  In this paper, we investigate the task-space consensus problem for multiple
robotic systems with both the uncertain kinematics and dynamics and address two
main issues, i.e., the separation of the kinematic and dynamic loops in the
case of no task-space velocity measurement and the quantification of the
manipulability of the system. We propose an observer-based adaptive controller
to achieve the manipulable consensus without relying on the measurement of
task-space velocities, and also formalize the concept of manipulability to
quantify the degree of adjustability of the consensus value. The proposed
adaptive controller employs a new distributed observer that does not rely on
the joint velocity and a new kinematic parameter adaptation law with a
distributed adaptive kinematic regressor matrix that is driven by both the
observation and consensus errors. In addition, it is shown that the proposed
controller has the separation property, which yields an adaptive kinematic
controller that is applicable to most industrial/commercial robots. The
performance of the proposed observer-based adaptive schemes is shown by
numerical simulations.
