| 摘要： | | 本文是以環境模型為基礎，建構一條連接起始點到終點之B-spline平滑軌跡。除了滿足車輛轉彎時最小旋轉半徑的限制以及起始點與終點之運動約束外，並可成功地通過事先設定的中繼點。我們採用B-spline解析函數作為平滑路徑的設計，其中B-spline曲線是由一組基底函數以及控制點參數所構成，具有快速收斂、局部學習與分段調整等特質，非常適合作為平滑曲線的描述工具。將曲率限制以及運動約束引入通過點的代價函數中，將軌跡規劃的問題轉換成求解約束最佳化的問題。利用約束最佳化的演算法求解控制點，進一步建構最佳化的B-spline曲線。為了驗證本文架構的可行性，我們以Matlab 程式語言的GUI介面完成B-spline軌跡規劃模擬軟体。由模擬結果可以證實，利用約束最佳化求解B-spline參考軌跡不僅具有實用的可行性，並可獲至良好的效果。 |
| A solution for the problem of path planning for a vehicle moving in the model-based environment is solved in this paper. The main objective is to generate a feasible path with the initial posture and the final one so that no collisions with obstacles would occur and various constraints are satisfied. Treated as the reference trajectory in the tracking control level, the path may be characterized by analytical description functions. The parametric B-spline curve is adopted, which is typically defined by a set of control points and a set of B-spline basis functions. The B-spline curves have satisfactory properties, such as affine invariance, convex hull, locally refined without changing their global shape, continuity and differentiation, making them appropriate for trajectory planning application. The curvature restrictions and kinematic constraints are introduced into the constrained optimization problem to choose the control points and to characterize the optimized B-spline curve. The synthesis of the above concepts leads to a successful methodology for path planning, which is demonstrated by simulation results based on MATLAB GUI toolbox. |
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