发表机构
Kyung Hee University（庆熙大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出双线性Koopman基于模型的扩散（BK-MBD），通过高维提升和双线性动力学加速滚动预测，实现实时轨迹优化，在仿真和物理机械臂上均达到高成功率与实时性。
AI 中文摘要
传统的基于模型的扩散（MBD）通过利用噪声退火实现了有效的轨迹优化。然而，其高昂的计算成本主要源于对植物动力学进行重复的滚动预测，这使其应用在很大程度上局限于离线场景。为解决这一局限，本文提出了双线性Koopman基于模型的扩散（BK-MBD）。所提方法仅在每个控制步骤将机器人的状态提升到高维空间一次，此后所有候选轨迹都在提升空间中进行传播，因此每次滚动预测简化为固定次数的矩阵-向量乘法。提升后的动力学是双线性的，允许预测的输入增益随机器人构型变化，而线性提升模型无法表示这一点。在仿真中，BK-MBD在50毫秒的控制周期内，每次规划更新最多耗时14.7毫秒，并在每次试验中均到达目标，而线性提升几乎从未成功。在学习的滚动预测下，退火调度相比固定噪声调度提高了闭环精度。在精确滚动预测下，退火和固定窄噪声调度均能到达每个目标，表明退火降低了对替代模型误差的敏感性。BK-MBD还穿过了单一凸区域无法覆盖的通道，而凸化的双线性控制器很少成功。在物理机械臂上，BK-MBD在控制周期内跟踪了初始未知的移动目标，并且是唯一同时满足跟踪任务和截止时间的方��。项目页面可在以下网址获取：此https URL。
英文摘要
Conventional model-based diffusion (MBD) achieves effective trajectory optimization by leveraging noise annealing. However, its high computational cost, primarily arising from repeated rollouts of the plant dynamics, has largely confined its use to offline settings. To address this limitation, this paper proposes bilinear Koopman model-based diffusion (BK-MBD). The proposed method lifts the robot's state into a high-dimensional space only once per control step and propagates all candidates in the lifted space thereafter, so each rollout reduces to a fixed number of matrix-vector multiplications. The lifted dynamics are bilinear, allowing the predicted input gain to vary with the robot's configuration, which a linear lifted model cannot represent. In simulation, BK-MBD completed each planning update in at most 14.7 ms within a 50 ms control period and reached the goal on every trial, whereas a linear lift almost never did. The annealed schedule improves closed-loop accuracy over fixed-noise schedules under the learned rollout. Under the exact rollout, both the annealed and fixed-narrow schedules reach every goal, indicating that annealing reduces sensitivity to surrogate-model error. BK-MBD also threaded a passage that no single convex region covers, whereas a convexified bilinear controller rarely succeeded. On a physical manipulator, BK-MBD tracked an initially unknown moving target within the control period and was the only method that met both the tracking task and the deadline. The project page is available at https://rcilab.khu.ac.kr/bkmbd/.
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