In this paper a new concept, named the
Extended Operational Space (EXOS), has been proposed for the effective
analysis and the real-time control of the robot manipulators with
kinematic redundancy. The EXOS consists of the operational space (OS)
and the optimal null space (NS): the operational space is
used to describe manipulator end-effector motion; whereas the optimal null
space, described by the minimum number of NS vectors, is
used to express the self motion.Based upon the EXOS formulation,
the kinematics, statics, and dynamics of redundant manipulators have been
analyzed, and control laws based on the dynamics have been
proposed. The inclusion of only the minimum number of NS
vectors has changed the resulting dynamic equations into a very
compact form, yet comprehensive enough to describe: not only the
dynamic behavior or the end effector, but also that of
the self motion; and at the same time the interaction
of these two motions. The comprehensiveness is highlighted by the
demonstration of the dynamic couplings between OS dynamics and NS
dynamics, which are quite elusive in other approaches.Using the proposed
dynamic controls, one can optimize a performance measure while tracking
a desired end-effector trajectory with a better computational efficiency than
the conventional methods. The effectiveness of the proposed method has
been demonstrated by simulations and experiments.
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