Evaluation models and criteria of motion performance for underwater gliders

Highlights

• The evaluation models of motion performance of UGs are established.

• The evaluation criteria of motion performance of UGs are proposed.

• The motion preformation for a UG is analyzed using the proposed evaluation models.

• The effects of seawater depth on the motion performance of the UG are studied.

• The analysis of motion performance of the UG is verified by sea trials.

Abstract

The motion performance of underwater gliders (UGs) is an important basis for their preliminary design. Because of their unique buoyancy-driven mode, the UGs differ greatly in dynamic model and working principle from the propeller-driven underwater vehicles, such as submarines, torpedoes and autonomous underwater vehicles (AUVs). Therefore, it's inadvisable to use the evaluation models and criteria of motion performance for the latters, which are established on the basis of their dynamic models, to evaluate the performance of UGs. There is a lack of applicable evaluation models and criteria to motion performance of UGs. In addition, as the effects of seawater depth on UGs are generally neglected in the dynamic model, its effects on the motion performance of UGs still need to be investigated further. In this paper, based on an established applicable dynamic model and evaluation models (the free perturbation and maneuverability equations) in the vertical plane, the applicable evaluation criteria are derived and the characteristics of motion performance of UGs under the effects of seawater depth variation are investigated. The results show that, the evaluation models and criteria of motion performance for the buoyancy-driven UGs show significant difference from those for the propeller-driven underwater vehicles. As velocity of the UG is affected by seawater depth variation, its dynamic stability is also affected obviously. With the increasing seawater depth, its dynamic stability becomes stronger, and its change rate of surfacing speed (maneuverability) increases obviously with seawater depth. The present work enriches motion performance theory of UGs, and provides valuable guidance for their applications in the deep-sea region.

Introduction

The ocean stores abundant natural and fish resources, which provides a solution for the energy crisis on land. The special marine environment makes it difficult to collect the oceanic data. To fully utilize and understand the ocean, some effective tools have been developed to aid the researchers, such as autonomous underwater vehicles (AUVs), remotely operated vehicles (ROVs) and underwater gliders (UGs). The unique features of UGs, including low consumption, low cost and long range, make more oceanic researches possible and realizable, such as the explorations of typhoon [1], [2], iceberg [3], [4], [5], and eddy [6], [7], [8].

UGs are novel tools to advance our understanding of the ocean. After their concept was first proposed by Stommel in 1993 [9], the design technology and application of UGs are rapidly developed. The early UGs are purely driven by buoyancy and some famous representatives are Slocum, Spray and Seaglider [10], [11], [12]. The gliding range of these UGs could satisfy the common engineering applications. However, to break through the limitations of purely buoyancy-driven UGs, such as low speed, low resistance to currents and the lack of depth-keeping motion, the hybrid-driven UGs (HUGs) jointly actuated by the propeller propulsion unit/thermal engine and buoyancy-driven unit were proposed. Some typical HUGs have demonstrated their improved performance against the common ones, such as hybrid Slocum [13], PETREL-II [14] and Fòlaga III [15], [16] as well as some famous thermal gliders(Slocum Thermal [10] and the thermal version of PETREL [17]). Besides the above UGs, recently, several novel designs of UGs have been proposed to improve the performance of UGs. For example, the wave glider is used to capture the wave energy for power supplement [18], [19]. The solar-powered UGs are developed to utilize the solar energy [20]. Currently, the UGs are developed aiming at deeper diving depth and longer range. Deepglider [21] has a design depth of 6000 m. The PETREL-X [22] finished the sea trials and its diving depth reached 8213 m in April 2018, which makes the current record of submergence depth for UGs. The Slocum glider even glided across the Atlantic [23]. Therefore, how to improve the performance of UGs will be a key aspect to meet the demands for UGs in the application of long range and deep region.

