###### Abstract  
Autonomous underwater vehicles (AUVs) commonly use screw propellers to move in a water environment. However, compared to the propeller-driven AUV, bio-inspired AUVs feature a higher energy efficiency, longer lifespan (due to a lack of cavitation), and better eco-friendliness (due to lower noise, a lack of vibrations, and a weaker wake). To generate propulsion, the design of fish robots--viewed as a special case of a bio-inspired AUV--comprise multiple actuated joints. Underactuated joints have also been adopted in bio-inspired AUVs, primarily for the purpose of achieving a simpler design and more realistic and biologically plausible locomotion. In our work, we propose a limitedly underactuated posterior (tail) joint of a fish robot with the intention of achieving a higher swimming speed and better energy efficiency of the robot. The limited underactuation is achieved by allowing the joint to move freely but only within a limited angular range. The experimental results verified that, for relatively small angular ranges, the limitedly underactuated joint is superior to both fully actuated and fully underactuated joints in that it results in faster and more energy-efficient locomotion of the fish robot.  
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time-consuming phase of the evolution--the fitness trials [3; 12; 13]. However, in all of our previous efforts, we focused on a fully actuated robot, as an eventual underactuation was beyond the scope of our research. Unlike actuated joints, underactuated joints are not actuated by servo motors and are fully free to move depending on the environmental conditions.  
Conversely, in our current work, we intend to explore the possibility of optimizing the performance (e.g., speed, and energy efficiency) of the robot by enhancing its _morphology_ (rather than control) and, specifically, by adopting a _limited underactuated_ posterior (tail) joint as a special case of underactuation.  
The primary inspiration of our research is fueled by our understanding of the dynamics of fish undulation. We assume that, during a single undulation, the thrust is mainly generated by the movement of the posterior segment (tail fin) of the bot. Moreover, such generation occurs during the initial phase of the undulation while, in the remaining undulation, the fin inflicts a certain amount of hydrodynamic drag as it moves against the flow of the surrounding water. Based on such decomposition of the undulation into thrusting and braking phases, we speculate that a limited underactuation of the posterior (tail) joint would enhance the effect of the thrusting phase while, at the same time, it would also diminish the effect of braking. We introduce the notion of _limited underactuation_ for the (posterior) joint that is allowed to move freely, but only within a limited angular range. Such a joint could be seen as a specific case--yet with different characteristics--of a flexing tail fin [14].  
To the best of our knowledge, we are not aware of any previous research dedicated to the enhancement of the performance of fish robots via underactuation. Indeed, full underactuation has been proposed so far solely for the sake of simplicity, realism, and biological plausibility [5; 9]. Underactuated joints seem to be the solution for environment-dependent joints; however, compared to fully actuated joints, these kinds of joints do not yield a better thrust and do not result in a faster speed and (or) better energy efficiency of the bot.  
The remainder of this paper is structured as follows. In the next section, we elaborate on the proposed concept of limited underactuation and why we believe it should have a positive effect on the speed and energy efficiency of the robot. In the same section, we introduce the experimental setup. In Section 3, we present the experimental results that verify the beneficial effect of limited underactuation of the speed and energy efficiency of the fishbot. In Section 4, we discuss some limitations of the proposed approach. Section 5 draws a conclusion.