Uncontrolled Manifold Reference Feedback Control of Multi-Joint Robot Arms

Shunta Togo, Takahiro Kagawa, Yoji Uno

The brain must coordinate with redundant bodies to perform motion tasks. The aim of the present study is to propose a novel control model that predicts the characteristics of human joint coordination at a behavioral level. To evaluate the joint coordination, an uncontrolled manifold (UCM) analysis that focuses on the trial-to-trial variance of joints has been proposed. The UCM is a nonlinear manifold associated with redundant kinematics. In this study, we directly applied the notion of the UCM to our proposed control model called the "UCM reference feedback control." To simplify the problem, the present study considered how the redundant joints were controlled to regulate a given target hand position. We considered a conventional method that pre-determined a unique target joint trajectory by inverse kinematics or any other optimization method. In contrast, our proposed control method generates a UCM as a control target at each time step. The target UCM is a subspace of joint angles whose variability does not affect the hand position. The joint combination in the target UCM is then selected so as to minimize the cost function, which consisted of the joint torque and torque change. To examine whether the proposed method could reproduce human-like joint coordination, we conducted simulation and measurement experiments. In the simulation experiments, a three-link arm with a shoulder, elbow, and wrist regulates a one-dimensional target of a hand through proposed method. In the measurement experiments, subjects performed a one-dimensional target-tracking task. The kinematics, dynamics, and joint coordination were quantitatively compared with the simulation data of the proposed method. As a result, the UCM reference feedback control could quantitatively reproduce the difference of the mean value for the end hand position between the initial postures, the peaks of the bell-shape tangential hand velocity, the sum of the squared torque, the mean value for the torque change, the variance components, and the index of synergy as well as the human subjects. We concluded that UCM reference feedback control can reproduce human-like joint coordination. The inference for motor control of the human central nervous system based on the proposed method was discussed.