Ehresmann Connection in the Geometry of Nonholonomic Systems
Entropy and complexity of a path in sub-riemannian geometry
We characterize the geometry of a path in a sub-riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset of a metric space is the minimum number of balls of a given radius needed to cover . It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-riemannian manifold as the infimum of the lengths of all trajectories contained in an -neighborhood of the path,...
Entropy and complexity of a path in sub-Riemannian geometry
We characterize the geometry of a path in a sub-Riemannian manifold using two metric invariants, the entropy and the complexity. The entropy of a subset A of a metric space is the minimum number of balls of a given radius ε needed to cover A. It allows one to compute the Hausdorff dimension in some cases and to bound it from above in general. We define the complexity of a path in a sub-Riemannian manifold as the infimum of the lengths of all trajectories contained in an ε-neighborhood of the path,...
Equilibrium stability of a servo actuating flight controls in a servoelastic framework.
Esistenza e determinazione delle precessioni semiregolari ad asse verticale di un corpo rigido in un campo di forze newtoniano
Euler-Poincaré reduction of externally forced rigid body motion
Evaluation of the half-periods of the Weierstrass -function for the absolute invariant greater than one
Flocking control of multi-agent systems with application to nonholonomic multi-robots
In this paper, we revisit the artificial potential based approach in the flocking control for multi-agent systems, where our main concerns are migration and trajectory tracking problems. The static destination or, more generally, the moving reference point is modeled by a virtual leader, whose information is utilized by some agents, called active agents (AA), for the controller design. We study a decentralized flocking controller for the case where the set of AAs is fixed. Some results on the velocity...
From Gaudin models to integrable tops.
Geometry of non-holonomic diffusion
We study stochastically perturbed non-holonomic systems from a geometric point of view. In this setting, it turns out that the probabilistic properties of the perturbed system are intimately linked to the geometry of the constraint distribution. For -Chaplygin systems, this yields a stochastic criterion for the existence of a smooth preserved measure. As an application of our results we consider the motion planning problem for the noisy two-wheeled robot and the noisy snakeboard.
Hyperbolic functions that linearize inverted manifold surfaces.
Integrable Hamiltonian systems on Lie groups: Kowalewski type.
Integrable systems, Poisson pencils, and hyperelliptic Lax pairs
Invariant varieties of periodic points for the discrete Euler top.
Isomorphism and Hamilton representation of some nonholonomic systems.
Large quadratic programming problems generated by rigid body simulation.
LQR and MPC controller design and comparison for a stationary self-balancing bicycle robot with a reaction wheel
A self-balancing bicycle robot based on the concept of an inverted pendulum is an unstable and nonlinear system. To stabilize the system in this work, the following three main components are required, i. e., (1) an IMU sensor that detects the tilt angle of the bicycle robot, (2) a controller that is used to control motion of a reaction wheel, and (3) a reaction wheel that is employed to produce reactionary torque to balance the bicycle robot. In this paper, we propose three control strategies: linear...
Microscopic Modelling of Active Bacterial Suspensions
We present two-dimensional simulations of chemotactic self-propelled bacteria swimming in a viscous fluid. Self-propulsion is modelled by a couple of forces of same intensity and opposite direction applied on the rigid bacterial body and on an associated region in the fluid representing the flagellar bundle. The method for solving the fluid flow and the motion of the bacteria is based on a variational formulation written on the whole domain, strongly...
Motion of a rigid body under random perturbation.
Mouvement d'un projectile dans l'air