  Coordinated dual-arm manipulation tasks can be broadly characterized as
possessing absolute and relative motion components. Relative motion tasks, in
particular, are inherently redundant in the way they can be distributed between
end-effectors. In this work, we analyse cooperative manipulation in terms of
the asymmetric resolution of relative motion tasks. We discuss how existing
approaches enable the asymmetric execution of a relative motion task, and show
how an asymmetric relative motion space can be defined. We leverage this result
to propose an extended relative Jacobian to model the cooperative system, which
allows a user to set a concrete degree of asymmetry in the task execution. This
is achieved without the need for prescribing an absolute motion target.
Instead, the absolute motion remains available as a functional redundancy to
the system. We illustrate the properties of our proposed Jacobian through
numerical simulations of a novel differential Inverse Kinematics algorithm.
