Maneuver Time Research Articles

Dynamic Problem of Optimal Control of Spacecraft Attitude under Restriction on Phase Variables

An analytical solution to the optimal control problem of spacecraft reorientation from an arbitrary initial angular position into a required final angular position under the restrictions on control functions and phase variables is presented (the controlling moment and angular velocity are restricted). Time of slew maneuver is minimized. The specific case was considered when maximum admissible kinetic energy of rotation is significant restriction. Constructing the optimal control of reorientation is based on Pontryagin’s maximum principle and the quaternionic variables and models. It is shown that optimal mode is piecewise-continuous control when a direction of spacecraft’s angular momentum is constant relative to the inertial coordinate system during rotation of a spacecraft; for a per forming an optimal turn, the moment of forces is parallel to a straight line fixed in inertial space. Two types of optimal control are possible depending on the given initial and final positions and spacecraft’s moments of inertia — relay control with one switching point when the controlling moment is maximal over the entire time interval of control (segments of acceleration and braking), and relay control with two switching point consisting of intensive acceleration, motion by inertia with the absented moment and an exit onto restriction of rotation energy, and then final braking with the maximum controlling moment. The analytical equations and relations for a finding the optimal control program are written down. The calculation formulas for determining the time characteristics of maneuver and computing a duration of acceleration and braking are given. The proposed algorithm of control provides maximally fast implementation of spacecraft reorientation under the limited kinetic energy of rotation. For an axially symmetric solid body (spacecraft), the optimal control problem, in dynamical statement, was solved completely — we obtained the dependences as explicit functions of time for the control variables, and relations for calculating the key parameters of the law of control are derived. The numerical example and results of mathematical simulation of spacecraft motion under the optimal control are presented, demonstrating the practical feasibility of the developed method for control of spacecraft attitude.

A concept of critical safety area applicable for an obstacle-avoidance process for manned and autonomous ships

In times of increased automation of maritime transportation, ship collision with a stationary obstacle (allision) remains a significant problem. There are many existing solutions rooted primarily in the concept of ship domain and path-planning algorithms. However, among these, a geometrical approach to the determination of a required maneuvering area considering the dynamic nature of ship operations in close-quarters situations is still missing. Therefore, an improved concept of the CADCA (Collision Avoidance Dynamic Critical Area) is introduced for the case of ship allision. The CADCA is a deterministic zone that geometrically delimits required maneuvering space of a vessel. Its shape changes depending on the operational parameters of a ship, such as the magnitude of rudder angle, initial forward speed, or planned alteration of the course. In contrast to ship domain, the CADCA is determined using the critical distance between two objects called MDTC (Minimum Distance to Collision). Therefore, the CADCA concept can be used to appoint a position of no-return in a close-quarters situation, so as to determine the time and distance of the last-minute maneuver. An improved method of CADCA determination is introduced, along with an investigation of operational factors influencing the ship's critical area in allision scenarios. The simulations have been conducted for large passenger and container ship in encounters with various stationary obstacles differing in size and shape. The results indicate that from the operational point of view, a deflection of the rudder is the most influencing factor on the size of the CADCA, while the impact of ship speed is negligible for the investigated vessels. Besides, various applications of the CADCA are proposed and discussed for both manned and prospective autonomous vessels.

Robust multi-steps input command for liquid sloshing control

A robust input command based on multiple steps for eliminating the residual vibrations of a multimode linear system is proposed. Only the system resonant frequencies are needed to determine the step magnitudes in the shaped command. The command duration is selectable to help in designing an optimum command that compensates between the reduction in the transient vibration, the enhancement in the command robustness, and the increase in the total maneuver time. The induced transient and residual sloshing oscillations of a suspended water-filled container are suppressed using the proposed command. The dynamics of the sloshing is numerically simulated using finite element method that accommodates the interactions between the fluid, structural, and multi-body dynamics. A short move time penalty is incurred with the price of significant reduction in the liquid sloshing. The performance of the shaped command to the system parameters and the robustness to their uncertainty are investigated. An improved robust input command in the presence of uncertainties in the cable length and water depth is also introduced. The effectiveness and excellence of the proposed command is demonstrated through a comparison with multimode zero-vibration input shaper and time-optimal flexible-body control.

