  This paper presents the VLEIBot^* (Very Little Eel-Inspired roBot), a
45-mg/23-mm^3 microrobotic swimmer that is propelled by a bioinspired
anguilliform propulsor. The propulsor is excited by a single 6-mg
high-work-density (HWD) microactuator and undulates periodically due to wave
propagation phenomena generated by fluid-structure interaction (FSI) during
swimming. The microactuator is composed of a carbon-fiber beam, which functions
as a leaf spring, and shape-memory alloy (SMA) wires, which deform cyclically
when excited periodically using Joule heating. The VLEIBot can swim at speeds
as high as 15.1mm * s^{-1} (0.33 Bl * s^{-1}}) when driven with a
heuristically-optimized propulsor. To improve maneuverability, we evolved the
VLEIBot design into the 90-mg/47-mm^3 VLEIBot^+, which is driven by two
propulsors and fully controllable in the two-dimensional (2D) space. The
VLEIBot^+ can swim at speeds as high as 16.1mm * s^{-1} (0.35 Bl * s^{-1}),
when driven with heuristically-optimized propulsors, and achieves turning rates
as high as 0.28 rad * s^{-1}, when tracking path references. The measured
root-mean-square (RMS) values of the tracking errors are as low as 4 mm.
