arXiv:2604.00391cs.ROcs.SY2026-04

无需训练和模型,用数据直接估算轨迹扩散得分。

Behavioral Score Diffusion: Model-Free Trajectory Planning via Kernel-Based Score Estimation from Data

  • 通过核加权法从轨迹库中直接估计扩散得分
  • 仅用1000条数据即达基线98.5%性能
  • 适合无动力学模型的复杂机器人规划

基于扩散的轨迹优化已成为一种强大规划范式,但现有方法需依赖大规模数据训练的得分网络或解析动力学模型来计算得分。本文提出行为得分扩散(BSD),一种无需训练且无需模型的轨迹规划器,通过核加权估计直接从轨迹数据库中计算扩散得分函数。在每个去噪步骤中,BSD使用三重核加权方案——扩散相似性、状态上下文与目标相关性——检索相关轨迹,并采用Nadaraya-Watson估计方法计算去噪轨迹。扩散噪声调度自然控制核带宽,形成多尺度非参数回归:高噪声时对全局行为模式进行广义平均,低噪声时实现精细局部插值。这种粗到细结构在不进行线性化或参数假设的情况下处理非线性动力学。安全性通过在核估计的状态轨迹上应用屏蔽滚动实现,与现有基于模型的方法一致。我们在四个复杂度递增的机器人系统(3D–6D状态空间)的停车场景中评估了BSD。BSD在固定带宽下,跨系统平均奖励达到基于模型基线的98.5%,且无需动力学模型,仅需1,000条预收集轨迹。相比最近邻检索,BSD性能提升18%至63%,证实扩散去噪机制对数据驱动规划至关重要。

原文摘要 · Abstract (English)

Diffusion-based trajectory optimization has emerged as a powerful planning paradigm, but existing methods require either learned score networks trained on large datasets or analytical dynamics models for score computation. We introduce \emph{Behavioral Score Diffusion} (BSD), a training-free and model-free trajectory planner that computes the diffusion score function directly from a library of trajectory data via kernel-weighted estimation. At each denoising step, BSD retrieves relevant trajectories using a triple-kernel weighting scheme -- diffusion proximity, state context, and goal relevance -- and computes a Nadaraya-Watson estimate of the denoised trajectory. The diffusion noise schedule naturally controls kernel bandwidths, creating a multi-scale nonparametric regression: broad averaging of global behavioral patterns at high noise, fine-grained local interpolation at low noise. This coarse-to-fine structure handles nonlinear dynamics without linearization or parametric assumptions. Safety is preserved by applying shielded rollout on kernel-estimated state trajectories, identical to existing model-based approaches. We evaluate BSD on four robotic systems of increasing complexity (3D--6D state spaces) in a parking scenario. BSD with fixed bandwidth achieves 98.5\% of the model-based baseline's average reward across systems while requiring no dynamics model, using only 1{,}000 pre-collected trajectories. BSD substantially outperforms nearest-neighbor retrieval (18--63\% improvement), confirming that the diffusion denoising mechanism is essential for effective data-driven planning.

轨迹规划扩散模型无模型数据驱动

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