This paper presents a geometric gait design and optimization framework for an idealized model of a planar starfish-inspired robot with curvature-controlled soft actuator arms. We describe the range of motion for each arm under the assumption of constant curvature along the length. Two modes of attachment of the ends of the arms to the ground are considered: fixed in position and orientation, and fixed in position but free to rotate. For each mode, we derive mathematical expressions for the local connection relating controlled shape changes to the displacement of the robot’s center. For the rotating case, we additionally model the individual arms as ideal elastica beams and design gaits based on expected buckling behavior for a special case of symmetric (mirrored) curvature inputs via numerical simulations.

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