Oriented robot motion planning in Riemannian manifolds

Joint Manifolds and Markov Decision Process in Robot Motion Planning

Learning trajectories for a robot in unknown environments which can be generalized to different types of robots is a challenging problem. The input space is very high dimensional and any type of algorithm and computation has a very high time complexity and challenging to define problems in such a high state space. Applying low-dimensional reduction to such problems does the trick for us. We can...

Lazzeri’s Jacobian of oriented compact riemannian manifolds

The subject of this paper is a Jacobian, introduced by F. Lazzeri (unpublished), associated to every compact oriented riemannian manifold whose dimension is twice an odd number. We start the investigation of Torelli type problems and Schottky type problems for Lazzeri’s Jacobian; in particular we examine the case of tori with flat metrics. Besides we study Lazzeri’s Jacobian for Kähler manifold...

Mobile Robot Online Motion Planning Using Generalized Voronoi Graphs

In this paper, a new online robot motion planner is developed for systematically exploring unknown environ¬ments by intelligent mobile robots in real-time applications. The algorithm takes advantage of sensory data to find an obstacle-free start-to-goal path. It does so by online calculation of the Generalized Voronoi Graph (GVG) of the free space, and utilizing a combination of depth-first an...

A Geometry Preserving Kernel over Riemannian Manifolds

Abstract- Kernel trick and projection to tangent spaces are two choices for linearizing the data points lying on Riemannian manifolds. These approaches are used to provide the prerequisites for applying standard machine learning methods on Riemannian manifolds. Classical kernels implicitly project data to high dimensional feature space without considering the intrinsic geometry of data points. ...

Robot Motion Planning