Development of Cubic Bezier Curve and Curve-Plane Intersection Method for Parametric Submarine Hull Form Design to Optimize Hull Resistance Using CFD

Optimization analysis and computational fluid dynamics （CFDs） have been applied simultaneously, in which a parametric model plays an important role in finding the optimal solution. However, it is difficult to create a parametric model for a complex shape with irregular curves, such as a submarine hull form. In this study, the cubic Bezier curve and curve-plane intersection method are used to generate a solid model of a parametric submarine hull form taking three input parameters into account： nose radius, tail radius, and length-height hull ratio （L/H）. Application program interface （API） scripting is also used to write code in the ANSYS DesignModeler. The results show that the submarine shape can be generated with some variation of the input parameters. An example is given that shows how the proposed method can be applied successfully to a hull resistance optimization case. The parametric design of the middle submarine type was chosen to be modified. First, the original submarine model was analyzed, in advance, using CFD. Then, using the response surface graph, some candidate optimal designs with a minimum hull resistance coefficient were obtained. Further, the optimization method in goal-driven optimization （GDO） was implemented to find the submarine hull form with the minimum hull resistance coefficient （Ct）. The minimum C, was obtained. The calculated difference in （7, values between the initial submarine and the optimum submarine is around 0.26%, with the C, of the initial submarine and the optimum submarine being 0.001 508 26 and 0.001 504 29, respectively. The results show that the optimum submarine hull form shows a higher nose radius （rn） and higher L/H than those of the initial submarine shape, while the radius of the tail （r1） is smaller than that of the initial shape.

A Hybrid Path Planning Method Based on Articulated Vehicle Model

Due to the unique steering mechanism and driving characteristics of the articulated vehicle,a hybrid path planning method based on the articulated vehicle model is proposed to meet the demand of obstacle avoidance and searching the path back and forth of the articulated vehicle.First,Support Vector Machine(SVM)theory is used to obtain the two-dimensional optimal zero potential curve and the maximum margin,and then,several key points are selected from the optimal zero potential curves by using Longest Accessible Path(LAP)method.Next,the Cubic Bezier(CB)curve is adopted to connect the curve that satisfies the curvature constraint of the articulated vehicle between every two key points.Finally,Back and Forth Rapidly-exploring Random Tree with Course Correction(BFRRT-CC)is designed to connect paths that do not meet articulated vehicle curvature requirements.Simulation results show that the proposed hybrid path planning method can search a feasible path with a 90-degree turn,which meets the demand for obstacle avoidance and articulated vehicle back-and-forth movement.