针对车辆轨迹规划中的模型误差问题，提出动态调整安全约束的新方法。
Mismatch-Aware Adaptive Constraint Tightening for Bicycle-Model Trajectory Optimization
- 根据车速与转向曲率动态调整安全边界，避免固定裕量浪费
- 高曲率或高速时安全裕量增大，平缓路径几乎无冗余
- 无需仿真即可计算，适用于实时自动驾驶系统
自主车辆轨迹优化通常依赖于计算简单的运动学自行车模型，但在实际执行中因侧滑、轮胎刚度和横摆-侧向耦合等真实动力学影响，可能导致安全约束被突破。本文有三项理论贡献：首先推导出临界速度 $v_c = \sqrt{C_αL/M}$，其将模型失配分为两种模式——低于 $v_c$ 时车辆初始内偏（安全），高于 $v_c$ 时外偏（危险）；其次证明最大向外偏离 $\varepsilon^*$ 随规划时域 $T$ 呈 $T^2$ 标度，系数在瞬态与稳态间过渡；第三获得仅依赖车辆参数和规划时域的解析系数 $a_2^{\mathrm{anal}} = \frac{1}{2}(1 - v_c^2/v_{\max}^2)T^2$。基于此，提出不匹配感知自适应约束收紧（MACT）方法，$ε(v,κ) = a_2 v^2|κ|$，以状态相关裕量替代固定最坏情况裕量，在高速/高曲率时增加，平缓路径则近乎为零。八组数值实验验证了标度律，MACT在2-自由度车辆上实现100%安全，相比固定裕量基线减少84%冗余；可扩展至非线性倾斜自行车模型；在闭环直接射击模型预测控制对比中，相比管状模型预测控制降低34%施加裕量，且保持同等安全性。
原文摘要 · Abstract (English)
Trajectory optimization for autonomous vehicles usually relies on the kinematic bicycle model because of its computational simplicity. However, when the planned trajectory is executed under the true vehicle dynamics, which include lateral slip, tire stiffness and yaw-lateral coupling, safety constraints can be violated owing to the model mismatch. In this paper, we make three theoretical contributions. First, we derive a characteristic speed $v_c=\sqrt{C_αL/M}$ which separates two different mismatch regimes: below $v_c$ the dynamic bicycle initially oversteers inward (safe); above $v_c$ it understeers outward (safety-critical). Second, we prove that the peak outward deviation $\varepsilon^*$ follows a $T^2$ horizon scaling whose coefficient transitions between a transient bound $\frac{1}{2}(v^2-v_c^2)κ$ and a steady-state bound. Third, we obtain a simulation-free analytical coefficient $a_2^{\mathrm{anal}}=\frac{1}{2}(1-v_c^2/v_{\max}^2)T^2$ that is computable from vehicle parameters and the planning horizon alone. Putting these together, we propose Mismatch-Aware Adaptive Constraint Tightening (MACT), $ε(v,κ)=a_2 v^2|κ|$, which replaces a fixed worst-case margin by a state-dependent one that is large at high speed/curvature but nearly zero on gentle paths. Eight numerical experiments confirm the scaling laws. MACT reaches 100% safety with 84% less wasted margin than a fixed-margin baseline on the 2-DOF vehicle, extends to a nonlinear leaning bicycle, and in a closed-loop direct-shooting MPC comparison it cuts the applied margin by 34% compared with tube MPC while keeping the same safety.
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