AUV Terrain-Following Method Based on B-Spline Planning and Meta-Learning LTV-MPC
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摘要: 针对自主水下航行器(AUV)在复杂海底地形下近底自主航行时难以同时满足跟踪精度、离底安全和执行器约束的问题, 文中提出一种基于滑动窗口B样条规划的地形跟踪方法, 并在控制层引入基于元学习的权重自适应线性时变模型预测控制(LTV-MPC)策略。规划层采用3次B样条在坡度约束下生成保持定高裕度的参考路径, 结合滑动窗口机制实现局部优化与全局连续性的平衡; 控制层采用 LTV-MPC控制器, 由元学习网络根据地形曲率、深度及姿态误差等特征在线调整代价函数权重, 以适应不同地形条件下的跟踪难度变化。元网络参数通过贝叶斯优化在多组合成地形闭环仿真数据上离线训练, 学习地形特征与最优权重的映射关系, 在线阶段仅需前向推理, 计算效率高。在所设定的仿真场景中, 合成地形与实测地形数据验证表明, 相比LOS-PID, 所提方法的均方根(RMS)跟踪误差在两种地形下分别降低42.5%和31.3%, 相比标准LTV-MPC, RMS跟踪误差分别降低4.5% 和6.1%, 同时满足俯仰角和舵角约束, 有效解决了复杂地形下跟踪精度与安全性的平衡问题。
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关键词:
- 自主水下航行器 /
- 地形跟踪 /
- 滑动窗口B样条 /
- 线性时变模型预测控制 /
- 元学习权重自适应
Abstract: To address the difficulty of simultaneously satisfying tracking accuracy, bottom-clearance safety and actuator constraints for autonomous underwater vehicle(AUV) navigating close to complex seabed terrain, this paper proposes a terrain-following method based on sliding-window B-spline planning and meta-learning-based adaptive linear time-varying model predictive control(LTV-MPC). The planning layer employs cubic B-spline under slope constraints to generate a reference path that maintains a prescribed altitude margin, combined with a sliding-window mechanism to achieve a balance between local optimization and global continuity. The control layer implements LTV-MPC with a meta-learning network that adaptively adjusts cost weights based on terrain curvature, depth and pitch errors to adapt to varying tracking difficulty under different terrain conditions. The meta-network parameters are trained offline via Bayesian optimization on closed-loop simulation data from multiple synthetic terrains, learning the mapping relationship between terrain features and optimal weights, requiring only forward inference online with high computational efficiency. In the specified simulation scenarios, validations on synthetic and real seabed terrain data demonstrate that, compared with LOS-PID, the proposed method reduces root mean square(RMS) tracking error by 42.5% and 31.3% under the two terrain scenarios respectively, compared with standard LTV-MPC, RMS tracking error is reduced by 4.5% and 6.1% respectively, while satisfying pitch angle and rudder angle constraints, effectively solving the balance problem between tracking accuracy and safety under complex terrain conditions. -
表 1 滑动窗口在线规划流程
Table 1. Sliding window online planning process
步骤 执行内容 1 初始化窗口参数$ ({L}_{\text{win}},\Delta {x}_{\text{win}}) $及权重$ ({\lambda }_{s},{\lambda }_{t}) $ 2 获取窗口$ {\mathcal{W}}_{k} $内地形点数据$ ({x}_{i},{\textit{z}}_{i}) $ 3 构建局部优化问题(式(12)) 4 求解最优控制点子集$ P_{k}^{*} $ 5 施加相邻窗口间路径连续性约束(式(13)) 6 更新全局B样条参考路径$ S\left(x\right) $ 7 输出路径至底层控制模块, 滑动窗口返回步骤2 
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表 2 主要参数取值
Table 2. Key parameter values
模型参数 取值 算法参数 取值 $ m $ 73 kg $ {\gamma }_{\max } $ ±25° $ L $ 2.2 m $ {\kappa }_{\max } $ 0.08 m−1 $ {X}_{\dot{u}} $ −6.5 kg $ {N}_{p} $ 17 $ {Z}_{\dot{w}} $ −64.2 kg $ {N}_{c} $ 9 $ {M}_{\dot{q}} $ −14.1 kg·m2 $ \Delta t $ 0.1 s $ {X}_{u} $ 0.0 N·s/m $ {u}_{r} $ 1.5 m/s $ {X}_{u|u|} $ 2.974 N·s2/m2 $ \boldsymbol{Q} $ diag(0.15, 350,
150, 120, 8, 3)$ {Z}_{w} $ 134.051 N·s/m $ \boldsymbol{R} $ diag(0.05, 0.35) $ {Z}_{w|w|} $ 9.375 N·s2/m2 $ \begin{aligned}& [\alpha _{\mathrm{i}}^{\min },\alpha _{i}^{\max }],\\& i\in \{{\textit{z}}, \theta ,\delta \}\end{aligned} $ [0.8, 2.0] $ {M}_{q} $ 35.145 N·m·s — — $ {M}_{q|q|} $ 0.369 N·m·s2 — —
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表 3 合成地形场景下控制器性能对比
Table 3. Performance comparison of controllers in synthetic terrain scene
控制器 RMS误差/m 峰值误差/m 滞后时间/s LOS-PID 0.073 0.282 0.00 标准LTV-MPC 0.044 0.310 0.00 自适应LTV-MPC 0.053 0.345 0.00 元学习LTV-MPC 0.042 0.289 0.00
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表 4 真实地形下控制器性能对比
Table 4. Performance comparison of controllers in real terrain
控制器 RMS误差/m 峰值误差/m 滞后时间/s LOS-PID 0.067 0.357 0.00 标准LTV-MPC 0.049 0.349 0.00 自适应LTV-MPC 0.052 0.367 −0.10 元学习LTV-MPC 0.046 0.337 0.00
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表 5 不同时域参数下的MPC求解时间
Table 5. MPC solution time under different time domain parameters
预测时
域$ {N}_{p} $控制时
域$ {N}_{c} $元学习推
理时间/ms元学习MPC
调用时间/ms单步控制
总耗时/ms15 8 0.70±0.19 4.7±1.2 5.0±1.6 17 9 0.74±0.10 4.9±0.7 5.3±0.7 20 10 0.92±0.19 6.2±1.3 6.6±1.3 注: 元学习MPC调用时间中包含元学习推理时间; 单步控制总耗时除元学习MPC调用外还包括状态估计、参考生成及数据记录等开销。
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表 6 不同历史采样点配置下的规划层求解时间
Table 6. Planning layer solving time under different historical-sample configurations
历史采样点数 拟合点数 B样条控制点数 求解时间/ms 20 8 4 33.0±6.8 40 18 6 75.9±17.2 60 28 10 125.9±35.6 80 38 14 235.7±55.9
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