Autonomous avoidance decision-making and control method for eVTOL aircraft under non-cooperative differential games
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摘要: 为保障电动垂直起降(eVTOL)航空器在城市空域安全自主运行，针对非合作航空器入侵场景，提出了非合作博弈下eVTOL航空器自主避让决策与控制方法。针对具有不同飞行目标及避让意图的航空器，分别构建最优控制模型，并采用连续、混合动作空间表达控制输入；建立了基于非合作微分博弈的多机决策模型，以刻画冲突场景下航空器之间的避让或抢行行为；融合事件触发机制与模型预测控制框架，采用航迹预测-冲突检测-优化计算-控制执行的滚动优化流程，为航空器实时求解单步最优控制指令；采用迭代最优响应算法，逐步逼近非合作微分博弈问题的纳什均衡解，以提高在线计算效率；基于上述模型与算法，在双机对向、同向、交叉冲突场景下，开展了eVTOL航空器的自主避让仿真试验。试验结果表明：当预判入侵机不具备避让意图时，避让效果更优；采用“调速+调向+调高度”的复合机动策略能够使避让安全性提升32%，避让效率提升53%，并且能够减少88%的最大偏移距离；基于迭代最优响应的博弈优化算法单步内平均计算时间小于0.3 s，响应速度快。提出的自主避让决策与控制方法能够使eVTOL航空器在面对非合作目标冲突时，快速生成最优控制策略，从而实现安全、高效的自主避让。Abstract: To ensure the safe autonomous operation of electric vertical take-off and landing (eVTOL) aircraft in urban airspace, an autonomous avoidance decision-making and control method for eVTOL aircrafts under non-cooperative games was proposed for non-cooperative aircraft intrusion scenarios. Optimal control models were constructed respectively for aircraft with different flight goals and avoidance intentions, and continuous and hybrid action spaces were adopted to express control inputs. A multi-aircraft decision-making model based on non-cooperative differential game theory was established to characterize the avoidance or priority-taking behaviors of aircraft in conflict scenarios. An event-triggered mechanism was integrated with a model predictive control framework, and a rolling optimization process of trajectory prediction, conflict detection, optimization calculation, and control execution was adopted to solve the single-step optimal control command for aircraft in real time. An iterative best response algorithm was adopted to progressively approach the Nash equilibrium solution of the non-cooperative differential game to improve online computational efficiency. Based on the proposed models and algorithms, autonomous avoidance simulation experiments of eVTOL aircraft were conducted under head-on, same-direction, and crossing conflict scenarios. Simulation results show that when the intruding aircraft is predicted to have no avoidance intention, the avoidance effect is better. The composite maneuver strategy of "speed adjustment+direction adjustment+altitude adjustment" improves avoidance safety by 32%, increases avoidance efficiency by 53%, and reduces maximum deviation distance by 88%. The average computation time per step of the game optimization algorithm based on iterative best response is less than 0.3 s, and the response speed is fast. The proposed autonomous avoidance decision-making and control method enables eVTOL aircraft to rapidly generate optimal control strategies when facing non-cooperative target conflicts, thereby achieving safe and efficient autonomous avoidance.
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图 1 基于事件触发MPC的避让决策与控制流程
Figure 1. Avoidance decision and control process based on event-triggered MPC
图 6 试验1中双机轨迹与控制输入变化曲线(对向相遇)
Figure 6. Variation curves of trajectories and control inputs of two aircrafts in experiment 1 (head-on encounter)
图 7 双机间隔曲线(对向相遇)
Figure 7. Curves of separation distance between two aircrafts (head-on encounter)
图 8 控制策略计算时间(对向相遇)
Figure 8. Computational time for control strategy (head-on encounter)
图 9 试验1中双机轨迹与控制输入变化曲线(同向相遇)
Figure 9. Variation curves of trajectories and control inputs of two aircrafts in experiment 1 (overtaking encounter)
图 10 双机间隔曲线(同向相遇)
Figure 10. Curves of separation distance between two aircrafts (overtaking encounter)
图 11 控制策略计算时间(同向相遇)
Figure 11. Computational time of control strategy (overtaking encounter)
图 15 双机间隔曲线(交叉相遇)
Figure 15. Curves of separation distance between two aircrafts (crossing encounter)
表 1 仿真参数设置
Table 1. Simulation parameter settings
参数 取值 时间步长Δt /s 1 预测与优化步数T 5 最低安全间隔d0/m 100 航迹偏离阈值δ/m 1 迭代收敛阈值c 1.0×10-4 飞行高度范围(zmin, zmax)/m (200, 600) 水平速度范围(vminXY, vmaxXY)/(m·s-1) (0, 36.1) 垂直速度范围(vminZ, vmaxZ)/(m·s-1) (0, 10) 航向角范围(Ψmin, Ψmax)/rad (-π, π) 俯仰角范围(θmin, θmax)/rad (-π/6, π/6) 加速度范围(amin, amax)/(m·s-2) (-10, 10) 航向角速率范围(ωmin, ωmax)/(rad·s-1) (-π/6, π/6) 俯仰角速率范围(αmin, αmax)/(rad·s-1) (-π/18, π/18) 代价项权重系数w1~w6 1, 102, 104, 106, 108, 1 注：表中参数值范围可根据实际情况调整。 
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表 2 避让效果评价指标
Table 2. Evaluation metrics of avoidance performance
指标 含义 双机间隔/m 任意两架eVTOL在三维空间中的欧氏距离 计算时间/s 单时间步内，从开始求解博弈/跟踪优化问题到求解器返回最优控制输入所用的时间 避让时间/s 从系统首次检测到冲突开始，到冲突完全解除为止所经历的时间 最大横向偏离距离/m 实际航迹相对于参考航迹的偏离程度
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表 3 试验1~4避让效果对比(对向相遇)
Table 3. Comparison of avoidance performances in experiments 1-4 (head-on encounter)
试验 避让时间/ s 最大横向偏移距离/m 平均博弈优化时间/s 平均跟踪优化时间/s 1 113 77.04 0.28 0.03 2 35 134.27 0.24 0.03 3 107 63.46 0.29 0.03 4 50 112.76 0.13 0.03
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表 4 试验1~4避让效果对比(同向相遇)
Table 4. Comparison of avoidance performances in experiments 1-4 (overtaking encounter)
试验 避让时间/ s 最大横向偏移距离/m 平均博弈优化时间/s 平均跟踪优化时间/s 1 111 75.72 0.19 0.03 2 111 121.81 0.18 0.03 3 112 72.11 0.17 0.03 4 111 132.71 0.08 0.03
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表 5 不同控制策略下的避让效果对比
Table 5. Comparison of avoidance performances under different control strategies
控制策略 双机最小间隔/m 避让时间/s 最大横向偏移距离/m 平均博弈优化时间/s 调速 82.52 15 0.00 0.08 调向 76.34 45 788.47 0.14 调高度 77.60 6 99.06 0.14 调速+调向 95.58 13 182.02 0.17 调速+调高度 104.71 10 66.22 0.19 调向+调高度 107.20 14 192.80 0.23 调速+调向+调高度 119.78 8 27.12 0.22
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