We survey recent developments about random real trees, whose prototype is the Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain the formalism of real trees, which yields a neat presentation of the theory and in particular of the relations between discrete Galton-Watson trees and continuous random trees. We then discuss the particular class of self-similar random real ...

In arXiv:1609.05666v1 [math.PR] a functional limit theorem was proved. It states that symmetric processes associated with resistance metric measure spaces converge when the underlying respect to Gromov-Hausdorff-vague topology, and certain uniform recurrence condition is satisfied. Such finds particularly nice applications if space tree. To illustrate this, we state theorems in old new examples...

SKI-combinator trees are a simple model of computation, which are computationally complete (in a Turing sense), but are suggestive of basic biochemical processes and can be used as a vehicle for understanding processes of biological (and prebiotic) self-organization. After a brief overview of SKI-combinator trees, we describe the results of a series of preliminary experiments exploring the stat...

Techniques for testing cyberphysical systems (CPS) currently use a combination of automatic directed test generation and random testing to find undesirable behaviors. Existing techniques can fail to efficiently identify bugs because they do not adequately explore the space of system behaviors. In this paper, we present an approach that uses the rapidly exploring random trees (RRT) technique to ...

In this paper, I explore the application of various random sampling based algorithms to dynamic models of bicycles. Starting with relatively simple 3-dimensional state space models of bicycle and working up to a more realistic 7dimensional model that incorporates skidding, I examine RRT, RG-RRT, RRT*, and LQR-RRT*.

Traversing challenging structures like boulders, rubble, stairs and steps, mobile robots need a special level of mobility. Robots with reconfigurable chassis are able to alter their configuration to overcome such structures. This paper presents a two-stage motion planning scheme for reconfigurable robots in rough terrain. First, we consider the robot’s operating limits rather than the complete ...

Limit theorems are established for some functionals of the distances between two nodes in weighted random b-ary recursive trees. We consider the depth of the nth node and of a random node, the distance between two random nodes, the internal path length and the Wiener index. As application these limit results imply by an imbedding argument corresponding limit theorems for further classes of rand...

This paper addresses the problem of teaching a robot interaction behaviors using the imitation learning paradigm. Particularly, the approach makes use of Gaussian Mixture Models (GMMs) to model the physical interaction of the robot and the person when the robot is teleoperated or guided by an expert. The learned models are integrated into a sample-based planner, an RRT*, at two levels: as a cos...