Nonlinearity in dynamics has long been a major challenge in robotics, often causing significant performance degradation in existing control algorithms. For example, the navigation of bipedal robots can exhibit nonlinear behaviors even under simple velocity commands, as their actual dynamics are governed by complex whole-body movements and discrete contacts. In this work, we propose a safe navigation framework inspired by Koopman operator theory. We first train a low-level locomotion policy using deep reinforcement learning, and then capture its low-frequency, base-level dynamics by learning linearized dynamics in a high-dimensional lifted space. Then, our model-predictive controller (MPC) efficiently optimizes control signals via a standard quadratic objective and the linear dynamics constraint in the lifted space. We demonstrate that the Koopman model more accurately predicts bipedal robot trajectories than baseline approaches. We also show that the proposed navigation framework achieves improved safety with better success rates in dense environments with narrow passages.

翻译：动力学中的非线性长期以来一直是机器人学的主要挑战，常导致现有控制算法性能显著下降。例如，双足机器人的导航即使在简单速度指令下也可能表现出非线性行为，因为其实际动力学受复杂的全身运动和离散接触支配。本工作提出一种受Koopman算子理论启发的安全导航框架。我们首先通过深度强化学习训练底层运动策略，随后在高维提升空间中学习线性化动力学以捕捉其低频基础动力学特性。接着，我们的模型预测控制器（MPC）通过标准二次目标函数和提升空间中的线性动力学约束高效优化控制信号。实验证明，相较于基线方法，Koopman模型能更精确地预测双足机器人运动轨迹。我们还表明，所提出的导航框架在具有狭窄通道的密集环境中以更高的成功率实现了更强的安全性。