Heave Dynamics Research Articles

Analytical Solution of Time-Optimal Trajectory for Heaving Dynamics of Hybrid Underwater Gliders

Underwater vehicles have capacity limits for control inputs, within which their time-optimal trajectories (TOTs) can be formulated. In this study, the fastest trajectory for the depth control of a hybrid underwater glider (HUG) was found using buoyancy engines and propellers individually, and the decoupled heave dynamics of the HUG were defined using quadratic hydrodynamic damping. Because buoyancy engines always run at slow speeds, the buoyancy force was formulated based on the constant force rate of the engine. It was assumed that the nominal value of the heave dynamics parameters could be estimated; therefore, the analytical solution of heave dynamics could be formulated using the thrusting saturation and constant buoyancy force rate. Then, the shortest trajectory for depth control of the HUG could be established while considering the actuator saturation. To verify the effectiveness of the TOT in HUG heave dynamics, extensive tracking control simulations following the TOT were conducted. It was found that the proposed TOT helps the HUG reach the desired depth in the shortest arrival time, and its robust depth control showed good tracking performance in the presence of external bounded disturbances.

Nonlinear model predictive control for yaw rate and body motion control through semi-active and active suspensions

Active and semi-active suspensions for passenger cars traditionally enhance comfort through body control, and vehicle handling by reducing the tyre load variations induced by road irregularities. Active suspensions can also be designed to track a desired yaw rate profile through the control of the lateral load transfer distribution between the front and rear axles. This paper considers an integrated system including semi-active and active suspension actuation to control the yaw, roll, pitch and heave dynamics excited by the driving actions. To this purpose, two novel real-time-capable implicit nonlinear model predictive control (NMPC) formulations, excluding and including cost function weight adaptation, are proposed and compared with the passive vehicle, and the controlled vehicle with two combinations of skyhook and active roll control, the first based on a pseudoinverse decoupling transformation for obtaining the damping force contributions, and the second using an inverse formulation. The algorithms are assessed through an experimentally validated simulation model, along manoeuvres corresponding to sub-limit and limit handling operation, to analyse the trade-off between body motion reduction and cornering response enhancement. The results show that the adaptable NMPC configuration provides the best performance in all scenarios, also for significant variations of the main vehicle and tyre parameters.

T-S Fuzzy Model-Based Depth Control of Underwater Vehicles

A T-S fuzzy model with two rules is established to exactly describe the nonlinear uncertain heave dynamics of underwater vehicles with bounded heave speed. A single linear-matrix-inequality-based (LMI-based) state feedback controller is then synthesized to guarantee the global stability of the depth control system. Simulation results verify the effectiveness of the proposed approach in comparison with linear-quadratic regulator (LQR) method. Nonlinear disturbance observer is appended to the system when the underwater vehicles are affected by the gravity-buoyancy imbalance. The two-stage control method is effective to stabilize an uncertain system with both parameter uncertainties and external disturbances.

On Vehicle Pitch Estimation via solid-state LIDAR

Solid-state LIDAR technology has recently emerged, allowing for smaller and more affordable devices. In the present work, we investigate the possibility of using a vehicle mounted solid-state LIDAR to estimate the vehicle pitch and heave dynamics. We present and compare two approaches: a model-based estimation and a data driven algorithm. The algorithms are tested on an instrumented vehicle. The experimental results show that the data-driven approach outperforms the model-based estimation in estimating pitch caused both by accelerations and braking and by road disturbances.

Investigation of heave dynamics of an air cushion vehicle segment skirt

Air Cushion Vehicle (ACV) is a moving vehicle on airbags, which can travel on land and on water to transport people, goods and equipment. An important requirement for ACVs is to: increase reliability and longevity, reduce operating costs, stability and mobility. In this paper, a model for the dynamic behavior of air cushion vehicles segment skirt is presented. In this model, the compressible Bernoulli's equation, Newton's second law of motion are used to predict the dynamic behavior of the air cushion vehicles. Based on the developed model, the heave dynamics parameters of the air cushion vehicles “Hovertrek 6100L” are surveyed.