A Robust and Fast Collision-Avoidance Approach for Micro Aerial Vehicles Using a Depth Sensor

Collision-avoidance is a crucial research topic in robotics. Designing a collision-avoidance algorithm is still a challenging and open task, because of the requirements for navigating in unstructured and dynamic environments using limited payload and computing resources on board micro aerial vehicles. This article presents a novel depth-based collision-avoidance method for aerial robots, enabling high-speed flights in dynamic environments. First of all, a depth-based Euclidean distance field mapping algorithm is generated. Then, the proposed Euclidean distance field mapping strategy is integrated with a rapid-exploration random tree to construct a collision-avoidance system. The experimental results show that the proposed collision-avoidance algorithm has a robust performance at high flight speeds in challenging dynamic environments. The experimental results show that the proposed collision-avoidance algorithm can perform faster collision-avoidance maneuvers when compared to the state-of-art algorithms (the average computing time of the collision maneuver is 25.4 ms, while the minimum computing time is 10.4 ms). The average computing time is six times faster than one baseline algorithm. Additionally, fully autonomous flight experiments are also conducted for validating the presented collision-avoidance approach.

Optimal control on the attitude rotation of a flexible satellite model base on tetrahedral configured reaction wheels

The increase in demand for performance for satellite capabilities has pushed the design of the system to be more power consuming. Currently, most of the satellite design are equipped with large solar panel in order to produce sufficient power. Thus, this translates to a higher flexibility in the satellite which makes the satellite prone to vibratory motion. The primary cause of vibratory motion in satellite is the attitude rotation. Reaction wheel is a widely used attitude rotation actuator for a satellite Commonly, the reaction wheels are configured in the tetrahedral form. This causes uneven maximum torque at any direction. Hence, an iterative optimal control method is applied using GPOPS toolbox to achieve minimum time of rotation with low level of induced vibratory motion. The optimized control is compared with the Eigen-axis Quaternion Feedback control to observe the performance of the optimal control. Depending on the direction of attitude manoeuvre, the optimal control has shown an improvement between 3.49% to 25.11% in manoeuvre time. Overall, the optimal control outperformed the traditional the Eigen-axis Quaternion Feedback control.

Navigation safety control system development through navigator action prediction by data mining means

Taking into account current trends in the development of ergatic maritime transport systems, the factors of the navigator’s influence on vessel control processes were determined. Within the framework of the research hypothesis, to improve navigation safety, it is necessary to apply predictive data mining models and automated vessel control. The paper proposes a diagram of the ergatic vessel control system and a model for identifying the influence of the navigator “human factor” during navigation. Within the framework of the model based on the principles of navigator decision trees, prediction by data mining means is applied, taking into account the identifiers of the occurrence of a critical situation. Based on the prediction results, a method for optimal vessel control in critical situations was developed, which is triggered at the nodes of the navigator decision tree, which reduces the likelihood of a critical impact on vessel control. The proposed approaches were tested in the research laboratory “Development of decision support systems, ergatic and automated vessel control systems”. The use of the Navi Trainer 5,000 navigation simulator (Wärtsilä Corporation, Finland) and simulation of the navigation safety control system for critical situations have confirmed its effectiveness. As a result of testing, it was determined that the activation of the system allowed reducing the likelihood of critical situations by 18–54 %. In 11 % of cases, the system switched the vessel control processes to automatic mode and, as a result, reduced the risk of emergencies. The use of automated data mining tools made it possible to neutralize the negative influence of the “human factor” of the navigator and to reduce the average maneuvering time during vessel navigation to 23 %

A smooth optimized input shaping method for two-dimensional crane systems using Bezier curves

Conventional input shaping commands have been successfully employed to suppress residual vibration in the payload rest-to-rest transportation process. Most of these methods introduce an impractical large and sudden variation on the acceleration profile. This paper presents a new smooth command input with adjustable time length and limited jerks. The command input is generated from the trolley displacement using a Bezier curve function by adjusting the position of the control points, which were divided into boundary and intermedium points. The boundary control points are selected to accurately move the trolley to its desired position with zero velocity and acceleration at the closing motion. The positions of the intermedium points were optimized using a particle swarm scheme for reducing maneuvering time while suppressing the payload oscillations at the end of the process and satisfying physical system constraints. Several cases were discussed for fixed cable length, variable cable involving single and multi-hoisting mechanisms, and different maneuver times. Simulated results were validated experimentally on a laboratory size crane. The results demonstrated that the proposed input Bezier-curve shaper provides an effective, reliable, and practical technique to be used for the payload transportation process. Moreover, the proposed method can generate asymmetrical acceleration and deceleration motions, which cannot be achieved using existing smoother commands.

