As the trend of moving away from high-precision maps gradually emerges in the
autonomous driving industry,traditional planning algorithms are gradually
exposing some problems. To address the high real-time, high precision, and high
trajectory quality requirements posed by the automatic parking task under
real-time perceived local maps,this paper proposes an improved automatic
parking planning algorithm based on the A* algorithm, and uses Model Predictive
Control (MPC) as the control module for automatic parking.The algorithm
enhances the planning real-time performance by optimizing heuristic functions,
binary heap optimization, and bidirectional search; it calculates the
passability of narrow areas by dynamically loading obstacles and introduces the
vehicle's own volume during planning; it improves trajectory quality by using
neighborhood expansion and Bezier curve optimization methods to meet the high
trajectory quality requirements of the parking task. After obtaining the output
results of the planning algorithm, a loss function is designed according to the
characteristics of the automatic parking task under local maps, and the MPC
algorithm is used to output control commands to drive the car along the planned
trajectory. This paper uses the perception results of real driving environments
converted into maps as planning inputs to conduct simulation tests and ablation
experiments on the algorithm. Experimental results show that the improved
algorithm proposed in this paper can effectively meet the special requirements
of automatic parking under local maps and complete the automatic parking
planning and control tasks.

本文提出了基于 A * 算法的改进自动停车规划算法，并使用模型预测控制 (MPC) 作为自动停车的控制模块，通过优化启发函数、二叉堆优化和双向搜索来增强规划的实时性，通过动态加载障碍物和引入车辆自身体积来计算狭窄区域的通行能力，在满足停车任务的高轨迹质量要求方面，使用邻域扩展和贝塞尔曲线优化方法改善轨迹质量。在获得规划算法的输出结果后，根据本地地图下自动停车任务的特点设计损失函数，并使用 MPC 算法输出控制指令以沿着规划的轨迹行驶。实验结果表明，本文提出的改进算法能够有效满足本地地图下自动停车的特殊要求，并完成自动停车的规划和控制任务。

基于改进的 A * 算法的自动停车规划控制方法

Automatic parking planning control method based on improved A* algorithm

In this paper we derive and test a probability-based weighting that can
balance residuals of different types in spline fitting. In contrast to previous
formulations, the proposed spline error weighting scheme also incorporates a
prediction of the approximation error of the spline fit. We demonstrate the
effectiveness of the prediction in a synthetic experiment, and apply it to
visual-inertial fusion on rolling shutter cameras. This results in a method
that can estimate 3D structure with metric scale on generic first-person
videos. We also propose a quality measure for spline fitting, that can be used
to automatically select the knot spacing. Experiments verify that the obtained
trajectory quality corresponds well with the requested quality. Finally, by
linearly scaling the weights, we show that the proposed spline error weighting
minimizes the estimation errors on real sequences, in terms of scale and
end-point errors.

提出了一种概率加权的方法来平衡样条拟合中不同类型的残差，并综合考虑了样条拟合的近似误差的预测。利用该方法可以估计一般第一人称视频的具有度量尺度的 3D 结构，并提出了一种质量度量标准来自动选择节点间隔，验证结果显示该方法可以最小化估计误差。