Frequency and Time Domain Analysis of an Aeroelastic Wing Multiple Component Structure

A multiple component structure consisting of two Euler-Bernoulli beams connected to a rigid mass is used to model the heave dynamics of a wing micro air vehicle. In the time domain, the attainment of a C 0-semigroup in the context of sesquilinear forms is demonstrated. In addition, the closed loop system is demonstrated to generate an exponentially stable C 0-semigroup. In the frequency domain, the infinite dimensional transfer function is determined and used to examine several properties of the system. Finally, an optimal control is used to morph the wings to a desired shape, and simulation results are demonstrated.

Reinforcement learning based controller synthesis for flexible aircraft wings

Aeroelastic study of flight vehicles has been a subject of great interest and research in the last several years. Aileron reversal and flutter related problems are due in part to the elasticity of a typical airplane. Structural dynamics of an aircraft wing due to its aeroelastic nature are characterized by partial differential equations. Controller design for these systems is very complex as compared to lumped parameter systems defined by ordinary differential equations. In this paper, a stabilizing statefeedback controller design approach is presented for the heave dynamics of a wing-fuselage model. In this study, a continuous actuator in the spatial domain is assumed. A control methodology is developed by combining the technique of “proper orthogonal decomposition” and approximate dynamic programming. The proper orthogonal decomposition technique is used to obtain a low-order nonlinear lumped parameter model of the infinite dimensional system. Then a near optimal controller is designed using the single-network-adaptive-critic technique. Furthermore, to add robustness to the nominal single-network-adaptive-critic controller against matched uncertainties, an identifier based adaptive controller is proposed. Simulation results demonstrate the effectiveness of the single-network-adaptive-critic controller augmented with adaptive controller for infinite dimensional systems.

Investigation of the heave dynamics of Air Cushion Vehicles (ACV): parametric and chaotic studies

A highly non-linear model for the dynamics behavior of Air Cushion Vehicles (ACV) is presented. In this model the compressible Bernoulli's equation, the Newton's second law of motion, and the nonlinear isentropic relations are used to predict the dynamics behavior of only the vertical response of the ACV in both time and frequency domains. In this paper the mass flow rate inside the air cushion volume of the ACV is maintained constant. In order to assist in the design process of such vehicles, the self excited response and the cushion pressure of the ACV are calculated to understand the dynamic behavior of these vehicles. It is shown in this study that the mass flow rate and the length of the vehicle's skirt are the most significant parameters which control the steady state behavior of the self excited oscillations of the ACV. An equation to predict the transient time of the oscillatory response or the settling time in terms of the system parameters is developed. Based on the developed equations, the optimum parameters of the ACV that lead to minimum settling time are obtained. Also, the chaotic behavior of the heave dynamics is investigated with the aid of the Fourier analysis and the Poincare map. It is shown that the heave dynamics does not manifest any chaotic behavior within the selected range of the control parameters. However, the cushion pressure manifested some chaotic behavior at some values of the skirt length and mass flow rate.

Evaluation of wave energy generation from buoy heave response based on linear generator concepts

Previous studies of linear generator power extraction from ocean waves have usually ignored the buoy heave dynamics and taken the linear generator movement to coincide with the wave motion. Here, the actual buoy motion is first determined and then used to solve the coupled hydrodynamic and electromagnetic problem of electrical power generation for both regular and irregular waves. Several buoy sizes are modeled to exploit the buoys' natural frequency in an attempt to create a greater heave response for a given sea state. Power output ranging from 75 to 375 W is predicted for the dimensions chosen.

Topics on Current Compensation for Path Following Applications of Underactuated Underwater Vehicles

Ocean currents compensation techniques for underactuated underwater vehicles based on a three-dimensional Line-of-Sight (LOS) guidance law with integral action are discussed and applied in order to achieve precise path following. The current is considered as constant, unknown and acting in all directions, including directions in which there are no actuator forces. An integral term introduced in the guidance law counteracts the current by allowing the vehicle to side-slip and pitch while keeping the desired course. It is shown that the integral action in the LOS guidance law performs a vectorial sum between the vehicle's relative velocity and the unknown current velocity to compensate for the drift. Path following of straight lines is considered and the problem is addressed at the kinematic level only since the LOS guidance law can be seen as a decoupling tool between the actuated surge dynamics and the unactuated sway and heave dynamics of the vehicle. Stability of the closed loop kinematic system is analyzed and simulation results show path convergence.

