Curve-straight probabilistic engagement zones (CSPEZ) quantify the spatial regions an evader should avoid to reduce capture risk from a turn-rate-limited pursuer following a curve-straight path with uncertain parameters including position, heading, velocity, range, and maximum turn rate. This paper presents methods for generating evader trajectories that minimize capture risk under such uncertainty. We first derive an analytic solution for the deterministic curve-straight basic engagement zone (CSBEZ), then extend this formulation to a probabilistic framework using four uncertainty-propagation approaches: Monte Carlo sampling, linearization, quadratic approximation, and neural-network regression. We evaluate the accuracy and computational cost of each approximation method and demonstrate how CSPEZ constraints can be integrated into a trajectory-optimization algorithm to produce safe paths that explicitly account for pursuer uncertainty.

翻译：曲线-直线概率交战区域（CSPEZ）量化了规避者应避免的空间区域，以降低被转向速率受限追击者捕获的风险；该追击者遵循参数不确定的曲线-直线路径，不确定参数包括位置、航向、速度、射程和最大转向速率。本文提出了在此类不确定性下生成最小化捕获风险的规避者轨迹的方法。我们首先推导了确定性曲线-直线基本交战区域（CSBEZ）的解析解，随后通过四种不确定性传播方法——蒙特卡洛采样、线性化、二次近似和神经网络回归——将该公式扩展至概率框架。我们评估了每种近似方法的精度与计算成本，并展示了如何将CSPEZ约束集成至轨迹优化算法中，以生成明确考虑追击者不确定性的安全路径。