A learning control method and an adaptive control method are proposed for coordinated control of multiple manipulators even when position of the mass center of a target object is unknown. Proposed methods can achieve exact tracking of any desired trajectories of each joint of the manipulators and so-called “internal force” which does not affect motion of the object.
Firstly, it is shown that dynamics of whole coordinated control system composed of multiple manipulators and a target object can be regarded as a dynamics of a single manipulator moving under geometric constraints in the joint-angle coordinate system. This implies that control of both the trajectory of the object and the internal force is regarded as that of both the joint angle trajectory and the contact force of a geometrically constrained manipulator. In addition to this, based on the passivity property of the dynamics and the orthogonality between the joint torque caused by the internal force and the joint angle velocity, conventional methods of learning control and model-based adaptive control for a geometrically constrained manipulator are extended to coordinated control of multiple manipulators in the joint coordinate system.
Effectiveness of the proposed methods is illustrated by computer simulation results based on a dynamics model of coordinating two 3-DOF manipulators.