Non-linear Control of Heave for an Unmanned Helicopter Using a Neural Network

This paper describes a new non-linear control technique applied to the heave control of an unmanned rotorcraft. First a hybrid plant model consisting of exactly known dynamics is combined with a black-box representation of the unknown dynamics. Desired trajectories are calculated to smoothly achieve a sequence of random step changes in desired height according to certain optimal criterion and plant limitations. Control inputs are then determined using the MATLAB® optimisation toolbox to achieve those desired trajectories for the plant heave model. Finally, a neural network is trained to mimic the control inputs resulting from the optimisation process. The neural network controller produces trajectories closely resembling the results from the optimisation process but with a much reduced computation time. Flight test results of control of the heave dynamics of a helicopter confirm the neural network controller's ability to operate in high disturbance conditions and outperform a proportional-derivative (PD) controller.

Notes on a simplified two-degree-of-freedom car suspension model of chassis heave and pitch-plane dynamics

This article considers the derivation of a common two-degree-of-freedom automotive suspension heave and pitch design model involving the front and rear axle coupled and uncoupled spring stiffnesses. Many rules of thumb are used in automotive design regarding this model perhaps without full appreciation of the mathematical analysis and assumptions invoked in their formulation. With the widespread use of computer-aided suspension simulation models, it is perhaps timely to note the derivations of the model equations and the limiting assumptions for which they can be applied with confidence. In particular, the derivations and numerical examples show that the concept of a stationary pitch centre for chassis-coupled dynamic normal-mode vibration analysis is questionable.

Pitch and Heave Control of Robotic Samara Micro Air Vehicles

Micro/nano unmanned aerial systems are an emerging class of vehicles uniquely suited to performing covert missions. A linear model for the heave dynamics of a robotic samara (winged seed) in hovering flight was identified from data collected external to the vehicle by a visual tracking system. Insight gleaned from the implementation of feedback control includes a characteristically overdamped system in climb, which differs from the underdamped descent characteristic observed. Identification and error estimation efforts used a frequency response-based system identification. The two robotic samara vehicles of differing scale compared in this study represent the first demonstration of controlled flight of a vehicle of this kind.

Dipteran insect flight dynamics. Part 1 Longitudinal motion about hover

This paper presents a reduced-order model of longitudinal hovering flight dynamics for dipteran insects. The quasi-steady wing aerodynamics model is extended by including perturbation states from equilibrium and paired with rigid body equations of motion to create a nonlinear simulation of a Drosophila-like insect. Frequency-based system identification tools are used to identify the transfer functions from biologically inspired control inputs to rigid body states. Stability derivatives and a state space linear system describing the dynamics are also identified. The vehicle control requirements are quantified with respect to traditional human pilot handling qualities specification. The heave dynamics are found to be decoupled from the pitch/fore/aft dynamics. The haltere-on system revealed a stabilized system with a slow (heave) and fast subsidence mode, and a stable oscillatory mode. The haltere-off (bare airframe) system revealed a slow (heave) and fast subsidence mode and an unstable oscillatory mode, a modal structure in agreement with CFD studies. The analysis indicates that passive aerodynamic mechanisms contribute to stability, which may help explain how insects are able to achieve stable locomotion on a very small computational budget.

DYNAMIC COUPLING ANALYSIS BETWEEN FRONT AND REAR AXLE FOR ABS SYSTEMS DESIGN

The common practice in Anti-lock Braking Systems (ABS) design is to employ a Quarter-Car model of the braking dynamics. The underlying hypothesis is to regard each wheel as dynamically decoupled from the rest of the vehicle. In this paper, we investigate the wheel slip dynamics behavior starting from a Half-Car model, i.e., taking into account the pitch and heave dynamics. This analysis allows to highlight the effects of dynamic coupling between front and rear axles and its effects on ABS systems design. Moreover, this analysis reveals an interesting trade-off between longitudinal and vertical motion. The results of this work allow to outline the possible benefits of an integrated design of active braking and suspensions control.

