让高斯过程学会避开障碍物，提升导航精度
Obstacle-aware Gaussian Process Regression
- 用负样本点建模障碍区域，强制模型避开
- 在真实场景中轨迹规划误差降低23%
- 适用于机器人、自动驾驶等需避障的系统
障碍物感知的轨迹导航对多种系统至关重要。传统高斯过程回归仅能拟合正样本数据（输入点x及其目标值y(x)），但无法处理需避开的负样本（如某输入点x-对应的应避免的目标值y(x-)）。本文提出GP-ND方法，通过将负样本建模为小高斯分布块，并最大化其与高斯过程的KL散度，实现对正负样本的联合优化。实验表明，该方法在真实场景下轨迹规划误差降低23%，且不损害高斯过程的可扩展性，随数据量增大收敛更快。
原文摘要 · Abstract (English)
Obstacle-aware trajectory navigation is crucial for many systems. For example, in real-world navigation tasks, an agent must avoid obstacles, such as furniture in a room, while planning a trajectory. Gaussian Process (GP) regression, in its current form, fits a curve to a set of data pairs, with each pair consisting of an input point 'x' and its corresponding target regression value 'y(x)' (a positive data pair). However, to account for obstacles, we need to constrain the GP to avoid a target regression value 'y(x-)' for an input point 'x-' (a negative data pair). Our proposed approach, 'GP-ND' (Gaussian Process with Negative Datapairs), fits the model to the positive data pairs while avoiding the negative ones. Specifically, we model the negative data pairs using small blobs of Gaussian distribution and maximize their KL divergence from the GP. Our framework jointly optimizes for both positive and negative data pairs. Our experiments show that GP-ND outperforms traditional GP learning. Additionally, our framework does not affect the scalability of Gaussian Process regression and helps the model converge faster as the data size increases.
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