This paper presents a methodology based on a variation of the Rapidly-exploring Random Trees (RRTs) that generates feasible trajectories for autonomous vehicles with holonomic constraints in environments with obstacles. Our approach is based on seventh order Bézier curves to connect vertexes of the tree, generating paths that do not violate the main kinematic constraints of the vehicle. The met...

This article aims to investigate the points of equilibrium and associated convergence basins in a seventh-order generalized Hénon–Heiles potential. Using well-known Newton–Raphson iterator, we numerically locate positions equilibrium, while also obtain their linear stability. Furthermore, demonstrate how two variable parameters, entering potential, affect dynamics system as well fractal degree ...

We use a generalized Cole-Hopf transformation to obtain a condition that allows us to find exact solutions for several forms of the general seventh-order KdV equation KdV7 . A remarkable fact is that this condition is satisfied by three well-known particular cases of the KdV7. We also show some solutions in these cases. In the particular case of the seventh-order Kaup-Kupershmidt KdV equation w...

The purpose of this paper is to solve the seventh-order functional equation as follows:  --------------------------- Next, we study the stability of this type of functional equation. Clearly, the function ----------  holds in this type functional equation. Also, we prove Hyers-Ulam stability for this type functional equation in the β-Gaussian Banach space.