Meaningful Centroidal Frame Orientation of Multi-body Floating Locomotion Systems

In this paper, we propose a meaningful definition of rotational centroidal orientation which is somewhat missed in the state-of-the-art centroidal momentum and dynamics theory for locomotion robots with one floating base. This centroidal instantaneous orientation rotates as the robot runs, and it is extracted from the total system angular inertia. The new centroidal frame is proposed to be parallel with the principal axes of the centroidal angular inertia, which can describe the whole-robot rotational motion. To avoid high fluctuations of centroidal frame orientation parameters between adjacent control loops, we develop one algorithm to enable the centroidal instantaneous frame to be smooth. The relationship between the centroidal angle rate and the centroidal angular velocity is derived, as well as the relationship in the acceleration level, which can be used for whole-body torque control. The new centroidal orientation or Euler angle is verified by two-scenario simulations, and another scenario is used to track and control the centroidal angular motion in the first-order kinematics level. The idea has considerable potential for system design, motion generation, and torque control in robotics communities with different research topics and theoretical backgrounds.