Mobile manipulators require whole-body inverse kinematics (IK), encompassing both the mobile base and arm, to execute manipulation tasks. One of the challenges associated with whole-body IK is the redundancy of degrees of freedom when combining those of the mobile base and arm, which generates an infinite number of solutions. Therefore, in this study, we focus on the trend in mobile manipulators where the positional precision of the mobile base is lower than that of the manipulator. We propose a definition for the robustness value to base position control error and discuss a methodology to quickly obtain robust whole-body IK solutions. In an assessment utilizing a dataset that simulates domestic environments and a human support robot, which is a research platform for mobile manipulators designed to operate with humans, we validated that the quick acquisition of IK solutions robust to base position control error is achievable. In addition, we integrated the proposed IK approach into motion planning and evaluated its performance. Our results revealed that motion planning integrated with the proposed IK approach was superior to conventional methods in terms of both computation time and robustness for base position control error.