Adaptive Meshfree Method And A Mew Algorithm Of Path Planning

Meshfree Method is a kind of new numerical method in recent years, it was attracting so many researchers to study and has a rapidly development. The adaptive meshfree method is one of an important direction of meshfree method. A new adaptive meshfree method is introduced in this paper and applied to solve the classical problems of cantilever beam and plate with a circle hole. Global path planning is a critical problem in the area of robot control technique. We construct a whole new algorithm for global path planning problem, and realized a lot of numerical experiments. It reveals the efficiency of this method. The main contents in this paper are as bellow:1. It gives a simply description of present adaptive meshfree methods. Based on the technique of the error estimate at different support domains, and the new nodes insert by the Voronoi graph, a new adaptive meshfree method is introduced.2. By coupling the adaptive technique with the MLS and RPIM meshfree method, it yields the adaptive MLS and RPIM meshfree methods. Applying these two methods to solve the classical problems of cantilever beam and plate with a circle hole respectively, the results have a good agreement with the exact solution, and validate this new algorithm.3. It analyzed the classic global path planning methods in the area of robot control technique. It presents a new algorithm, namely the Blind Groping algorithm, for mobile robots collision avoidance planning. A detailed account of the algorithm process is given and a proof has been presented for the convergence. Compared with the classical global path planning methods, the obstacle environment doesn't need to be simplified before planning. The theory of this algorithm is simple, and the calculation is easy. It is only need a small storage of information. A free path could be found out quickly. At last, some numerical experiment results have justified and validated the algorithm.