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摘要: 提出了一種基于雙維度搜索的實時軌跡規劃方法，用來解決自主地下鏟運機轉彎軌跡規劃問題。該方法是一種結合采樣思想和最優化算法的復合軌跡規劃方法，包含三個主要步驟：基于雙維度搜索策略的優化模型參數生成，基于二次規劃的軌跡計算，以及基于約束檢查的最優軌跡確定。該方法新穎之處在于提出的基于轉彎區域行駛時間和里程的雙維度搜索策略，以及基于平穩目標的軌跡最優化模型，可根據彎道區域入口速度和位置，快速生成縱橫向都有最優性保證的最優軌跡。該方法結構簡單、易于實施，可通過關鍵參數的調整滿足控制器對軌跡生成速度的實時性要求。基于該軌跡規劃方法的特點，使其不僅適用于實時軌跡規劃，還可為未來智慧礦山的智能管控與優化調度提供底層約束。多組算例驗證了該方法的有效性和優越性。Abstract: To solve the problem of smooth turning of an autonomous underground load-haul-dump loader (LHD), in this paper, a method for turning trajectory planning of an LHD was proposed. This method is a type of hybrid trajectory planning method based on a bidimensional search. According to the characteristic of the problem, the longitudinal and lateral decomposition method was applied, and the basic algorithms are a sampling method and an optimization algorithm. The algorithm consists of three main steps that are parameter generation of the optimal model based on a bidimensional search strategy, trajectory calculation based on quadratic programming models, and determination of the optimal trajectory based on an articulated angle and collision avoidance constraints check. The novelty of this method lies in the proposed two-dimensional search strategy and trajectory optimization models. The two dimensions are the driving time and mileage of the trajectory in the turning area; the trajectory optimization model is based on the quadratic programming that can quickly generate the optimal trajectory in both dimensions according to the turning area entering speed and position of the LHD. This trajectory planning method is simple in structure and easy to implement. Moreover, it can satisfy the real-time requirement of the controller on the trajectory generation time by adjusting the key parameters. Based on the characteristics of the trajectory planning method, it is not only suitable for real-time trajectory planning but can also provide basic constraints for intelligent control and optimal scheduling of intelligent mines. A series of case studies was conducted to show the effectiveness and superiority of the proposed method. The case studies show that the optimal trajectories according to different entering speeds and positions can be obtained through the proposed method. A prototype experiment was performed to show the feasibility of the proposed trajectory planning method. This method generates trajectories that are easy to track and control because the velocity, articulated angle, and angular velocity change gently.
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圖 2 地下巷道轉彎區域。（a）磨角之前的轉彎區域；（b）磨角之后的轉彎區域
Figure 2. Roadway tuning area: (a) before grinding; (b) after grinding
圖 3 雙維度搜索軌跡規劃方法流程圖
Figure 3. Flow chart for the two-dimensional search-based trajectory planning method
圖 4 位置曲線（
${y_{{\rm{in}}}} = 2.5,{v_{{x_{{\rm{in}}}}}} = 2$ ）Figure 4. Position trajectory (
${y_{{\rm{in}}}} = 2.5,{v_{{x_{{\rm{in}}}}}} = 2$ )
