The design of open-loop manipulator arms with decoupled and configuration-invariant inertia tensors

A manipulator design theory for reduced dynamic complexity is presented. The kinematic structure and mass distribution of a manipulator arm are designed so that the inertia matrix in the equation of motion becomes diagonal and/or invariant for an arbitrary arm configuration. For the decoupled and invariant inertia matrix, the system can be treated as linear, single-input, single-output systems with constant parameters. As a result, the control of the manipulator arm is simplified, and, more importantly, control performance can be improved due to the reduced dynamic complexity. First, the problem of designing such an arm with the decoupled and/or configuration-invariant inertia matrix is defined. The inertia matrix is then analyzed in relation to the kinematic structure and mass properties of the arm links. Necessary conditions for the manipulator arm to possess a decoupled and/or configuration-invariant inertia matrix are obtained. Using the necessary conditions, we find the kinematic structure and mass properties for which the inertia matrix reduces to a constant, diagonal form. For 2 and 3 degree-of-freedom arms, possible arm designs for decoupled and/or invariant inertia matrices are then determined.