Gradient-based trajectory optimization with B-spline curves is widely used for unmanned aerial vehicles (UAVs) due to its fast convergence and continuous trajectory generation. However, the application of B-spline curves for path-velocity coupled trajectory planning in autonomous vehicles (AVs) has been highly limited because it is challenging to reduce the over-approximation of the vehicle shape and to create a collision-free trajectory using B-spline curves while satisfying kinodynamic constraints. To address these challenges, this paper proposes novel disc-type swept volume (SV), incremental path flattening (IPF), and kinodynamic feasibility penalty methods. The disc-type SV estimation method is a new technique to reduce SV over-approximation and is used to find collision points for IPF. In IPF, the collision points are used to push the trajectory away from obstacles and to iteratively increase the curvature weight, thereby reducing SV and generating a collision-free trajectory. Additionally, to satisfy kinodynamic constraints for AVs using B-spline curves, we apply a clamped B-spline curvature penalty along with longitudinal and lateral velocity and acceleration penalties. Our experimental results demonstrate that our method outperforms state-of-the-art baselines in various simulated environments. We also conducted a real-world experiment using an AV, and our results validate the simulated tracking performance of the proposed approach.

翻译：基于B样条曲线的梯度轨迹优化因其快速收敛和连续轨迹生成能力，在无人机领域得到广泛应用。然而，由于难以在满足运动学动力学约束的同时，利用B样条曲线减少车辆形状的过度近似并生成无碰撞轨迹，该方法在自动驾驶车辆路径-速度耦合轨迹规划中的应用受到极大限制。为解决这些挑战，本文提出了新型圆盘型扫掠体积估计方法、增量路径平坦化方法以及运动学动力学可行性惩罚方法。圆盘型扫掠体积估计是一种减少扫掠体积过度近似的新技术，用于为增量路径平坦化寻找碰撞点。在增量路径平坦化过程中，碰撞点被用于将轨迹推离障碍物，并通过迭代增加曲率权重来减小扫掠体积，从而生成无碰撞轨迹。此外，为满足自动驾驶车辆使用B样条曲线时的运动学动力学约束，我们采用钳位B样条曲率惩罚以及纵向/横向速度与加速度惩罚。实验结果表明，本方法在多种仿真环境中均优于现有先进基线方法。我们还在真实自动驾驶车辆上进行了实验，结果验证了所提方法的仿真跟踪性能。