Efficient motion planning for problems lacking optimal substructure

We consider the motion-planning problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We suggest a natural cost function that balances path length and risk-exposure time. Specifically, we consider the discrete setting where we are given a graph, or a roadmap, and we wish to compute the minimal-cost path under this cost function. Interestingly, paths defined using our cost function do not have an optimal substructure. Namely, subpaths of an optimal path are not necessarily optimal. Thus, the Bellman condition is not satisfied and standard graph-search algorithms such as Dijkstra cannot be used. We present a path-finding algorithm, which can be seen as a natural generalization of Dijkstra's algorithm. Our algorithm runs in $O\left((n_B\cdot n) \log( n_B\cdot n) + n_B\cdot m\right)$ time, where~$n$ and $m$ are the number of vertices and edges of the graph, respectively, and $n_B$ is the number of intersections between edges and the boundary of the risk zone. We present simulations on robotic platforms demonstrating both the natural paths produced by our cost function and the computational efficiency of our algorithm

Second-Order Convergence of a Projection Scheme for the Incompressible Navier–Stokes Equations with Boundaries

A rigorous convergence result is given for a projection scheme for the Navies–Stokes equations in the presence of boundaries. The numerical scheme is based on a finite-difference approximation, and the pressure is chosen so that the computed velocity satisfies a discrete divergence-free condition. This choice for the pressure and the particular way that the discrete divergence is calculated near the boundary permit the error in the pressure to be controlled and the second-order convergence in the velocity and the pressure to the exact solution to be shown. Some simplifications in the calculation of the pressure in the case without boundaries are also discussed

Stable Fourth Order Stream-Function Methods for Incompressible Flows with Boundaries

Fourth-order stream-function methods are proposed for the time dependent, incompressible Navier-Stokes and Boussinesq equations. Wide difference stencils are used instead of compact ones and the boundary terms are handled by extrapolating the stream-function values inside the computational domain to grid points outside, up to fourth-order in the noslip condition. Formal error analysis is done for a simple model problem, showing that this extrapolation introduces numerical boundary layers at fifth-order in the stream-function. The fourth-order convergence in velocity of the proposed method for the full problem is shown numerically

Numerical analysis of concrete-filled spiral welded stainless steel tubes subjected to compression

[EN] Spiral welded stainless tubes are produced by helical welding of a continuous strip of stainless steel. Recently, concrete-filled spiral welded stainless steel tubes have found increasing application in the construction industry due to their ease of fabrication and aesthetic appeal. However, an in-depth understanding of the behaviour of this type of structure is still needed due to the lack of proper design guidance and insufficient experimental verification. In this paper, the mechanical performance of concrete-filled spiral welded stainless steel tubes will be numerically investigated with a commercial finite element software package, through which an experimental program can be designed properly. Specifically, the proposed finite element models take into account the effects of material and geometric nonlinearities. Moreover, the initial imperfections of stainless steel tubes and the form of helical welding will be appropriately included. Enhancement of the understanding of the analysis results can be achieved by extending results through a series of parametric studies based on the developed finite element model. Thus, the effects of various design parameters will be further evaluated by using the developed finite element model. Furthermore, for the purposes of wide application of such types of structure, the accuracy of the behaviour prediction in terms of ultimate strength based on current design codes will be studied. The authors herein compared the load capacity between the finite element analysis results and the existing codes of practice.Li, D.; Uy, B.; Aslani, F.; Hou, C. (2018). Numerical analysis of concrete-filled spiral welded stainless steel tubes subjected to compression. En Proceedings of the 12th International Conference on Advances in Steel-Concrete Composite Structures. ASCCS 2018. Editorial Universitat Politècnica de València. 365-371. https://doi.org/10.4995/ASCCS2018.2018.7200OCS36537