The path planning problem for arbitrary devices is rst and foremost a geometrical problem. For the eld of control theory, advanced mathematical techniques have been developed to describe and use geometry. In this paper, we use the notions of the ow of vector elds and geodesics in metric spaces to formalize and unify path planning problems. A path planning algorithm based on ow propagation is br...

For the first time, both non-holonomic and quasi-integrable deformations are obtained for AB system of coupled equations. The models geophysical atmospheric fluid motion along with ultra-short pulse propagation in nonlinear optics serves as a generalization well-known sine-Gordon equation. deformation retains integrability subjected to higher-order differential constraints whereas quasi-AB syst...

Autonomous navigation in real-world industrial environments is a challenging task in many respects. One of the key open challenges is fast planning and execution of trajectories to reach arbitrary target positions and orientations with high accuracy and precision, while taking into account non-holonomic vehicle constraints. In recent years, lattice-based motion planners have been successfully u...

There are many methods that address navigation and path planning for mobile robots with non-holonomic motion constraints using clever techniques and exploiting application-specific data, but it is always better not to have any such constraints at all. In this document we re-examine the capabilities of some popular driving mechanisms from a different perspective and describe a method to obtain h...