Human-like movements of robotic arms with redundant DOFs: virtual spring-damper hypothesis to tackle the Bernstein problem

A natural control method for resolving the ill-posedness of inverse kinematics of multi-joint reaching movements under redundancy of degrees-of-freedom (DOF) is proposed, which need neither introduce any artificial performance index to determine the inverse kinematics uniquely nor calculate the pseudo-inverse of the Jacobian of task coordinates with respect to joint coordinates. The control signal is composed of a linear superposition of three terms 1) damping shaping, 2) task-space position-error feedback with a single stiffness parameter, and 3) gravity compensation by means of estimation of uncertainty in the potential energy. It is shown through computer simulation and theoretical analysis that the signal can generate smooth reaching motions provided that a set of damping factors and the stiffness parameter are selected in a synergistic way. A physical meaning of each term of the control signal is discussed from the viewpoints of Newtonian mechanics and neuro-physiology. It can be concluded from those illustrative examples that mechanical robots with redundant DOFs can be endowed by synergistic adjustments of damping factors and a stiffness parameter with ability of generating human-like skilled motions