**3. Bio-inspired robots with SMA muscle-like actuation**

The use of SMAs as artificial muscles allows for more realistic bio-inspired actuation presented in nature [26]. SMA wires acting as muscle fibers can respond upon electrical signals, taking advantage of the large pull force and its excellent strength-weight tradeoff. Currently, the use of SMAs in biomimetic robotic systems [3],[13],[9] can be found in ground, water and air robots, in many sizes, including those micro-robots or microstructures [25],[78],[53],[35],[63],[82],[37],[37]. In the following sections, we describe the most representative bio-inspired robots and structures that integrate SMAs as muscle-like actuation mechanisms.

### **3.1. Water**

Biologically inspired robots that operate in water can be found in two categories. Firstly, robots that use SMAs for actuating appendices (fins), and secondly, robots that use SMAs to actuate the robot's body. In the latter body actuation is used for undulatory motion (fish-like robots). Some animals can move by bending their body in such a way to produce a backward-propagating propulsive wave. The movement obtained by bending a continuous structure is much more natural than others where joints are presented. In Section 4.2 our bending structure prototype is presented.

#### *3.1.1. A micro-robot fish with embedded SMA wire actuated by flexible biomimetic fin*

In [78] it has been proposed a micro robot fish that uses a flexible biomimetic fin propeller with embedded SMA wires to mimic the musculature and flexible bending of squid fin. The propulsion consists of an active component (the biomimetic fin) and a passive component (the caudal fin). The biomimetic fin-based propulsion mechanism is an actuator that combines the SMA wire and an elastic substrate.

This micro-robot fish introduces a new concept in the world of biomimetic robotics due to its ability to swim noiseless. This means the robot avoid the use of any traditional components like gears, bearings and joints, only using the SMAs as actuators that produce the propulsion. The robot is able to achieve a swimming speed of 112*mm*/*s* when the SMAs actuate at 2.1*Hz* (contracting upon electrical heating), and a minimum turning radius of 136*mm*, which makes the robot the fastest micro robot-fish compared to other prototypes that use IPMCs like actuators [14],[54],[33]. The authors have measured the robot performance based on the Strouhal number [15], [24], which typically varies between 0.25 to 0.35 for the biological counterparts. Their robot has a Strouhal number of 0.58 (at maximum swimming speed). This upper value highlights the optimal movement of the robot, however, high amounts of input power have been required to actuate the SMAs.