圖 5 行駛方向速度曲線（
${y_{{\rm{in}}}} = 2.5,{v_{{x_{{\rm{in}}}}}} = 2$ ）Figure 5. Heading velocity trajectory (
${y_{{\rm{in}}}} = 2.5,{v_{{x_{{\rm{in}}}}}} = 2$ )
圖 6 鉸接角、前后車體航向角及角速度（
${y_{{\rm{in}}}} = 2.5,{v_{{x_{{\rm{in}}}}}} = 2$ ）Figure 6. Angle and angular velocity for
$\gamma $ ,${\theta _{\rm{f}}}$ and${\theta _{\rm{r}}}$ (${y_{{\rm{in}}}} = 2.5,{v_{{x_{{\rm{in}}}}}} = 2$ )
圖 7 位置曲線（
${T_i} = 70\;{\rm{s}}$ ）Figure 7. Position trajectory (
${T_i} = 70\;{\rm{s}}$ )
圖 8 行駛方向速度曲線（
${T_i} = 70\;{\rm{s}}$ ）Figure 8. Heading velocity trajectory (
${T_i} = 70\;{\rm{s}}$ )
圖 9 鉸接角、前后車體航向角及角速度（
${T_i} = 70\;{\rm{s}}$ ）Figure 9. Angle and angular velocity for
$\gamma $ ,${\theta _{\rm{f}}}$ , and${\theta _{\rm{r}}}$ (${T_i} = 70\;{\rm{s}}$ )
圖 10 位置曲線（出口位置為（32.25, 35））
Figure 10. Position trajectory (exit position is (32.25, 35))
圖 11 行駛方向速度曲線（出口位置為（32.25, 35））
Figure 11. Heading velocity trajectory (exit position is (32.25, 35))
圖 12 鉸接角、前后車體航向角及角速度（出口位置為（32.25, 35））
Figure 12. Angle and angular velocity for
$\gamma $ ,${\theta _{\rm{f}}}$ , and${\theta _{\rm{r}}}$ (exit position is (32.25, 35))表 1 算例參數表
Table 1. Parameters for case studies
${W_{\rm{A}}}$/m ${W_{\rm{B}}}$/m ${L_{\rm{A}}}$/m ${L_{\rm{B}}}$/m $\alpha $/rad ${L_{{\rm{safe}}}}$/m $\Delta v$/（m·s?1） $\Delta d$/（m·s?1） $m$ 5 4.5 30 30 ${\text{π}}/2$ 1.5 0.1 0.5 4 ${L_{\rm{f}}}$/m ${L_{\rm{r}}}$/m ${\gamma _{\min }}$/rad ${\gamma _{\max }}$/rad ${\dot \gamma _{\min }}$/（rad·s?1） ${\dot \gamma _{\min }}$/（rad·s?1） $L_{\rm{A}}'$/m $L_{\rm{B}}'$/m $N$ 1.5 2 ?0.69 0.69 ?0.17 0.17 24 24 33 
下載: 導出CSV
表 2 第一組算例結果
Table 2. Results of the first group
${v_{{\rm{in}}}}$/（m·s?1） $i$ $j$ ${T_{{\rm{best}}}}$/s ${\gamma _{\max }}$/rad ${\dot \gamma _{\max }}$/（rad·s?1） 1 2 3 66.67 0.51 0.06 2 7 4 42.84 0.51 0.06 3 13 4 33.33 0.47 0.06 4 17 4 28.54 0.42 0.06
下載: 導出CSV
表 3 第二組算例結果
Table 3. Results of the second group
${v_{{\rm{in}}}}$/（m·s?1） $i$ $j$ ${T_{{\rm{best}}}}$/s ${\gamma _{\max }}$/rad ${\dot \gamma _{\max }}$/（rad·s?1） 1 2 3 66.67 0.51 0.06 2 7 4 42.84 0.53 0.06 3 13 4 33.33 0.5 0.07 4 17 4 28.54 0.45 0.08
下載: 導出CSV
表 4 第三組算例結果
Table 4. Results of the third group
${v_{{\rm{in}}}}$/（m·s?1） $i$ $j$ ${T_{{\rm{best}}}}$/s ${\gamma _{\max }}$/rad ${\dot \gamma _{\max }}$/（rad·s?1） 1 2 3 66.67 0.53 0.06 2 7 4 42.84 0.56 0.07 3 13 4 33.33 0.53 0.08 4 17 4 28.54 0.48 0.09
下載: 導出CSV
表 5 試驗參數表
Table 5. Parameters for experiments
${W_{\rm{A}}}$/m ${W_{\rm{B}}}$/m ${L_{\rm{A}}}$/m ${L_{\rm{B}}}$/m $\alpha $/rad ${L_{{\rm{safe}}}}$/m $\Delta v$/（m·s?1） $\Delta d$/（m·s?1） $m$ 2.2 2.2 3.6 3.6 ${{\text{π}}{ /2}}$ 0.3 0.1 0.8 3 ${L_{\rm{f}}}$/m ${L_{\rm{r}}}$/m ${\gamma _{\min }}$/rad ${\gamma _{\max }}$/rad ${\dot \gamma _{\min }}$/（rad·s?1） ${\dot \gamma _{\min }}$/（rad·s?1） $L_{\rm{A}}'$/m $L_{\rm{B}}'$/m $N$ 0.6 0.6 ?0.69 0.69 ?0.17 0.17 3.6 3.6 33
下載: 導出CSV
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