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Automated particle transport using optical tweezers requires the use of motion planning to move the particle while avoiding collisions with randomly moving obstacles. This paper describes a stochastic dynamic programming based motion planning framework developed by modifying the discrete version of an infinite-horizon partially observable Markov decision process algorithm. Sample trajectories generated by this algorithm are presented to highlight effectiveness in crowded scenes and flexibility. The algorithm is tested using silica beads in a holographic tweezer set-up and data obtained from the physical experiments are reported to validate various aspects of the planning simulation framework. This framework is then used to evaluate the performance of the algorithm under a variety of operating conditions.