## 1 Introduction  
Diving buoys (DB) [1; 2; 3] and underwater gliders (UG) [4; 5; 6; 7; 8; 9; 10] have become well-established economical instruments of ocean exploration both for use as separate devices and in swarms vastly extending our capacity to provide efficient spacial-temporal monitoring of water basins. Chronologically the UGs originated from the DBs through addition of lifting elements which secure horizontal component of motion. One of the problems attracting attention of engineers who develop DBs and UGs in the large range of depths is _buoyancy control_ which requires account of various factors, and, in the first place, those of depth-wise density gradient and pressure hull compression. One needs to emphasize that these issues are important to retain most valuable quality of a properly designed underwater glider- _low expense of energy_. Sometimes, neglecting the issue of buoyancy control would result in difficulties on the way to conquering the depth. Enough to recall that reaching the bottom of Marianna trench required use of dedicated thrusters for [PERSON]'s Challenger venture, [11]. Note that dynamics of _diving buoys_ (profilers) and _underwater gliders_ along with their buoyancy engines as well as corresponding energy consumption modeling have been discussed in several preceding papers. Reference [12] reported details on construction of a buoyancy engine for an underwater glider design challenge being to build a vertically translating programmable buoyancy engine capable of diving to the depth of 20 m.  
It is emphasized in [13] that in the <<depth-varying oceanic environment, the buoyancy of deep-sea underwater gliders (UGs) will change with depth due to pressure hull deformation and seawater density variation. As the buoyancy variation caused by these two factors is of the same order of magnitude as the nominal net buoyancy, hull deformation and seawater density variation will accordingly affect the dynamic behaviors of deep-sea UGs>>. Comparison of simulated results obtained with account of density gradient and hull compressibility with a simpler mathematical model not accounting for these properties and sea trials showed that hull deformation and sea water density variation have considerable effect on pitch angle and velocity of the gliders. Ensuing from this analysis was a proposed buoyancy compensation scheme validated to be effective in the course of sea trials. It is underlined in [14] that full assessment of the energy loss due to the hull and water compressibility effects is very important in view of necessity of using thus saved UG battery power for indispensable additional instrumentation, such, for example, as Doppler velocity logger, and, in any case, for extended range capability for a given battery power. This power-saving vector of the UG development would bring along various improvements including hydrodynamic optimization of the hull and lifting system and energy harvesting capacity of the vehicle. The authors of [15] comment that variation of sea water density and hull compressibility affects driving buoyancy of the UG, resulting in unstable motion, and propose a novel hybrid passive buoyancy compensation system based on three standalone systems with the goal to reduce buoyancy change. Buoyancy control issues are closely interrelated with the problem of energy consumption modeling (ECM) for underwater gliders. Paper [16] deals with ECM and states that such modeling is indispensable for efficient energy management of the UG as well as for their safe operation. This paper sets forth a comprehensive ECM of UGs which comprises consideration of ocean currents, seawater density variation, deformation of the pressure hull and asymmetry of gliding motion during descending and ascending. Sea trial data used by the authors shows that account of the currents brings about a significantly higher accuracy of the ECM. The paper also reveals how energy consumption relates to multiple parameters of the UG such as gliding velocity with respect to the current and diving depth.