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After the experience of Tesla when automatic driving function, I found the car at the time of vexation over the long lateral ramp will occur, feel the car is shifted to the centrifugal direction, offset some time, the car will automatically toward the centripetal direction. " back to "correct. Although this sign is not obvious, but it reveals the existence of this problem and smooth cornering. I think using a cubic polynomial to approximate centerline of the road, when the curvature of the road is large, the effect of a cubic polynomial approximation will be unsatisfactory, resulting in planning the trajectory does not meet the actual state of roads and the environment, the vehicle will travel or even shake collision.
To solve this problem there are two kinds of ideas, a mathematical model of the curve is approximated to be treated in a safe and accurate premise, to reduce the curvature; 2 is switching to a mathematical model closer to the actual situation of the curvature of the curve. The share of literature "Real-Time Trajectory Planning for Autonomous Urban Driving_ Framework, Algorithms, and Verifications" the idea of using the method 1.
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The most innovative place is herein pretreatment reference line, divided into the following three steps: a- obtaining a digital road map from a centerline (high precision map), i.e. the initial reference lines; conjugate gradient linear B- optimization method to smooth; using the C-cubic B-spline curve interpolation. Lift is brought: the more urgent curve, the curvature of the reference line becomes smaller and smoother, reduce the risk of lateral displacement of the vehicle when cornering. Of course, this does not solve the problem of the vehicle difficult too sharp turn fundamentally.
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The remaining steps and Apollo Lattice Planner Similarly, the details are different. At the same: a- at frenet coordinate system is decomposed into horizontal and vertical trajectory are solved, and a function of the lateral longitudinal L (s); b- establishing a series of cost function to evaluate a large number of candidate locus; the C-collision detection. After the evaluation of horizontal and vertical sort-merge, in fact, this step is very simple, skip worth mentioning.
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There are real cars, real road test. But the test road is narrow, single lane, the speed is very slow, 22Km / h, the implementation cycle is slow, 100ms / cycle.
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behavioral decision making of this planning is, the output is with the car, turn left, change lanes, parking and other instructions.
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Calculating the planning process in 2 parts: pre-processing the reference line of approximately 50ms, trajectory planning 20ms. Is defined as the maximum number of candidate trajectories 500, I less than the number of samples in the lattice, be a small amount of medium. However, defines the maximum number of candidate trajectories, it defines the sampling density, feasible? If the top decision-making and environmental information more accurate and effective sampling narrow range, is also possible.
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Obstacle avoidance is not considered a reference line smoothing. The reference line is static, with only about static map, regardless of obstacle avoidance. Objective function of optimization is divided into three: an offset between two adjacent a-; b- angle between two adjacent orientation change; point falls within the C-road. a and b are smooth so that the reference line, c such that the road does not exceed the range of the reference line. (P4)
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Smoothing points before and after the same path optimization, the optimized points as control points of the B-spline interpolation.
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速度曲线的生成分3步：a- 求各种speed limit并取其中的最小值，受当前决策和交通规则、最大横向加速度、最大加减速度、安全距离等因素的限制，其中，考虑横向加速度是一个有趣的点。b- 根据加速-平稳-减速的模型采样；c- 把b产生的速度曲线分为3段，依次用3次多项式拟合平滑。这个过程有点类似Apollo的piecewise optimization。
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碰撞检测时采用多个圆形代替矩形表示车辆自身，以降低计算复杂度。不知依据何在，如何应用？
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评价轨迹使用了4项cost functions，分别是：a- s更长的轨迹；b- 曲率的积分（限制平滑）；c- 与参考线的偏移；d- 连续规划cycle间的轨迹一致性，用（上次规划轨迹的终点横向偏移-本次终点横向偏移）表征。（P8）
