Temporal Correlations and Persistence in the Kinetic Ising Model: the Role of Temperature

We study the statistical properties of the sum $S_t=\int_{0}^{t}dt' \sigma_{t'}$, that is the difference of time spent positive or negative by the spin $\sigma_{t}$, located at a given site of a $D$-dimensional Ising model evolving under Glauber dynamics from a random initial configuration. We investigate the distribution of $S_{t}$ and the first-passage statistics (persistence) of this quantity. We discuss successively the three regimes of high temperature ($T>T_{c}$), criticality ($T=T_c$), and low temperature ($T<T_{c}$). We discuss in particular the question of the temperature dependence of the persistence exponent $\theta$, as well as that of the spectrum of exponents $\theta(x)$, in the low temperature phase. The probability that the temporal mean $S_t/t$ was always larger than the equilibrium magnetization is found to decay as $t^{-\theta-\frac12}$. This yields a numerical determination of the persistence exponent $\theta$ in the whole low temperature phase, in two dimensions, and above the roughening transition, in the low-temperature phase of the three-dimensional Ising model.Comment: 21 pages, 11 PostScript figures included (1 color figure

Path-Following with a Bounded-Curvature Vehicle: a Hybrid Control Approach

In this paper, we consider the problem of stabilizing the kinematic model of a car to a path in the plane under rather general conditions. The path is subject to very mild restrictions, while the car model, although rather simplified, contains the most relevant limitations inherent in wheeled robots kinematics. Namely, the car can only move forward, its steering radius is lower bounded and a limited sensory information only provides a partial knowledge of some state parameters. In particular, we consider the case that the current distance and the heading angle error with respect to the closest point on the reference path can be measured but only the sign of the path curvature is detected. These constraints are such to make classical control techniques inefficient. As the feedback information is both continuous and discrete, the hybrid systems formalism turns out to be well appropriate to model the problem. The proposed approach is based on optimal control techniques successfully applied in a previous work for following rectilinear path. We propose here an extension to the tracking of more general paths with moderate curvature. The stability of the closed-loop system is proved by means of the hybrid system formalism and hybrid formal verification techniques. Finally, the practicality of the proposed approach, in spite of non--idealities in real-world applications, is discussed by reporting experimental results

Optimal feedback control for line tracking with a bounded--curvature vehicle

The problem of driving a vehicle along a given path is considered. The vehicle is supposed to move forward only, with a given velocity profile, and to have a bounded turning radius. Such a model, also known as 'Dubins' vehicle', is relevant to the kinematics of road vehicles as well as aircraft cruising at constant altitude, or sea vessels. We consider the optimal control problem consisting of minimizing the length travelled by the vehicle starting from a generic configuration to connect to a specified route. A feedback law is proposed, such that straight routes can be approached optimally, while the system is asymptotically stabilized. Experimental results are reported showing real-time feasibility of the proposed approach

Stability and Robustness of Optimal Synthesis for Route Tracking by Dubins' Vehicles

We consider the properties of stability and robustness of an optimal control synthesis obtained for the problem of route tracking by a kinematic vehicle moving forward only with a lower bounded turning radius. This model, sometimes referred to as “Dubins' vehicle”, is relevant to the kinematics of road vehicles as well as aircraft cruising at constant altitude, or sea vessels

Nonholonomic distance to polygonal obstacles for a car-like robot of polygonal shape

This paper shows how to compute the nonholonomic distance between a polygonal car-like robot and polygonal obstacles: The solution extends previous work of Reeds and Shepp by finding the shortest path to a manifold (rather than to a point) in configuration space. Based on optimal control theory, the proposed approach yields am analytic solution to the problem

Evidence of dynamic postural control performance in parkour landing

International audienc

Angular momentum regulation strategies for highly dynamic landing in Parkour

International audiencePrevious studies have shown that angular momentum is regulated during daily life activities like walking and during dynamic motions such as somersaults and twists. In this paper, we propose to extend these works by studying how the regulation of the angular momentum derivative AMD contributes to mechanical stability after a highly dynamic drop. To this end, five healthy Parkour experts participated in this study and were asked to perform the Parkour precision landing technique. The derivative of angular momentum expressed at the center of mass position and the contribution of each segment to its variation were analyzed. Results show that the AMD is regulated to zero throughout landing. Our study also reveals complex whole-body strategies of Parkour practitioners such as opposed segment cancellations and a temporal organization of the motion. This study provides a new basis to better understand dynamic landing performances. Results could also be used to generate landing motions with humanoid robots or virtual avatars (human-inspired motion)