平面載具運動軌跡產生法則之研究

Study of Trajectory Generation Approaches for Planar Vehicles

林書賢(Shu-Hsien Lin)

指導教授 ： 連豊力

國立臺灣大學/電機資訊學院/電機工程學研究所/碩士(2004年)

https://doi.org/10.6342/NTU.2004.01318

摘要

本論文針對平面式載具提出一套連續軌跡產生法則。開始時提出了三種軌跡產生的方法。首先分析平面式載具在直線軌跡下的行為，然而在此情況下載具必須要在起始點和終點有原地自轉的動作，因此我們再規劃出單純由直線和弧形的段落組成的弧-直線軌跡。然而在此軌跡中，直線與弧形的接續處會產生曲率不連續點。最後我們以B-spline 曲線演算法提供平面式載具更具平滑性的軌跡產生法則。根據上述三種法則設計參考軌跡後，再參考文獻上前人提出的軌跡追蹤的控制器，使用一Lyapunov函數分析其穩定度。在討論直線及直線和弧形區段組成的軌跡當中，我們想找出具有連續曲率性質的軌跡。故我們使用B-spline曲線演算法取代由直線和弧型區段組成的弧-直線軌跡。首先根據環境提供的資訊做前端處理後得到控制點，組成B-spline 曲線軌跡。然後對B-spline曲線微分得到曲線上的速度和角速度資訊，根據此速度和角速度我們便可得到曲線上的曲率時間函數。接下來的問題便是據此軌跡做行進的動作。
本論文中，首先簡述自動載具的一些應用與我們要解決的問題針對軌跡，其次則介紹軌跡產生的方法和設計平面式載具的控制器。我們也做了演算法上的模擬結果以使用Pioneer 3做軌跡追蹤的實驗。比較這些演算法的性能後，提出結論和未來工作方向。

關鍵字

弧-直線 ； 平面式載具 ； Lyapunov分析 ； B-spline曲線 ； 軌跡產生

並列摘要

This thesis presents continuous trajectory generation methods for a planar vehicle. Three trajectory generation methods are proposed. First, a line trajectory directly for the planar vehicle is studied. Second, because the vehicle must rotate at the start and target points for the line trajectory generation methods, a trajectory composed of line and arc segments for the vehicle is then planned. But such “arc-line” paths have discontinuities at the line-arc-line transition points. The curvature of the path is discontinuous at these points. Finally, a smoother trajectory generation method based on the B-spline algorithm for a planar vehicle is proposed. After designing the reference trajectory, a tracking control rule for vehicles is developed. Stability of the rule is proved through the use of a Lyapunov function. We use the B-spline algorithm to replace the arc-line trajectory. First, designing a continuous trajectory based on the environment information, we get some control points according to the pre-handling information. Then we differentiate the B-spline curve to get the translational and rotational velocity vectors. By the translational and rotational velocity information, we can get the curvatures of the curve. The problem is then to follow the designed path.
In this thesis, we introduce the applications of the Autonomous vehicles and talk about our problems first. Second we introduce the trajectory generation methods and design the controller for the planar vehicle. We also do the simulation results of the algorithms and use Pioneer 3 to do the experiments. After comparing the performances, we summarize the conclusions and future work.

並列關鍵字

Planar vehicle ； Lyapunov analysis ； Trajectory generation ； B-spline ； Arc-line

參考文獻

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