1. Introduction
With rapid advancements in unmanned underwater vehicles (UUVs), a variety of propulsion systems are emerging for specific applications, including marine resource exploration, underwater structure inspection, environmental monitoring, etc. [
1,
2]. To conduct surveillance or marine biologic studies, biomimetic propulsion techniques are preferred, as they are relatively quiet, energy efficient and flexible in operation [
3]. However, the classic rear propeller and control surface (rudder) architectures still dominate the propulsion systems of autonomous underwater vehicles (AUVs) for achieving high speeds at long-range cruising. In particular, the commercial AUVs of torpedo shapes, such as the RTsys COMET 300 [
4], WHOI REMUS-600 [
5] and KONGSBERG HUGIN [
6], play an important role in the fields of seabed mapping and search and rescue. This type of propulsion may result in low maneuverability because the control surfaces or rudders are incapable of generating sufficient torques when AUVs are operating at low speeds. Therefore, some researchers have developed over-actuated AUVs with redundant fixed propellers to realize full holonomic propulsion [
7,
8], while others focus on designing vectored thrusters [
9] that can reorient the thrust vectors in more than one degree of freedom (DOF), making the underwater vehicles highly maneuverable with fewer thrusters.
Considering the pros and cons of the propulsion systems introduced above, hybrid propulsion-based underwater vehicles have been proposed, which combine different propulsion systems to improve the vehicle’s performance in terms of motion pattern, speed or whatever is required. For example, a thermal-electric hybrid propulsion underwater glider was proposed in [
10] due to the abundant storage of thermal energy in the ocean. The hybrid propulsion integrates both thermal propulsion and electric propulsion to drive the buoyancy systems for long endurance. To improve the performance of underwater tasks, a bio-inspired hybrid propulsion underwater robotic vehicle (HPURV) was conceptually designed as far as the minimum energy consumption in ocean observations is concerned [
11]. The HPURV consists of a caudal fin, a pair of pectoral fins, a pitch-roll moving mass mechanism, and a dual buoyancy controlling module, allowing flexible operation strategies by combining any two propulsion modes. Also, through bio-inspired propulsion, Guo et al. presented a micro underwater robot with hybrid propulsion of a 3-DOF fishtail and a pair of 1-DOF propellers [
12]. This hybrid propulsion has a lot of advantages in the cruise and tracking motion modes, respectively. In addition, underwater robots sometimes need to move fast but sometimes need to maintain a low speed and low noise in a complex environment. These task requirements motivated Gu et al. to develop a hybrid propulsion system with an integrated waterjet and propeller for the spherical underwater robot (SUR IV) [
13]. Compared to a single waterjet thruster, the propeller generates powerful thrust but high noise, while the hybrid propulsion system provides the alternative of switching between the propeller, waterjet and hybrid modes for different motion control. Based on the above multiple propulsion modes, Li and Guo further introduced an adaptive multi-mode switching strategy for the SUR IV to achieve a smooth and stable mode of transition in the marine environment during operation [
14].
Although a number of propulsion techniques along with propulsion modes have been extensively discussed, motion stability and accuracy, in terms of the robot trajectory tracking issue, remain challenging due to the model uncertainties and the unknown disturbances in the underwater environment. The recent control architectures are classified and summarized in [
15,
16]. To simplify the complexity of the controller, the work in [
17,
18] decoupled the underwater robot dynamic model and utilized the sliding mode control (SMC) to realize trajectory tracking but only in the horizontal plane, although the tracking tasks typically require AUVs to follow the time-parameterized path in 3D space. Based on the reduced 4-DOF kinematic and dynamic models, Karkoub et al. proposed a hierarchical nonlinear controller that employed the backstepping method and SMC to achieve asymptotic tracking performance [
19]. To make tracking controllers less dependent on the accurate AUV model, a 6-DOF adaptive controller was presented for an underactuated AUV in the presence of parameter uncertainties [
20]. Using Lyapunov’s direct method and backstepping method, the simulations prove that the adaptive nonlinear controller provides an asymptotic convergence of position and orientation tracking errors. For the fast convergence of adaption in working environmental disturbances, Wadi et al. devised a conditional adaptation law to tune the gains of kinematic and dynamic controllers in two ways: adaptive proportional control and universal adaptive stabilization-based control [
21]. Moreover, intelligent methods, including fuzzy control [
22], model predictive control [
23], and reinforcement learning-based control [
24], are combined with other control methods to improve the performance of trajectory tracking, taking into account complicated models, environments and system constraints.
Despite the above advance of trajectory control and some other high-level controls related to station-keeping [
25] or position-attitude [
26], harsh and hostile environments require underwater robots to be equipped with a flexible propulsion system to adapt to complicated marine situations or missions. Specifically, propeller-driven underwater robots are superior in speed and maneuverability when traveling in open water. However, they are not suitable for conducting underwater inspections in cluttered or confined environments, as spinning propellers carry the risk of becoming tangled, stuck or damaging wildlife when close interactions are necessary. Meanwhile, low-speed maneuvers are also essential for robots operating in narrow spaces. In this case, if the propeller-driven underwater robot is also available to employ a waterjet-based thruster, the hybrid propulsion mode of the propeller and waterjet provides the underwater robot with a promising way to meet high demands in terms of adaptivity to the underwater environment, maneuvering capability as well as thruster failure.
The above rationale inspires the hybrid propulsion-based underwater robot in
Figure 1. The main contributions are: (1) An underwater robot is conceptually designed with a multibody structure, equipped with a Coanda-effect jet thruster and a pair of propeller-based reconfigurable magnetic-coupling thrusters, which can work together or actuate each son robot independently after separation. (2) To track any smooth 3D trajectories, a planar motion mechanism (PMM)-based CFD simulation is performed to estimate the hydrodynamic coefficients, while a double-loop trajectory tracking control architecture is established, which consists of a Lyapunov-based outer-loop kinematic control and an inner-loop dynamic control using the full-state feedback L1-adaptive control to ensure fast adaption with guaranteed robustness. (3) The simulation results validate the good tracking performance despite the time-varying parameters in the model and the external unknown disturbance, even for separated son robots. This paper is organized as follows:
Section 2 not only presents the hybrid propulsion-actuated underwater robot but also describes its simplified model and a CFD simulation technique to estimate the hydrodynamic coefficients.
Section 3 establishes a double-loop control architecture of trajectory tracking. Finally, we illustrate the simulations of the underwater robot trajectory tracking under three different scenarios in
Section 4, and we summarize the paper in
Section 5.