A Mobile Cable-Driven Parallel Robot (MCDPR) is composed of a classical Cable-Driven Parallel Robot (CDPR) carried by multiple mobile bases. The additional mobilities due the motion of the mobile bases allow such systems to autonomously modify their geometric architecture, and thus make them suitable for multiple manipulation tasks in constrained environments. Moreover, these additional mobilities mean MCDPRs are kinematically redundant and may use this redundancy to optimize secondary task criteria. However, the high dimensional state space and closed chain constraints add complexity to the motion planning problem. To overcome this, we propose a method for trajectory planning for MCDPRs performing pick and place operations in cluttered environments by using direct transcription optimization. Two different scenarios have been considered and their results are validated using a dynamic simulation software (V-REP) and experimentally.