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This paper presents a coarse-grain parallel deoxyribonucleic acid (PDNA) algorithm for optimal configurations of an omnidirectional mobile robot with a five-link robotic arm. This efficient coarse-grain PDNA is proposed to search for the global optimum of the redundant inverse kinematics problem with minimal movement, thereby showing better population diversity and avoiding premature convergence. Moreover, the pipelined hardware implementation, hardware/software co-design, and System-on-a-Programmable-Chip (SoPC) technology on a field-programmable gate array (FPGA) chip are employed to realize the proposed PDNA in order to significantly shorten its processing time. Simulations and experimental results are conducted to illustrate the merit and superiority of the proposed FPGA-based PDNA algorithm in comparison with conventional genetic algorithms (GAs) for omnidirectional mobile robot performing fire extinguishment.