Principle of superposition in design of feedback control signals for dexterous multi-fingered robot hands

Concerns the skilled motions of a multifingered hand with soft fingertips in dexterous tasks, based on human ability. As an elementary example, dynamics of punching an object by means of two multi-DOF robot fingers with soft and deformable tips are derived and analyzed. It is shown that passivity analysis leads to effective design of a feedback control signal that realizes dynamic stable pinching, regardless of a complicated nonlinear structure of motion equation of the overall system in which extra terms of Lagrange's multipliers arise for holonomic constraints of tight area-contacts between finger-tips and object surfaces. It is shown that a principle of linear superposition is applicable to design of additional feedback signals for controlling both the posture (rotational angle) and the position (some of task coordinates of the mass center) of the object under the condition of unique stationary resolution of the controlled position-state variables. It is finally claimed that complexity of learning such an over-all skilled motion of pinching an object stably and controlling it at a prescribed posture and position can be drastically reduced from exponential order to linear order of the sum of complexities of learning each resolved from exponential order to linear order of the sum of complexities of learning each resolver motion separately, correspondingly to 1) stable pinching, 2) specification of the rotational angle for the object, and 3) that of some of position coordinates.