Optimal path planning for nonholonomic robotics systems via parametric optimisation

Abstract. Motivated by the path planning problem for robotic systems this paper considers nonholonomic path planning on the Euclidean group of motions SE(n) which describes a rigid bodies path in n-dimensional Euclidean space. The problem is formulated as a constrained optimal kinematic control problem where the cost function to be minimised is a quadratic function of translational and angular velocity inputs. An application of the Maximum Principle of optimal control leads to a set of Hamiltonian vector field that define the necessary conditions for optimality and consequently the optimal velocity history of the trajectory. It is illustrated that the systems are always integrable when n = 2 and in some cases when n = 3. However, if they are not integrable in the most general form of the cost function they can be rendered integrable by considering special cases. This implies that it is possible to reduce the kinematic system to a class of curves defined analytically. If the optimal motions can be expressed analytically in closed form then the path planning problem is reduced to one of parameter optimisation where the parameters are optimised to match prescribed boundary conditions.This reduction procedure is illustrated for a simple wheeled robot with a sliding constraint and a conventional slender underwater vehicle whose velocity in the lateral directions are constrained due to viscous damping

New Colloidal Lithographic Nanopatterns Fabricated by Combining Pre-Heating and Reactive Ion Etching

We report a low-cost and simple method for fabrication of nonspherical colloidal lithographic nanopatterns with a long-range order by preheating and oxygen reactive ion etching of monolayer and double-layer polystyrene spheres. This strategy allows excellent control of size and morphology of the colloidal particles and expands the applications of the colloidal patterns as templates for preparing ordered functional nanostructure arrays. For the first time, various unique nanostructures with long-range order, including network structures with tunable neck length and width, hexagonal-shaped, and rectangular-shaped arrays as well as size tunable nanohole arrays, were fabricated by this route. Promising potentials of such unique periodic nanostructures in various fields, such as photonic crystals, catalysts, templates for deposition, and masks for etching, are naturally expected

Two-degree-of-freedom based cross-coupled control for high-accuracy tracking systems

Recent work recognizes that cross-coupled control (CCC) can significantly improve the accuracy of contour tracking in biaxial systems. However, it's complicated to apply CCC to arbitrary contour because of extra requirements to calculation and switching the cross-coupled gains. In addition, since most of CCC are based on the PID controlled loops of the individual axes, performances are conserved in some sense. In this paper, we propose a structure for arbitrary regular contours by efficiently determining the cross-coupling gains for CCC with the two-degree-of-freedom (2DOF) controlled to the single axes. Furthermore, an approach for stability analysis of the CCC is posed. Experimental results for a two-axial motion system indicate that the proposed structure eliminates the contouring error significantly. © 2007 IEEE

Stillwater Populist

Weekly newspaper from Stillwater, Oklahoma Territory that includes local, territorial, and national news along with advertising