Natural resolution of DOF redundancy in execution of robot tasks under the gravity: a challenge to Bernstein´s problem and applications to handwriting robots

In order to enhance dexterity in execution of robot tasks, a redundant number of degrees-of-freedom (DOF) is adopted for design of robotic mechanisms like robot arms and multi-fingered robot hands. Associated with such redundancy in DOFs relative to the number of physical variables necessary and sufficient for description of a given task, an extra performance index is introduced for controlling such a redundant robot in order to avoid ill-posedness of inverse kinematics from task space to joint space. This paper shows that such ill-posedness of DOF redundancy can be resolved in a natural way without introducing any artificial performance index or calculating any pseudo-inverse. Instead, a sensory feedback composed with a term of task space position feedback and another term of adequate joint dampings together with gravity compensation based on estimates on unknown parameters is shown to be in effect to carry out the target task without incurring self-motion