Ground maneuver for front-wheel drive aircraft via deep reinforcement learning

The maneuvering time on the ground accounts for 10%–30% of their flight time, and it always exceeds 50% for short-haul aircraft when the ground traffic is congested. Aircraft also contribute significantly to emissions, fuel burn, and noise when taxiing on the ground at airports. There is an urgent need to reduce aircraft taxiing time on the ground. However, it is too expensive for airports and aircraft carriers to build and maintain more runways, and it is space-limited to tow the aircraft fast using tractors. Autonomous drive capability is currently the best solution for aircraft, which can save the maneuver time for aircraft. An idea is proposed that the wheels are driven by APU-powered (auxiliary power unit) motors, APU is working on its efficient point; consequently, the emissions, fuel burn, and noise will be reduced significantly. For Front-wheel drive aircraft, the front wheel must provide longitudinal force to tow the plane forward and lateral force to help the aircraft make a turn. Forward traction effects the aircraft’s maximum turning ability, which is difficult to be modeled to guide the controller design. Deep reinforcement learning provides a powerful tool to help us design controllers for black-box models; however, the models of related works are always simplified, fixed, or not easily modified, but that is what we care about most. Only with complex models can the trained controller be intelligent. High-fidelity models that can easily modified are necessary for aircraft ground maneuver controller design. This paper focuses on the maneuvering problem of front-wheel drive aircraft, a high-fidelity aircraft taxiing dynamic model is established, including the 6-DOF airframe, landing gears, and nonlinear tire force model. A deep reinforcement learning based controller was designed to improve the maneuver performance of front-wheel drive aircraft. It is proved that in some conditions, the DRL based controller outperformed conventional look-ahead controllers.

Dorsal approach with Glissonian approach for laparoscopic right anatomic liver resections

BackgroundLaparoscopic anatomic hepatectomy (LAH) has gradually become a routine surgical procedure. However, how to expose the whole hepatic vein and avoid the hepatic vein laceration is still a challenge because of the caudate lobe, particularly in right hepatectomy. We adopted a dorsal approach combined with Glissionian appraoch to perform laparoscopic right anatomic hepatectomy (LRAH).MethodsTwenty patients who underwent LRAH from January 2017 to November 2018 were retrospectively analysed. Of these patients, seven patients underwent laparoscopic right hemihepatectomy (LRH group), seven patients who underwent laparoscopic right posterior hepatectomy (LRPH group), and six patients who underwent laparoscopic hepatectomy for segment 7 (LS7 group). The paracaval portion of caudate lobe could be transected firstly through dorsal approach and the corresponding major hepatic vein could be exposed from its root to the peripheral branches safely. Due to exposure along the major hepatic vein trunk, the remaining liver parenchyma could be quickly transected from dorsal to cranial side.ResultsThe mean age of the patients was 53.8 years and the male: female ratio was 8:12. The median operation time was 306.0 ± 58.2 min and the mean estimated volume of blood loss was 412.5 ± 255.4 mL. The mean duration of postoperative hospital stay was 10.2 days. The mean Pringle maneuver time was 64.8 ± 27.7 min. Five patients received transfusion of 2–4 U of red blood cells. Two patients suffered from transient hepatic dysfunction and one suffered from pleural effusion. None of the patients underwent conversion to an open procedure. The operative duration, volume of the blood loss, Pringle maneuver time, and postoperative hospital stay duration did not differ significantly among the LRH, LRPH, and LS7 groups (P > 0.05).ConclusionsDorsal approach combined with Glissonian approach for right lobe is feasible and effective in laparoscopic right anatomic liver resections.

Evaluation of accuracy of laparoscopic liver mono-segmentectomy using the Glissonian approach with indocyanine green fluorescence negative staining by comparing estimated and actual resection volumes: A single-center retrospective cohort study.

