In this paper we present a novel probabilistic sampling-based motion planning algorithm called the Fast Marching Tree algorithm (FMT∗). The algorithm is specifically aimed at solving complex motion planning problems in high-dimensional configuration spaces. This algorithm is proven to be asymptotically optimal and is shown to converge to an optimal solution faster than its state-of-the-art coun...

Robot navigation in unknown environments requires an efficient exploration method. Exploration involves not only to determine towards the robot must to move but also motion planning, and simultaneous localization and mapping processes. The final goal of the exploration task is to build a map of the environment that previously the robot didn’t know. This work proposes the Voronoi Fast Marching m...

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a “budget” remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causal...

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a “budget” remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causal...

Spherical coordinates are a natural orthogonal system to describe wavefronts emanating from a point source. While a regular grid distribution in the Cartesian coordinate system tends to undersample the wavefront description near the source (the highest wavefront curvature) and oversample it away from the source, spherical coordinates, in general, provide a more balanced grid distribution to cha...

Solving the eikonal equation allows to compute a monotone front propagation of anisotropic nature and is thus a widely applied technique in different areas of science and engineering. Various methods are available out of which only a subset is suitable for shared-memory parallelization, which is the key focus of this analysis. We evaluate three different approaches, those being the recently dev...

A method for constructing the isosurface from a data set on a face-centered-cubic lattice has been developed. Generally, a three-dimensional scalar field is sampled on an orthogonal cubic lattice. And an algorithm called Marching Cubes is widely used for constructing the isosurface on this lattice. It is known, however, that data sampling of a three-dimensional scalar field on a face-centered-c...

In this paper, we propose to use image pixels for geometry reconstruction with a shape from silhouette approach. We aim at estimating shape and normal for the surface of a single object seen through calibrated images. From the voxel-based shape obtained with the algorithm proposed by R. Szeliski in [18], our main contribution concerns the use of image pixels together with marching cubes for con...

Abstract Image stitching is an important way to achieve large‐field high‐resolution imaging. The inconsistencies in brightness and structure defects ghosting, blurring misalignment between images, which are inevitable difficult eliminate, make a challenge image stitching, due the external lighting environment changes camera pose parameters. Here, novel method proposed search for optimal seamlin...