论文标题
伯恩斯坦基于多项式的转录方法，用于解决最佳轨迹产生问题
Bernstein polynomial-based transcription method for solving optimal trajectory generation problems
论文作者
论文摘要
本文介绍了一种方法和开源实现，即Bernstein/Bézier最佳轨迹（BEBOT），用于生成用于自主系统操作的轨迹。所提出的方法基于轨迹产生问题的无限维度最佳控制公式。通过使用Bernstein多项式近似轨迹，可以将这些问题转录为非线性编程问题，然后可以使用现成的求解器来解决。伯恩斯坦多项式具有有利的几何特性，使轨迹规划师能够有效评估和强制沿车辆轨迹的约束，包括最大速度和角速率，轨迹之间的最小距离，车辆和障碍物之间的最小距离。凭借这些特性，可以在多项式命令的命令下独立执行和保证在自动驾驶汽车操作中通常施加的可行性和安全限制。因此，轨迹生成算法可以有效地产生可行的和无碰撞的轨迹，并且可以在复杂的环境和多个车辆任务中部署用于实时安全性关键应用。
This paper presents a method and an open-source implementation, Bernstein/Bézier Optimal Trajectories (BeBOT), for the generation of trajectories for autonomous system operations. The proposed method is based on infinite dimensional optimal control formulations of trajectory generation problems. By approximating the trajectories using Bernstein polynomials, these problems can be transcribed as nonlinear programming problems, which can then be solved using off-the-shelf solvers. Bernstein polynomials possess favorable geometric properties that enable the trajectory planner to efficiently evaluate and enforce constraints along the vehicles' trajectories, including maximum speed and angular rates, minimum distance between trajectories and between the vehicles and obstacles. By virtue of these properties, feasibility and safety constraints typically imposed in autonomous vehicle operations can be enforced and guaranteed independently on the order of the polynomials. Thus, the trajectory generation algorithm can efficiently generate feasible and collision-free trajectories, and can be deployed for real-time safety critical applications in complex environments and for multiple vehicle missions.