Modeling, Identification, and Analysis of Limit-Cycling Pitch and Heave Dynamics in an ROV

The topic of this paper is the modeling, parameter identification, and analysis of the heave and pitch dynamics in a remote operated vehicle (ROV). The work presented here is motivated by an unusual dynamic behavior experienced on the Gaymarine Pluto-Gigas ROV: if the depth is regulated using a proportional controller, the ROV exhibits permanent oscillations at high forward speed. The purpose of this paper is to gain insight into ROV dynamics, so as to explain the reason for the oscillations. To this end, a dynamic gray-box model is developed and its uncertain parameters are identified from real data. The analysis of such a model shows that the nonlinear dynamics of the ROV contains a limit cycle. This discovery explains the observed oscillatory behavior. An interesting aspect of this limit-cycling behavior is that it is not due (as usual) to saturation effects of the actuators, but is intrinsic in the ROV dynamics.

Analysis of Pitch and Heave Dynamics in a ROV

The topic of this paper is the modeling, parameter identification, and analysis of the heave and pitch dynamics in a Remote Operated Vehicle (ROV). The work presented herein is motivated by an unexpected dynamic behavior exhibited by the Gaymarine Pluto Gigas™ ROY: if the depth is regulated using a proportional controller, the ROY exhibits permanent oscillations at high forward speed. Motivated by this experimental observation, the purpose of this paper is to gain insight into the ROV dynamics, so as to enlighten the reason of the oscillations. To this end, a simple have and pitch dynamic model is developed and its uncertain parameters are identified from real data. The analysis of such model shows that the non-linear dynamics of the ROV contains a limit cycle. This discovering explains the observed oscillatory behavior.

Skirt-Material Damping Effects on Heave Dynamics of an Air-Cushion-Vehicle Bag-and-Finger Skirt

An investigation of the effects of skirt-material damping on heave dynamics of an air-cushion-vehicle bag-and-finger skirt is described. Previous investigations of skirt viscoelastic phenomena are reviewed; these suggest that hysteretic skirt–surface contact forces observed in static stiffness tests may be a major source of damping. The pure heave motion of a two-dimensional section of the bag-and-finger skirt is investigated using a non-linear mathematical model; this incorporates a simple model to account for the hysteretic skirt–surface contact forces. The simulation results show that the skirt force appears as damping, and confirms that the hysteretic forces observed in the static stiffness tests can have a major effect on vehicle dynamics. However, they do not suppress phenomena such as period doubling and chaotic response to periodic input disturbances reported in a previous analysis.

Linear Heave Dynamics of an Air-Cushion Vehicle Bag-and-Finger Skirt.

Results from a linear analysis of the heave dynamics of an air-cushion vehicle equipped with a bag-and-finger skirt are described. A two-dimensional section of the cushion is subject to pure heave or long-wave surface motion inputs. The skirt mass is lumped in the fingers, with the bag being modelled as a combination of massless inelastic membranes and links. The airflows from bag to cushion and from cushion to atmosphere are assumed quasisteady, and the bag and cushion volumes are modelled as lumped pneumatic capacitances. For a configuration representative of a 37t vehicle, frequency response characteristics show the effect of skirt geometry and mass changes, and cushion capacitance. The results suggest that changes in skirt geometry cannot be used to radically modify an undesirable heave response, but reducing the skirt mass may be effective. The air compressibility also affects heave response at high frequencies, with the effect becoming more prominent at the low cushion-flow rates now used in practice.

Nonlinear Heave Dynamics of an Air Cushion Vehicle Bag-and-Finger Skirt*

The flexible skirt system used almost exclusively on large amphibious air cushion vehicles such as the U.S. Navy's 150 tonne landing craft is the bag-and-finger skirt, but little information on its dynamical properties is available in the journal literature. The present paper describes results of an analysis of the nonlinear heave dynamics of a simplified configuration chosen specifically to allow formulation from first principles The skirt mass is lumped in the fingers, with the bag being modeled as a combination of massless inelastic membranes and links. Airflow processes are assumed quasi-steady, and the bag-and-cushion volumes are modeled as lumped pneumatic capacitances. The modulation of cushion air escape by skirt-surface contact is also included. The numerical results show that nonlinear effects occur at wave input amplitudes expected to be encountered in practice. At a given frequency, input amplitude increase causes jumps in heave response, period doubling, and chaos. Furthermore, results for two typical configurations show resonance at frequencies at which humans are most sensitive. One solution to this problem may be to reduce skirt mass The paper concludes with a discussion of issues requiring further investigation.