用柯普曼算子建模四足机器人，实现高精度实时运动控制。
Koopman Operator Based Linear Model Predictive Control for Quadruped Trotting
- 基于柯普曼算子在高维空间构建线性模型，保留系统非线性特征。
- 在四足机器人上实现精准轨迹跟踪与抗干扰能力，提升控制精度。
- 首次将柯普曼算子用于四足步态的在线最优控制，适合机器人控制研究者。
四足机器人的在线最优控制可使其实时适应变化的输入与环境。常用方法为线性模型预测控制（LMPC），即在有限时域内通过线性化运动方程构建带二次代价和线性约束的二次规划（QP）问题并实时求解。然而，模型线性化可能导致模型失真。本文利用柯普曼算子在高维空间中构建四足系统的线性模型，保持运动方程的非线性特性。结合LMPC，在四足机器人上实现了高保真轨迹跟踪与扰动抑制。这是首个将柯普曼算子理论应用于四足步态LMPC的研究。
原文摘要 · Abstract (English)
Online optimal control of quadruped robots would enable them to adapt to varying inputs and changing conditions in real time. A common way of achieving this is linear model predictive control (LMPC), where a quadratic programming (QP) problem is formulated over a finite horizon with a quadratic cost and linear constraints obtained by linearizing the equations of motion and solved on the fly. However, the model linearization may lead to model inaccuracies. In this paper, we use the Koopman operator to create a linear model of the quadrupedal system in high dimensional space which preserves the nonlinearity of the equations of motion. Then using LMPC, we demonstrate high fidelity tracking and disturbance rejection on a quadrupedal robot. This is the first work that uses the Koopman operator theory for LMPC of quadrupedal locomotion.
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