用混合整数优化方法，104倍提速求解车辆最短时间路径与控制序列。
On Kinodynamic Global Planning in a Simplicial Complex Environment: A Mixed Integer Approach
- 将车辆运动规划转化为混合整数优化问题，同步求解路径与控制
- 在单纯复形环境中实现104倍于MPPI的计算速度，严格满足约束
- 适合高精度三维地形下的实时车辆全局规划场景
本文将适用于类汽车车辆的运动规划问题建模为优化任务，目标是在速度、加速度和转向的边界条件下，计算最小时间轨迹及其对应的速度剖面。该方法同时优化空间路径与加速和转向控制序列，确保从指定的初始位置和速度连续过渡到目标终点位置和速度。通过分析可接受的控制空间和地形特征，避免陷入局部极小值。所提方法在单纯复形环境（simplicial complex environment）中高效运行，该环境是表示复杂三维地形的优选方式。问题最初被建模为带有二次约束的混合整数分式规划，经变量变换后重构为混合整数双线性目标，并利用McCormick包络法松弛为混合整数线性规划。与MPPI及log-MPPI等规划器相比，本方法生成解决方案的速度快104倍，且严格遵守所有约束条件。
原文摘要 · Abstract (English)
This work casts the kinodynamic planning problem for car-like vehicles as an optimization task to compute a minimum-time trajectory and its associated velocity profile, subject to boundary conditions on velocity, acceleration, and steering. The approach simultaneously optimizes both the spatial path and the sequence of acceleration and steering controls, ensuring continuous motion from a specified initial position and velocity to a target end position and velocity.The method analyzes the admissible control space and terrain to avoid local minima. The proposed method operates efficiently in simplicial complex environments, a preferred terrain representation for capturing intricate 3D landscapes. The problem is initially posed as a mixed-integer fractional program with quadratic constraints, which is then reformulated into a mixed-integer bilinear objective through a variable transformation and subsequently relaxed to a mixed-integer linear program using McCormick envelopes. Comparative simulations against planners such as MPPI and log-MPPI demonstrate that the proposed approach generates solutions 104 times faster while strictly adhering to the specified constraints
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