A biological organism, such as an octopus tentacle or elephant trunk, exhibits complex 3D spatial trajectories. Although soft manipulators showing 2D in-plane deformations have been extensively studied and applied in many areas, the design method of soft manipulators with a mathematical model that can follow a particular 3D spatial trajectory remains elusive. In this paper, we present a methodology to automatically design bio-inspired multi-segment pneu-net soft manipulators that can match complex 3D trajectories upon single pressurization. The 3D motions can be characterized by a combination of twisting, bending, and helical deformations, which are enabled by the design of the soft segments with programmable chamber orientations. To inverse design the soft manipulators with trajectory matching, we develop an analytical framework that takes into account the material nonlinearity, geometric anisotropy, and varying loading directions. The spatial trajectory can be reconstructed by combining with a 3D rod theory. In this sense, multi-segment soft manipulators with trajectory matching are inversely designed by varying the geometric and material parameters. We further demonstrate the grasping of complex objects using the designed soft manipulators. The proposed methodology has immense potential to design soft manipulators in 3D space and broaden their application.
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