面向可扩展长时程多智能体运动预测的物理信息神经控制微分方程
Physics-Informed Neural Controlled Differential Equations for Scalable Long Horizon Multi-Agent Motion Forecasting
AI总结：
针对多自主机器人长时程运动预测难题，提出以多智能体目标为条件的PINCoDE模型，结合神经控制微分方程与物理约束，可无参扩展至百台机器人，长时程预测精度显著优于解析模型。
摘要：
多自主机器人的长时程运动预测因智能体间的非线性交互、预测误差累积以及动力学的连续时间演化而颇具挑战。这类系统的习得动力学可应用于行程时间预测、预测引导规划及生成式仿真等多种场景。本研究旨在开发一种以多智能体目标为条件的高效轨迹预测模型。受近期物理引导深度学习在部分已知动力学系统中取得的成功启发，我们构建了一种基于神经控制微分方程（CDEs）的长时程运动预测模型。与RNN、transformer等离散时间方法不同，神经CDEs在连续时间域运行，使我们能够结合物理信息约束与先验偏置，联合建模多机器人动力学。我们提出的方法名为PINCoDE（物理信息神经控制微分方程），其学习得到的微分方程参数可用于预测多智能体系统从初始状态出发的轨迹。PINCoDE以未来目标为条件，并在较长时间范围内对机器人运动施加物理约束。我们采用的策略可将模型从10个机器人扩展至100个机器人，且无需增加额外模型参数，同时在1分钟预测时域下的平均位移误差（ADE）低于0.5米。此外，对PINCoDE模型采用课程学习的渐进式训练后，在4分钟时域下的预测位姿误差较解析模型降低了2.7倍。
英文摘要：
Long-horizon motion forecasting for multiple autonomous robots is challenging due to non-linear agent interactions, compounding prediction errors, and continuous-time evolution of dynamics. Learned dynamics of such a system can be useful in various applications such as travel time prediction, prediction-guided planning and generative simulation. In this work, we aim to develop an efficient trajectory forecasting model conditioned on multi-agent goals. Motivated by the recent success of physics-guided deep learning for partially known dynamical systems, we develop a model based on neural Controlled Differential Equations (CDEs) for long-horizon motion forecasting. Unlike discrete-time methods such as RNNs and transformers, neural CDEs operate in continuous time, allowing us to combine physics-informed constraints and biases to jointly model multi-robot dynamics. Our approach, named PINCoDE (Physics-Informed Neural Controlled Differential Equations), learns differential equation parameters that can be used to predict the trajectories of a multi-agent system starting from an initial condition. PINCoDE is conditioned on future goals and enforces physics constraints for robot motion over extended periods of time. We adopt a strategy that scales our model from 10 robots to 100 robots without the need for additional model parameters, while producing predictions with an average ADE below 0.5 m for a 1-minute horizon. Furthermore, progressive training with curriculum learning for our PINCoDE model results in a 2.7X reduction of forecasted pose error over 4 minute horizons compared to analytical models.
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