Convex Approximation Based Avoidance Theory and Path Planning MPC for Driver-less Vehicles
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摘要: 提出了一种改进的无人驾驶车辆路径规划方法, 并搭建了相应的软件在环实时仿真系统, 对方法在结构化道路下的复杂动态交通工况进行性能验证.首先, 引入基于凸近似的避障原理, 对障碍物参考点的选取进行优化, 扩大了路径规划的可行域范围.采用改进后的方法, 并结合模型预测控制(Model predictive control, MPC)原理和曲线坐标系统, 综合考虑自车及障碍车的外形、道路几何约束及自车的机械结构约束、路径最短、侧向加速度、道路对中、逐次变道、车距安全度、左变道优先和前轮转角变化率等权重的影响, 实现了车辆在复杂动态交通工况下的路径规划.最后, 以长城H7运动多用途车作为无人驾驶实验及仿真平台, 搭建基于dSPACE多核架构的Carsim + Simulink软件在环实时仿真系统, 对算法进行验证.结果表明, 所提出的方法不仅可获得合理、平滑的行驶路径, 顺利避开运动障碍车的干扰, 而且具有良好的实时性.Abstract: An improved path planning algorithm for the driver-less vehicle is proposed in this paper, and a soft-ware in loop system is set up to evaluate its performance under complex dynamic traffic scenarios. First, a convex approximation based avoidance theory is introduced, and a method to optimize the obstacle's reference point is proposed for enlarging approachable region. Based on the proposed algorithm, the theory of MPC (Model predictive control) and the curvilinear coordination system, and nine key weighting factors are considered thoroughly to achieve an optimal path, including the dimensions of ego and obstacle vehicles, path geometric constraints and ego vehicle's mechanical constraints, shortest path, lateral acceleration, path alignment, lane changing successively, vehicle to vehicle safety distance, left lane changing priority and the rate of front wheel angle change. Finally, the GWM H7 SUV is used as the driver-less prototype vehicle, and a Carsim + Simulink based soft-ware in loop system is set up, via using the dSPACE multi-cores platform, in order to test the proposed algorithm. The simulation test results demonstrate that not only a reasonable and smooth path is achieved to avoid the disturbances from the moving vehicles, but also an expected real-time performance is obtained.
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Key words:
- Driver-less vehicles /
- path planning /
- convex approximation /
- obstacle avoidance theory /
- model predictive control (MPC)
1) 本文责任编委 李力 -
图 3 不同参考点计算的可行域对比
Fig. 3 Feasible area comparison calculated by different reference points
图 4 改进前后两种凸近似避障法的路径规划结果对比
Fig. 4 Path planning comparison results between un-developed and developed convex approximation avoidance methods
图 5 基于曲线坐标系统的车道偏移量计算原理
Fig. 5 Lane off-set calculation theory based on the curvilinear coordination system
图 7 权重函数松弛前后结果对比
Fig. 7 Comparison results of the cost functions before/after relaxation
图 12 基于SILS的H7 Carsim模型与实车实验性能对比
Fig. 12 Performance comparison between the H7 Carsim model and prototype vehicle based on SILS
表 1 长城H7车辆参数值
Table 1 Vehicle parameters of the GWM H7
参数 数值 单位 参数 数值 单位 $k_f$ $-$111187 N/rad $I_z$ 3522.1 ${\rm {kg\cdot m}}^{2}$ $k_r$ $-$90773 N/rad $M_v$ 2211 kg $a$ 1.25 m $v_r$ 6 m/s $b$ 1.59 m 
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表 2 MPC控制系统参数
Table 2 Parameters of MPC system
参数 数值 参数 数值 $k_1$ 0.3 $k_6$ 0.2 $k_2$ 8 $k_7$ 0.7 $k_3$ 3 $N$ 3 $k_4$ 2.5 $N_{\mu}$ 1 $k_5$ 15
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符号 说明 单位 $a/b$ 前/后轴距离质心的距离 m ${\pmb d_{\ast}}$ 自车外观几何形状向量 m $D_{0}$ 自车停车时自车和障碍车之间的距离 m $I_{z}$ 车辆绕$z$轴的转动惯量 kg$\cdot$s$^2$ $k_{f/r}$ 前/后轮的侧倾刚度 N/rad $l$ 车的轴距 m $M$ 障碍车的数量 $M_{v}$ 车辆质量 kg $N/N_{u}$ 预测/控制步长 $o_{L}$ 车辆质心点$p_{0}$投影到中间车道的最短距离 m $OXY/o_{V}x_{V}y_{V}/o_{L}x_{L}y_{L}$ 大地/车辆/道路坐标系 ${\pmb p}$ 可行域中的点 m ${\pmb p_{0}}$ 自车质心位置 m ${\pmb q_{\ast}}$ 障碍车参考点 $r$ 自车凸多边形外形端点数 $R$ 车辆转弯半径 m $s_{*}$ 障碍车凸多边形外形端点数 $S_{L}$ 车辆质心偏移中间道路的位移量 m $S_{L_ {\rm max/min}}$ 左/右道路边缘的极限位置偏移量 m $t$ 采样时间 s $v_{f/r}$ 自车前/后轴速度 m/s $v_{l}$ 障碍车速 m/s $v_{la/lg}$ 质心的侧/纵向速度 m/s $\dot{v_{la}}$ 质心的侧向加速度 m/s$^{2}$ $v_{rel}$ 自车和障碍车之间的相对速度 m/s ${\pmb w_{\ast}}$ 障碍车(物)外观几何形状向量 m $W_{c}$ 车宽 m $W_{L}$ 实时测得的车道宽 m $x/y$ 自车质心在大地坐标系下的横/纵坐标 m $\dot{x}/\dot{y}$ 质心沿大地坐标系$X/Y$轴的速度 m/s $\delta_{f}$ 前轮转角 rad $\mu_{*}$ 缩放系数 ${\pmb w}$ 障碍车(物)内部点 m $\varphi/\dot{\varphi}/\ddot{\varphi}$ 航向角/横摆角速度/角加速度 rad/rad/s/rad/s$^2$ $\gamma$ 实际车距与安全车距的比值
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