In this work we present the design of a swimming robot that is inspired by the body shape modulation of small microorganisms. Amoebas are small single celled organisms that locomote through deformation and shape change of their body. To achieve similar shape modulation for swimming propulsion in a robot we developed a novel flexible appendage using tape springs. A tape spring is an elongated strip of metal with a curved cross-section that can act as a stiff structure when loaded against the curvature, while it can easily buckle when loaded with the curvature. We develop a tape spring appendage that is capable of freely deforming its perimeter through two actuation inputs. In the first portion of this paper we develop the kinematics of the appendage mechanisms and compare with experiment. Next we present the design of a surface locomoting robot that uses two appendages for propulsion. From the appendage kinematics we derive the local connection vector field for locomotion kinematics and study the optimal gait for forward swimming. Lastly, we demonstrate robot swimming performance in open water conditions. The novel appendage design in this robot is advantageous because it enables omnidirectional movement, the appendages will not tangle in debris, and they are robust to collisions and contact with structures.

Isolated mechanical systems—e.g., those floating in space, in free-fall, or on a frictionless surface—are able to achieve net rotation by cyclically changing their shape, even if they have no net angular momentum. Similarly, swimmers immersed in “perfect fluids” are able to use cyclic shape changes to both translate and rotate even if the swimmer-fluid system has no net linear or angular momentum. Finally, systems fully constrained by direct nonholonomic constraints (e.g., passive wheels) can push against these constraints to move through the world. Previous work has demonstrated that the displacement induced by these shape changes corresponds to the amount ofconstraint curvaturethat the gaits enclose. Properly assessing or optimizing the utility of a gait also requires considering the time or resources required to execute it: A gait that produces a small displacement per cycle, but that can be executed in a short time, may produce a faster average velocity than a gait that produces more displacement, but takes longer to complete a cycle at the same instantaneous effort. In this paper, we consider gaits under two instantaneous measures of effort. For each of these costs, we demonstrate that fixing the average instantaneous cost to a unit value allows us to transform the effort costs into time-to-execute costs for any given gait cycle. We then illustrate how the interaction between the constraint curvature and these costs leads to characteristic geometries for optimal cycles, in which the gait trajectories resemble elastic hoops distended from within by internal pressures.