Soft pneumatic actuators (SPAs) are highly promising and have been extensively explored within the field of soft robotics. Under pneumatic pressure loads, an SPA undergoes bending deformation to perform specific tasks. A multi- or omni-directional SPA can bend and move in any direction within a 3D space, leveraging its multiple degrees of freedom to realize various mechanical functions. This work presents a systematic methodology using topology optimization (TO) to achieve an optimized design for a multi-directional SPAs. To ensure manufacturing robustness, a three-field TO formulation considering blueprint, dilated, and eroded designs is implemented. Additionally, Darcy's law, incorporating a drainage term, is used to model the design-dependent nature of the pneumatic loading. A min-max optimization problem is formulated based on the target output deformations of the SPA unit and solved using the Method of Moving Asymptotes. The optimization yields a high-performing, unconventional geometric design. Finally, numerical simulations demonstrate that the optimized SPA successfully achieves versatile multi-directional movements.

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