Robotic manipulators that are attached to mobile platforms are often used in workspaces that require the end-effector to mobilize beyond the manipulator's limited reach, such as in warehouse shelf stacking and similar applications. However, such assistive robots fall short of completing tasks that require the end-effector to be situated in a specific configuration at a critical time during the task. Traditionally, users control the mobile base to situate the arm such that the task can be completed through continuous operation. This requires an experienced operator who can predict the needed end-effector workspace, and can operate the base accordingly to maximize the likelihood of a successful task while avoiding any floor obstacles. In this work, we propose a straightforward control method that provides sufficient freedom to the end-effector to complete a task that is bound by time-dependent constraints. This is achieved by relaxing the time constraints on the mobile base trajectory in a floor space obstructed by obstacles. The trajectory of the platform is determined by sensor-assisted obstacle avoidance algorithm such that a single degree of freedom mobility can be represented through a safe obstacle-free time-independent path. The proposed control method is implemented in simulation and on physical hardware built in our labs. The simulation included a 5-DoF redundant Planar Mobile Manipulator (PMM). The hardware implementation and testing utilized a 9-DoF redundant mobile manipulator. The implementation results demonstrate the effectiveness of the control method in adjusting the mobile platform motion along its allowed obstacle-free path to enable the end-effector to follow its trajectory for task completion that would otherwise fail to complete when conventional control methods are used.