Laparoscopic liver mono-segmentectomy (LLMS) may improve patient outcomes, but it is difficult and its accuracy and safety are unknown. We evaluated the accuracy of LLMS using Glissonian approach with indocyanine green fluorescence (ICG) negative staining. Seventy-four patients eligible for LLMS except for segment 1 were enrolled. Preoperative three-dimensional CT-based surgical simulation was used to determine estimated liver resection volume (ELRV), which was compared with modified actual liver resection volume (ALRV) obtained from actual liver resection mass. The LLMS accuracy was also evaluated based on operator's experience (attending surgeon [AS] or trainee surgeon [TS]). Estimated liver resection volumes significantly correlated with ALRVs (r=.82) in all cases. Moreover, TS-conducted LLMS also showed acceptable difference between ELRV and ALRV compared with AS-conducted LLMS. There were no intergroup differences in estimated blood loss, operation time, time of Pringle maneuver, postoperative complications, and length of postoperative hospitalization (P<.05). Moreover, R0 resection was comparable between the AS and TS groups. Laparoscopic liver mono-segmentectomy with Glissonian approach using ICG negative imaging ensured safe and accurate procedure owing to facilitated visualization of the resection line. Our approach was effective in avoiding postoperative liver dysfunction and securing radical resection. In addition, it might be helpful in TS education of LLMS.

Minimum-Time Spacecraft Attitude Motion Planning Using Objective Alternation in Derivative-Free Optimization

This work presents an approach to spacecraft attitude motion planning which guarantees rest-to-rest maneuvers while satisfying pointing constraints. Attitude is represented on the group of three dimensional rotations. The angular velocity is expressed as weighted sum of some basis functions, and the weights are obtained by solving a constrained minimization problem in which the objective is the maneuvering time. However, the analytic expressions of objective and constraints of this minimization problem are not available. To solve the problem despite this obstacle, we propose to use a derivative-free approach based on sequential penalty. Moreover, to avoid local minima traps during the search, we propose to alternate phases in which two different objective functions are pursued. The control torque derived from the spacecraft inverse dynamics is continuously differentiable and vanishes at its endpoints. Results on practical cases taken from the literature demonstrate advantages over existing approaches.

Study on wave-induced motions of a turning ship in regular and long-crest irregular waves

A 6 degrees of freedom (DOF) maneuvering and seakeeping unified model is developed and validated for the accurate simulation of wave-induced motions of a turning ship (S175) in regular and long-crest irregular waves. In the model, a 3DOF surge-sway-yaw maneuvering model and a 5DOF sway-heave-roll-pitch-yaw seakeeping model are coupled weakly based on the unify theory. Maneuvering and seakeeping time steps are determined to balance between the time efficiency and accuracy. Numerical simulations of the S175 turning in regular and irregular waves under different wave lengths and directions are performed. In regular waves, the simulated turning trajectory, speed and wave-induced pitch, and roll motions are compared with free-running experimental results. It is found that the simulation model can capture general trends of motion characteristics while the ship turning in waves. Considerably good agreements are observed for the ship speed and pitch motion especially for cases with long wave length λ/Lpp≥0.70, while reasonable agreements of the turning trajectory and roll motion can also be observed. In irregular waves, ship turning motions are simulated under different wave patterns with the same spectrum. It is found that spectrums of pitch and roll motions under different wave patterns have large discrepancies.

Robust optimal solution for a smart rigid–flexible system control during multimode operational mission via actuators in combination

This paper is aimed at developing several control scenarios for vibration suppression of a flexible microsatellite as a multibody system with nonlinear fully coupled dynamics in different but interconnected in-orbit mission phases. The design approach is to exploit different actuators in a single and hybrid configuration with an optimal switching mechanism to achieve a desirable maneuvering performance by means of agility and accuracy. In this regard, a genetic algorithm (GA)-particle swarm optimization (PSO) based nonsingular terminal sliding mode control (GP-NSTSMC) and extended Lyapunov-based controller design (LD) are developed to cope with the limitations of bounded uncertainty and external disturbances. Great features of the GP-NSTSMC are its gains which are selected based on two major criteria, system energy and maneuver time, and for LD we consider the piezoelectric (PZT) and reaction wheel (RW) performance in the form of mechanical and electrical energies in the structure of the control algorithm. Despite the capabilities of these algorithms, they still excite high-frequency flexible modes. Accordingly, by applying feedback voltages to the PZTs, the extra vibration is actively damped, where the strain rate feedback (SRF) method is set to determine the control voltages. Furthermore, to satisfy one of the mission’s requirements, which is solar panels deployment, a classical Levenberg–Marquardt (CLM) technique for online mass property identification along with an effective fault detection scenario is employed. A comparative assessment of the proposed hybrid actuator/controllers is presented to clarify the technical aspects of this multimode scenario for further investigations and practical real-time space missions.

