TO-mdiSPAs: Topology Optimization of multi-directional Soft Pneumatic Actuators

Can a density-based topology optimization framework with design-dependent pneumatic loading produce a robust multi-directional soft pneumatic actuator whose bend direction is controlled by chamber pressure combinations?

Conventional soft pneumatic actuators are mostly designed heuristically and bend in one plane, while many soft robotics tasks require complex three-dimensional maneuvers. Automating design is hard because pneumatic pressure loads depend on the evolving material layout, which creates a coupled optimization problem.

Earlier SPAs such as McKibben muscles, Suzumori multi-chamber arms, and three-chamber omnidirectional actuators rely on designer intuition. Prior topology optimization for pneumatic compliant mechanisms has used Darcy-law pressure modeling, but generally targeted single-direction or bidirectional bending or specific gripper fingers rather than robust arbitrary multi-directional actuators.

The authors optimize a symmetric half-chamber with a density-based SIMP method. They use a three-field robust formulation (blueprint/dilated/eroded) to reduce sensitivity to manufacturing tolerances, model pressure via Darcy’s law with a drainage term to localize loads at solid-void interfaces, and solve a min-max output displacement problem with MMA. The design domain is 80×320 bilinear quadrilateral elements, with blueprint volume at most 0.20 and eroded strain energy constrained to 80%. The optimized chamber is converted to CAD and patterned into ten chambers per direction (front/back/left/right), then evaluated as a three-arm gripper in Abaqus using an Ogden material model with µ1=1.57, α=2, and D1=5×10⁻⁵.

In simulation, with equal 0.150 MPa pressures in front and left channels, arm 1 tip displacement was (1.948, -15.667, 15.658) mm, matching the expected 135°/45° resultant direction. Arm 2 with only the back channel at 0.150 MPa produced (0.994, 15.820, 0.004) mm and bent 3.58° from the y-axis. In a second case with unequal pressures, arm 2 with front 0.100 MPa and right 0.150 MPa displaced to (1.131, -7.809, -15.751) mm, again following the pressure vector sum. The study reports no physical prototype and no quantitative baseline comparison.

The authors state that fabrication via additive manufacturing and experimental validation are future work. The study is purely numerical: no real-robot trials, no repeatability, no comparison against heuristic or existing optimized actuators, no reported compute cost, and no released code or manufactured part. Only two pressure cases are reported, and material and boundary conditions may simplify real-world behavior.