A Simple Control Method Coping with a Kinematically Ill-posed Inverse Problem of Redundant Robots: Analysis in Case of a Handwriting Robot

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 manipulators and multi-fingered hands. Associated with such DOF redundancy 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 arising of an ill-posed problem of inverse kinematics from the task space to the joint space. This paper treats a handwriting robot as an illustrative example and shows that such an ill-posedness of DOF redundancy can be resolved in a natural way by using a novel concept named “stability on a manifold”. It is shown theoretically that sensory feedback signals with a simpler form computed on the basis of measurement data of task-description variables render the closed-loop dynamics to converge asymptotically to a target task-description lying on a lower-dimensional manifold of steady states. Computer simulation concerning specified robot tasks verifies the effectiveness of the proposed control scheme, which results in human-like distribution of joint motions.