Koopman Operator Based Linear Model Predictive Control for Quadruped Trotting

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.