function is given by the square of the sub-Riemannian distance. Under
appropriate assumptions, we generalize Brenier-McCann's Theorem proving
existence and uniqueness of the optimal transport map. We show the absolute
continuity property of Wassertein geodesics, and we address the regularity
issue of the optimal map. In particular, we are able to show its approximate
differentiability a.e. in the Heisenberg group (and under some weak assumptions
on the measures the differentiability a.e.), which allows to write a weak form
of the Monge-Amp\`ere equation
The rolling problem: overview and challenges
In the present paper we give a historical account -ranging from classical to
modern results- of the problem of rolling two Riemannian manifolds one on the
other, with the restrictions that they cannot instantaneously slip or spin one
with respect to the other. On the way we show how this problem has profited
from the development of intrinsic Riemannian geometry, from geometric control
theory and sub-Riemannian geometry. We also mention how other areas -such as
robotics and interpolation theory- have employed the rolling model.Comment: 20 page
Continuous-time link-based kinematic wave model: formulation, solution existence, and well-posedness
We present a continuous-time link-based kinematic wave model (LKWM) for
dynamic traffic networks based on the scalar conservation law model. Derivation
of the LKWM involves the variational principle for the Hamilton-Jacobi equation
and junction models defined via the notions of demand and supply. We show that
the proposed LKWM can be formulated as a system of differential algebraic
equations (DAEs), which captures shock formation and propagation, as well as
queue spillback. The DAE system, as we show in this paper, is the
continuous-time counterpart of the link transmission model. In addition, we
present a solution existence theory for the continuous-time network model and
investigate continuous dependence of the solution on the initial data, a
property known as well-posedness. We test the DAE system extensively on several
small and large networks and demonstrate its numerical efficiency.Comment: 39 pages, 14 figures, 2 tables, Transportmetrica B: Transport
Dynamics 201
Geometric Approach to Pontryagin's Maximum Principle
Since the second half of the 20th century, Pontryagin's Maximum Principle has
been widely discussed and used as a method to solve optimal control problems in
medicine, robotics, finance, engineering, astronomy. Here, we focus on the
proof and on the understanding of this Principle, using as much geometric ideas
and geometric tools as possible. This approach provides a better and clearer
understanding of the Principle and, in particular, of the role of the abnormal
extremals. These extremals are interesting because they do not depend on the
cost function, but only on the control system. Moreover, they were discarded as
solutions until the nineties, when examples of strict abnormal optimal curves
were found. In order to give a detailed exposition of the proof, the paper is
mostly self\textendash{}contained, which forces us to consider different areas
in mathematics such as algebra, analysis, geometry.Comment: Final version. Minors changes have been made. 56 page
Cantor type functions in non-integer bases
Cantor's ternary function is generalized to arbitrary base-change functions
in non-integer bases. Some of them share the curious properties of Cantor's
function, while others behave quite differently
Global stability of enzymatic chain of full reversible Michaelis-Menten reactions
International audienceWe consider a chain of metabolic reactions catalyzed by enzymes, of reversible Michaelis-Menten type with full dynamics, i.e. not reduced with any quasi- steady state approximations. We study the corresponding dynamical system and show its global stability if the equilibrium exists. If the system is open, the equilibrium may not exist. The main tool is monotone systems theory. Finally we study the implications of these results for the study of coupled genetic-metabolic systems
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