In this paper, we introduce a novel approach to centroidal state estimation, which plays a crucial role in predictive model-based control strategies for dynamic legged locomotion. Our approach uses the Koopman operator theory to transform the robot's complex nonlinear dynamics into a linear system, by employing dynamic mode decomposition and deep learning for model construction. We evaluate both models on their linearization accuracy and capability to capture both fast and slow dynamic system responses. We then select the most suitable model for estimation purposes, and integrate it within a moving horizon estimator. This estimator is formulated as a convex quadratic program, to facilitate robust, real-time centroidal state estimation. Through extensive simulation experiments on a quadruped robot executing various dynamic gaits, our data-driven framework outperforms conventional filtering techniques based on nonlinear dynamics. Our estimator addresses challenges posed by force/torque measurement noise in highly dynamic motions and accurately recovers the centroidal states, demonstrating the adaptability and effectiveness of the Koopman-based linear representation for complex locomotive behaviors. Importantly, our model based on dynamic mode decomposition, trained with two locomotion patterns (trot and jump), successfully estimates the centroidal states for a different motion (bound) without retraining.

翻译：本文提出一种新颖的质心状态估计方法，该方法在动态足式运动的预测模型控制策略中具有关键作用。我们利用Koopman算子理论，通过动态模态分解和深度学习构建模型，将机器人复杂的非线性动力学转化为线性系统。针对两种模型，我们评估了其线性化精度以及对快慢动态系统响应的捕捉能力。随后，选取最适合估计任务的模型，并将其集成至移动时域估计器中。该估计器被构造为凸二次规划问题，以实现鲁棒、实时的质心状态估计。通过在四足机器人执行多种动态步态的大量仿真实验，我们的数据驱动框架优于基于非线性动力学的传统滤波技术。该估计器能有效应对高动态运动中力/力矩测量噪声带来的挑战，并准确恢复质心状态，充分展现了基于Koopman的线性表示对复杂运动行为的适应性与有效性。值得注意的是，基于动态模态分解的模型仅通过两种运动模式（小跑和跳跃）训练，即可在无需重新训练的情况下，成功估计出另一种不同运动（跳跃）的质心状态。