Pure Laparoscopic Hepatectomy for Tumors Close to the Major Hepatic Veins: Intraparenchymal Identification of the Major Hepatic Veins using the Ventral Approach

Laparoscopic hepatectomy for tumors close to the major hepatic veins (HVs) is a technically demanding procedure that is relatively contraindicated. We investigated this surgical technique and the outcomes of intraparenchymal identification of the major HVs using the ventral approach in pure laparoscopic hepatectomy for tumors close to the major HVs. In the present study, tumors < 10mm from the major HVs were defined as lesions in proximity to the major HVs. The cranio-ventral part of the liver parenchyma along the targeted major hepatic veins was opened to facilitate an open cutting plane. After a wide exposure of the surgical plane, the targeted major HVs were identified. Thirteen patients with tumors close to the major HVs underwent laparoscopic hepatectomy. The median operative time was 260min (range, 160-410min), while the intraoperative blood loss was 100mL (range, 30-310mL). The median Pringle maneuver time was 45min (range, 40-75min). The median tumor size was 50mm (range, 17-140mm), and the median tumor margin was 4mm (range, 0-10mm). Three patients (23.1%) experienced minor postoperative complications. The median postoperative hospital stay was 7days (range, 4-25days). Pure laparoscopic hepatectomy for tumors close to the major HVs is technically feasible in selected patients. Intraparenchymal identification of the major HVs using the ventral approach achieves transection plane accuracy and avoids inadvertent injury to the major HVs.

Energy consumption optimization for AC drives position control

PurposeThe main purpose of this paper is to evaluate the two energy saving position control strategies for AC drives valid for a wide range of boundary conditions including an analysis of their energy expenses.Design/methodology/approachFor energy demands analysis, the optimal energy control based on mechanical and electrical losses minimization is compared with the near-optimal one based on symmetrical trapezoidal speed profile. Both control strategies respect prescribed maneuver time and define acceleration profile for preplanned rest-to-rest maneuver.FindingsPresented simulations confirm lower total energy expenditures of energy optimal control if compared with near-optimal one, but the differences are only small due to the fact that two energy saving strategies are compared.Research limitations/implicationsDeveloped overall control system consisting of energy saving profile generator, pre-compensator and position control system respecting principles of field-oriented control is capable to track precomputed state variables precisely.Practical implicationsEnergy demands of both control strategies are verified and compared to simulations and preliminary experiments. The possibilities of energy savings were confirmed for both control strategies.Originality/valueExperimental verification of designed control structure is sufficiently promising and confirmed assumed energy savings.

A multi-camera system for the integrated documentation of Underwater Cultural Heritage of high structural complexity; The case study of M/S Helma wreck

High structural complexity is quite common in underwater archaeological sites and perhaps on top of the list when it comes to challenges regarding 3D reconstruction. Advances in underwater robotics and optical sensors are providing solutions for high quality data acquisition for mapping and documentation of underwater cultural heritage (UCH) sites. This paper presents a workflow for the detailed 3D reconstruction of a disintegrated shipwreck from the 1920’s in Trondheimsfjord, Norway, a wreck site of high 3D structural complexity at 55 meters depth. The work focuses on the use of seven multi-purpose optical sensors, like low-cost action cameras, omnidirectional cameras, a depth camera and an RGB camera attached to an Underwater Hyperspectral Imaging sensor, all mounted on a Remotely Operated Vehicle (ROV). The 3D reconstruction of the wreck site was carried out offline, through the implementation of a typical Structure-from-Motion pipeline. Only one camera, considered as the master camera of the system, was connected to the ROV’s control system and to the navigation sensors, hence providing georeferenced images. With the assumption that all seven cameras were moving jointly in 3D space, an approach for estimating the relative positions of the six stand-alone cameras, with respect to the master camera, was followed. The geometric configuration of the multi-sensor system allowed scaling and georeferencing of all created 3D models, and a more rapid alignment process of the big amount of collected imagery data. The presented case study highlights the advantages of multi-vision setups for UCH documentation, such as near 360° field of view with robust geometry; full 3D coverage of challenging objects of interest; the possibility of sensor’s synchronization invariant approaches, and not least minimization of maneuvering and bottom time.

