Novel Path Curvature Optimization Algorithm for Intelligent Wheelchair to Smoothly Pass a Narrow Space
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摘要: 为了使用户更感舒适，智能轮椅应该能在具有复杂几何约束的室内环境下平滑地通过狭窄通道.本文提出一个基于路径曲率优化的算法以确保智能轮椅平滑地通过狭窄过道.考虑到路径平滑度取决于路径曲率及其变化率，在通过传感器数据计算出狭窄通道相对于轮椅的位置后，算法以贝塞尔曲线的曲率及其变化率最小为优化目标，以轮椅过通道时的方向及贝塞尔多边形应为凸多边形作为约束，规划出一条平滑的最优路径，然后控制轮椅实时跟踪这条路径.上述过程动态循环运行，实现了智能轮椅平滑通过狭窄通道.仿真中将本文算法同基于A*的路径规划导航算法进行了对比，结果表明本文提出的基于曲率优化的算法可以实现比A*算法路径曲率更小且更加平滑的过狭窄通道过程，并且即使在没有全局地图和定位信息情况下，算法也能控制轮椅平滑地通过狭窄过道.实验中详细阐述了算法的实现过程，实验结果也证实了算法的有效性.Abstract: This paper presents a novel algorithm to address the smooth narrow pass traversing issue, which is based on optimizing the curvature of the wheelchair path. Being aware of the fact that the path smoothness is determined by the path curvature and its change rate, after calculating the position of the narrow pass relative to the base frame of the wheelchair from perception sensor data, the algorithm takes the curvature and its change rate of Bezier curve as the optimal objective, and the wheelchair heading and the condition that the Bezier curve polygon should be convex polygon as constraints, and plans a smooth and optimal path for the controlled wheelchair to follow. This process is iterated dynamically to enable the intelligent wheelchair to traverse the narrow pass smoothly. Simulation is firstly conducted to compare the performances of our method and the A*-based path planning navigation algorithm, which shows that the proposed algorithm is able to achieve more smooth path with smaller curvature when the wheelchair traverses narrow path. Furthermore, the algorithm can control the wheelchair to traverse narrow pass smoothly even without any global map and localization. Real experiment with detailed explanation of algorithm implementation is also given to verify the effectiveness of the proposed algorithm.
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Key words:
- Intelligent wheelchair /
- curvature optimization /
- Bezier curve /
- pass traversing
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图 6 在场景$A$中每一条路径对应的轮椅的角速度和跟踪误差
Fig. 6 The angular rate and the tracking errors for each path in Scenario $A$
图 8 基于本文方法和A*算法的轮椅路径
Fig. 8 Actual trajectories generated by the proposed method and A* algorithm
图 9 基于本文方法和A*算法的路径曲率的比较
Fig. 9 The comparison of trajectory curvature generated by the proposed method and A* algorithm
图 10 算法每次循环中各模块运行时间及总时间
Fig. 10 Consuming time of each algorithm module and their total value for each iteration
图 13 一次激光扫描数据点及其分段
Fig. 13 A full scan of laser data points and its expected segmentations
图 16 轮椅从不同起点到达终点位置时的实际位置
Fig. 16 Actual wheelchair poses when arriving at the desired pose with different starting poses $A$, $B$, $C$ and $D$
图 18 轮椅从起点$A$和$D$出发过通道轨迹截图((a)~(f)对应于起点$A$, (g)~(l)对应于起点$D$)
Fig. 18 Snapshots of the wheelchair$'$s trajectories when passing gap, starting from pose $A$ and $D$ ((a)~(f), (g)~(l) are with pose $A$ and $D$, respectively.)
表 1 每条路径的输入参数
Table 1 The input parameters for each path
场景 Ps (m) Pd (m) Pt (m) 1 (Hs, Hd) 2 (Hs, Hd) 3 (Hd, Ht) 4 (Hd, Ht) A (0.1, 1.3) (1.6, 1.8) (0.0, 3.5) (-20, 90) (-40, 90) (90, 160) (90, 200) B (0.1, 1.3) (1.6, 1.8) (3.4, 3.5) (-10, 90) (10, 90) (90, 20) (90, -20) 
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