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As representative invertebrate zooplankton, jellyfish exhibit an efficient jet propulsion swimming mode that enables them to adapt to complex and ever-changing marine environments. This paper proposes a lightweight and energy-efficient bionic jellyfish robot capable of achieving high-efficiency spatial swimming and steering via asymmetric tentacles. Forward propulsion is achieved through a reciprocating cylindrical cam that swings six tentacles coated with a thick silicone membrane. Spatial steering is realized through an eccentric disc cam, which adjusts the circumferential asymmetry of the six tentacles. A compact controller based on STM32F4 is designed to receive commands wirelessly and generate the required control signals to drive three motors. Fluid simulation, integrated with a theoretical model, was performed to analyze the jet propulsion force of the jellyfish robot. The 287-g robot prototype measures 110\u00a0mm in diameter and 159\u00a0mm in height in its contraction state. It was tested under various swimming modes to verify its steering capability in three-dimensional space. Experimental results demonstrate that the bionic jellyfish robot achieves a maximum average swimming speed of 7.5\u00a0cm\/s, corresponding to 0.47 body lengths per second (BL\/s), placing its swimming efficiency among the best of existing bionic jellyfish robots. Furthermore, it exhibits remarkable maneuverability, with a maximum steering angle of 200\u00b0 and a maximum steering velocity of 22.7\u00b0\/s. 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