A Titan mission using the Direct Fusion Drive

The main purpose of this work is to perform an analysis of realistic new trajectories for a robotic mission to Saturn’s largest moon, Titan, in order to demonstrate the great advantages related to the Direct Fusion Drive (DFD). The DFD is a D -23He fueled, aneutronic, thermonuclear fusion propulsion system (Cohen et al., 2019). This fusion propulsion concept is based on a magnetically confined field reversed configuration plasma, where the deuterium propellant is heated by fusion products, and then expanded into a magnetic nozzle, providing both thrust and electrical energy to the spacecraft. The trajectories calculations and analysis for the Titan mission are obtained based on the characteristics provided by the PPPL (Cohen et al., 2019) for a 2 MW-class DFD engine. Two different profile missions are considered: the first one is a thrust–coast–thrust profile with constant thrust and specific impulse, the second scenario is a continuous and constant thrust profile mission. Each mission study is divided into four different phases, starting from the initial low Earth orbit departure, the interplanetary trajectory, Saturn orbit insertion, and the Titan orbit insertion. For all mission phases, maneuver time and propellant consumption are calculated. The results of calculations and mission analysis offer a complete overview of the advantages in term of payload mass and travel time. It is important to emphasize that the deceleration capability is one of the DFD game changers: in fact, the DFD performance allows to rapidly reach high velocities and decelerate in even shorter time period. This capability results in a total trip duration of 2.6 years for the thrust–coast–thrust profile and less than 2 years for the continuous thrust profile. The high payload enabling capability, combined with the huge electrical power available from the fusion reactor leads to a tremendous advantage compared to present technology.

Analytical Framework for Space Debris Collision Avoidance Maneuver Design

An analytical formulation for collision avoidance maneuvers involving a spacecraft and a space debris is presented, including solutions for the maximum deviation and minimum collision probability cases. Gauss’s planetary equations and relative motion equations are used to map maneuvers at a given time to displacements at the predicted close approach. The model is then extended to map changes in state between two times, allowing one to propagate covariance matrices. The analytical formulation reduces the optimization problem to an eigenproblem, for both maximum deviation and minimum collision probability. Two maximum deviation cases, total deviation and impact parameter, are compared for a large set of spacecraft–debris conjunction geometries derived from European Space Agency’s Meteoroid and Space Debris Terrestrial Environment Reference (MASTER-2009) model. Moreover, the maximum impact parameter and minimum collision probability maneuvers are compared assuming covariances known at the maneuver time, to evaluate the net effect of lead time in collision probability. In all cases, solutions are analyzed in the b-plane to leverage its natural separation of phasing and geometry change effects. Both uncertainties and maximum deviation grow along the time axis for long lead times, limiting the reduction in collision probability.

Cooperative Time and Energy-Optimal Lane Change Maneuvers for Connected Automated Vehicles

We derive optimal control policies for a Connected Automated Vehicle (CAV) cooperating with neighboring CAVs in order to implement a lane change maneuver consisting of a longitudinal phase where the CAV properly positions itself relative to the cooperating neighbors and a lateral phase where it safely changes lanes. For the first phase, we optimize the maneuver time subject to safety constraints and subsequently minimize the associated surrogate energy consumption of all cooperating vehicles in this maneuver. For the second phase, we jointly optimize time and energy approximation and provide three different solution methods including a real-time approach based on Control Barrier Functions (CBFs). We prove structural properties of the optimal policies which simplify the solution derivations and, in the case of the longitudinal maneuver, lead to analytical optimal control expressions. The solutions, when they exist, are guaranteed to satisfy safety constraints for all vehicles involved in the maneuver. Simulation results where the controllers are implemented show their effectiveness in terms of significant performance improvements compared to maneuvers performed by human-driven vehicles.

ANALYTICAL CALCULATION OF THE PARAMETERS

The skipper must be well aware of the maneuverability of his vessel, as well as the capabilities of the ship's controls to perform a particular maneuver. In the» Information «about the parameters of turnability, which is available on the ship, there is no data on the performance of such an important maneuver as «turn in place», which is often used in a confined area of water. Some assumptions have been taken in this article and the solution of the system of equations of the motion of the vessel in relation to the considered maneuver is proposed. The author obtained analytical expressions for calculation of angular speed and the angle of turn of the vessel at the time of the maneuver of «acceleration», the rotation by inertia and active damping rotational inertia. Using the obtained expressions, the calculation of the parameters of the turnover of the project 507 ship was performed. Graphs of the dependence of the angular speed and the angle of rotation of the vessel on the maneuver time are given.