  Robotic tasks, like reaching a pre-grasp configuration, are specified in the
end effector space or task space, whereas, robot motion is controlled in joint
space. Because of inherent actuation errors in joint space, robots cannot
achieve desired configurations in task space exactly. Furthermore, different
inverse kinematics (IK) solutions map joint space error set to task space
differently. Thus for a given task with a prescribed error tolerance, all IK
solutions will not be guaranteed to successfully execute the task. Any IK
solution that is guaranteed to execute a task (possibly with high probability)
irrespective of the realization of the joint space error is called a robust IK
solution. In this paper we formulate and solve the robust inverse kinematics
problem for redundant manipulators with actuation uncertainties (errors). We
also present simulation and experimental results on a $7$-DoF redundant
manipulator for two applications, namely, a pre-grasp positioning and a
pre-insertion positioning scenario. Our results show that the robust IK
solutions result in higher success rates and also allows the robot to
self-evaluate how successful it might be in any application scenario.
