منابع مشابه
Order in extremal trajectories . ̄
Given a chaotic dynamical system and a time interval in which some quantity takes an unusually large average value, what can we say of the trajectory that yields this deviation? As an example, we study the trajectories of the archetypical chaotic system, the baker’s map. We show that, out of all irregular trajectories, a large-deviation requirement selects (isolated) orbits that are periodic or...
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Previous work [3, 6, 9, 8, 7, 1] has presented the time optimal trajectories for three classes of non-holonomic mobile robots: steered cars that can only go forwards, steered cars that go forwards or backwards, and differential drives. Each of the vehicles is modelled as a rigid body in the plane with velocity and angular velocity controls. The systems are differentiated only by the bounds on t...
متن کاملSampling Extremal Trajectories for Planar Rigid Bodies
This paper presents an approach to finding the time-optimal trajectories for a simple rigid-body model of a mobile robot in an obstacle-free plane. Previous work has used Pontryagin’s Principle to find strong necessary conditions on time-optimal trajectories of the rigid body; trajectories satisfying these conditions are called extremal trajectories. The main contribution of this paper is a met...
متن کاملExtremal Trajectories for Bounded Velocity Differential Drive Robots
This paper applies Pontryagin’s Maximum Principle to the time optimal control of differential drive mobile robots with velocity bounds. The Maximum Principle gives necessary conditions for time optimality. Extremal trajectories are those which satisfy these conditions, and are thus a superset of the time optimal trajectories. This paper derives a compact geometrical structure for extremal traje...
متن کاملExtremal Graphs of Order Dimension 4
We will examine the maximal number of edges of a graph on p vertices of order dimension 4. We will show that the lower bound for this number is greater than 3 8 p 2 + 2p − 13. In particular the Turán-4 graph on p vertices does not have the maximal number of edges among the graphs of order dimension 4.
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2009
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-009-9828-8