The performance of UGs involves many aspects, such as motion characteristics [24], hydrodynamic performance [25], [26], dynamic stability [27], maneuverability [28], and energy consumption [29]. As an important aspect to evaluate the performance of UGs, the motion performance(defined by dynamic stability and maneuverability in the present work) needs to be predicted and considered in the early stage of design [30]. The evaluation model and criteria of motion performance as well as the precise dynamic model are necessary to precisely predict the motion performance of UGs. As the basis of motion performance prediction, controller design [31], and energy optimization [29], dynamic modeling is one of the focused fields for UGs. There have been three common models. Fossen [32], [33], [34] proposed a dynamic model for underwater vehicle with the Newton-Euler and Euler-Langrange forms. The model has been applied in various aspects of underwater vehicles, such as the motion simulation of UGs [35], controller design for AUVs [36] and path planning of UGs [37]. Leonard et al. [38] proposed a classic dynamic model for UGs. The model has been used in the motion simulation [39], [40], control [38], stability [41] and parameter identification of UGs [42]. Besides, Wang et al. [43] proposed another common method of dynamic modeling based on multibody dynamics theory. This method is also widely used in the dynamics and control of underwater vehicles [44], [45]. In addition, some previous work focused on the improvement of prediction accuracy by incorporating more environmental factors. For example, Woolsey and Thomasson proposed a model to capture the effects of flow on AUVs [46], which was also extended to the modeling of UGs [47]. Yang et al. [48] proposed a dynamic model to improve the prediction accuracy of UGs by considering the hull deformation and seawater density variation with depth. Currently, the existing dynamic models of UGs can satisfy some requirements for their practical applications. The dynamic model used in this study is established on the basis of the model in  [48].

The research of motion performance can be mainly tracked from the fields of marine vehicles, torpedoes and submarines. On the dynamic stability, in 1954, Bottaccini  [49] derived the characteristic equations of torpedoes and obtained the evaluation criteria of dynamic stability for the torpedoes in the vertical and horizontal planes. In 1956, Lambert [50] derived the same criteria, and investigated the effects of hydrodynamic coefficients on the torpedoes. After that, the above criteria were widely used to study the dynamic stability of underwater vehicles. Humphreys [51] used the criteria to compare the design of four concept AUVs. Wang et al. [52] used the criteria to predict the dynamic stability of AUV-HM1 AUV. Similarly, Phillips et al. [53] also adopted the criteria to evaluate the performance of an AUV by CFD method. Yi et al. [54] used the criteria to analyze the design and dynamic stability of a deep-sea AUV. Apart from the above applications, the criteria have also been applied to the dynamic stability of robotic fish [55] and submarines[56]. In addition, many methods and criteria have been developed to evaluate the maneuverability of marine vehicles and underwater vehicles. In 1932, Kempf [57] proposed the zig-zag maneuver, which was regarded as one of the early standard methods to test the maneuverability of ships by trials. In 1957, Nomoto et al. [58], [59] proposed a method to evaluate the maneuverability of ships by parameters K and T [60]. Guo et al. [30] used parameters K and T to evaluate the maneuverability of an AUV. In 1995, Shi [61] elucidated the theory of motion performance for submarines, which was extended in the study of AUVs. Zhang et al. [62] used the similar method in [61] to study the influence of balance weight parameters on the motion performance of a seafloor mapping AUV in the vertical plane, in which the dynamic stability and change rate of surfacing speed for an AUV were investigated. In addition to the above criteria, turning diameter was also regarded as one of the most popular criteria to evaluate the maneuverability of ships, AUVs and submarines in some work. For example, Page et al. [28] adopted the turning parameter as a criterion to evaluate the maneuverability of a UG.

AUVs are usually equipped with their propeller unit as the propulsion system, and their attitude angle and depth are changed by the external rudders. Therefore, they have the similar models with submarines or torpedoes in dynamics. The same evaluation criteria can be adopted to predict their motion performance, which are derived from the dynamic model. However, the buoyancy-driven mode and the way of changing the attitude angles and depth by the internal battery package or mass result in great difference between the dynamic models of UGs and those of the submarines or torpedoes. Therefore, the evaluation models and criteria of motion performance for the latters are not applicable to the UGs. The applicable models and criteria are needed to predict the motion performance and guide the design of UGs. Additionally, though the depth showed significant impact on the motion characteristics of UGs [48], the relationship between the depth and motion performance of UGs still needs to be clarified. To this end, based on the dynamic models for UGs in the vertical plane, the applicable free perturbation equations and maneuverability equations will be first derived by Taylor series expansion. Then, the applicable criteria will be derived to evaluate dynamic stability and maneuverability of UGs. To guide the design of UGs from the view of motion performance, their motion performance will be investigated under the effects of seawater depth as well as the motion strategies in the depth-keeping motion. Finally, sea trials will be conducted to verify the theoretical analysis in this paper.

This paper is organized as follows. In Section 2, the dynamic stability of UGs will be derived and discussed. In Section 3, the maneuverability of UGs will be derived and analyzed. In Section 4, the sea trials will be described. The conclusions as well as the future work will be summarized in Section 5.