  In many bi-manual robotic tasks, like peg-in-a-hole assembly, the success of
the task execution depends on the error in achieving the desired relative pose
between the peg and the hole in a pre-insertion configuration. Random actuation
errors in the joint space usually prevent the two arms from reaching their
desired task space poses, which in turn results in a random error in relative
pose between the two hands. This random error varies from trial to trial, and
thus depending on the tolerance between the peg and the hole, the outcome of
the assembly task may be random (sometimes the task execution succeeds and
sometimes it fails). In general, since the relative pose has $6$
degrees-of-freedom, there are infinite numbers of joint space solutions for the
two arms that correspond to the same task space relative pose. However, in the
presence of actuation errors, the joint space solutions are not all identical
since they map the joint space error sets differently to the task space. Thus,
the goal of this paper is to develop a methodical approach to compute a joint
space solution such that the maximum task space error is below a (specified)
threshold with high probability. Such a solution is called a robust inverse
kinematics solution for the bi-manual robot. Our proposed method also allows
the robot to self-evaluate whether it can perform a given bi-manual task
reliably. We use a square peg-in-a-hole assembly scenario on the dual-arm
Baxter robot for numerical simulations that shows the utility of our approach.
