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Heavy object manipulation by wheeled mobile manipulators may lead to serious consequences such as postural instability, and this necessitates dynamically stable planning based on systematic analysis to better predict and eliminate the possibility of toppling down. In the present study, stable motion planning is investigated for wheeled mobile manipulators during heavy object manipulation tasks. It is assumed that the initial and final poses of a heavy payload are specified. Based on these known postures of the payload two proper configurations for robotic system is defined. Then, between these two initial and final poses, appropriate trajectories for multiple robotic arms relative to the moving base are planned without considering the postural stability of the system. Next, motion of the moving base is planned so that the stability of the overall system is guaranteed while its predetermined initial and final positions and velocities are fulfilled. To this end, the problem of stable planning is solved as an optimization problem. A proper cost function is considered, to be minimized, which is a measure of the control effort to be used for the platform motion. Moreover, using the new dynamic postural Moment-Height Stability (MHS) measure, a constraint denoting the system dynamic stability is derived and satisfied. The proposed planning approach is applied to move a heavy object with a wheeled robotic system that consists of two manipulators, where the obtained results reveal a stable optimal motion besides satisfaction of various practical aspects.