Outer Gimbal Research Articles

A multi-axis alternating continuous rotation scheme for tri-axis rotational inertial navigation system (RINS) with fiber optic gyro

Benefiting from the rotational modulation technique and the gimbal structure, rotational inertial navigation system (RINS) can improve navigation accuracy by about one order of magnitude compared with the strap-down inertial navigation system (SINS). By continuously rotating around a fixed axis, the constant and slow variability errors perpendicular to the direction of the rotation axis can be effectively restrained while the errors in the direction of the rotation axis cannot be suppressed. Therefore, a multi-axis rotation scheme needs to be designed. Meantime, the fiber optic gyro (FOG), as a very popular inertial device, is well suited for RINS but has a larger scale factor error and poorer stability than the laser gyro; thus, it is not suitable to flip the inertial measurement unit (IMU) around the horizontal axis too much in the rotation scheme to avoid the rapid accumulation of horizontal misalignment angle. Accordingly, we propose a multi-axis alternating continuous rotation scheme for tri-axis RINS with FOG. During the navigation process, the inner, middle and outer gimbals rotate forward and reverse in sequence. The IMU rotates continuously in the three-axis direction can effectively suppress the effects of constant and slow-varying errors and also avoid the large velocity errors oscillation caused by flipping the IMU. The simulations and navigation tests show that the multi-axis alternating continuous rotation scheme can achieve navigation accuracy comparable to the multi-position rotation scheme and reduce the oscillation of velocity errors, which has important research significance and engineering value for the research of RINS with FOG.

An Improved Rotational Modulation Scheme for Tri-Axis Rotational Inertial Navigation System (RINS) with Fiber Optic Gyro (FOG)

An optimized scheme can improve the navigation accuracy of RINS without changing the inertial devices. In the multi-position stop scheme, the IMU remains stationary for most of the time, which makes motor control easier. However, the installation errors and the scale factor errors of FOG can cause platform misalignment after a certain angle of rotation around the horizontal axis, resulting in a velocity error. Continuous rotation can suppress time-varying errors better, which is of particular importance for FOG, but it can also increase the sawtooth error of the navigation output, and the error in the direction of rotation cannot be offset. To integrate the advantages of both rotation schemes, we propose an improved rotational modulation scheme for tri-axis RINS. In this scheme, the inner gimbal rotates in a two-position and four-order manner, while the middle and outer gimbals rotate continuously in the order of forward-reverse-reverse-forward. Simulation and navigation test results demonstrate that this improved rotational modulation scheme can effectively improve navigation accuracy by 50% and 25% compared with continuous rotation around the azimuth axis and a 16-position scheme with the same inertial devices, which is of great importance for RINS with FOG.

Design, modeling, and manufacturing of dual-axis inertially stabilized platform

A dual-axis inertially stabilized platform (DISP) was designed, modelled, and manufactured to control the pitch and yaw rotations continuously about Y and Z axes respectively for the purpose of tracking and observation of moving objects from a moving platform. The DISP structure consists of an inner gimbal that carries the payload (sensors) and revolves in the elevation direction about the trunnion -axis, and an outer gimbal that makes the cross-elevation rotation (azimuth). At first, 3D model of the DISP was constructed using the parametric computer-aided design (CAD) software. Then, to investigate the kinematic and dynamic performance of the systems under various excitations, A MATLAB model is generated. The designed model is optimized using CAD software to reduce and redistribute the DISP masses for better output of the model performance. The results show a small inertia effect due to the great reduction of masses of the inner and outer frames. In addition, the elevation and azimuth torques are also decreased.

Research on Innovative Self-Calibration Strategy for Error Parameters of Dual-Axis RINS

The rotational inertial navigation system (RINS) could greatly improve navigation accuracy by rotating the inertial measurement unit with gimbals. But it will also excite and amplify the corresponding error parameters, so it is more necessary to calibrate the typical error parameters accurately. Fortunately, the self-calibration strategy could be achieved conveniently in RINS. In this paper, an innovative self-calibration strategy for error parameters of dual-axis is proposed. The calibration strategy is designed that the inner and outer gimbals rotate at different angular speeds at the same time, and the whole calibration process lasts for 12 min. The relationship between the error parameters to be calibrated and the navigation error is derived, and the principle of error separation is analyzed, which proves the rationality of the strategy. The calibration strategy is verified by simulation and experiment, and the 21 error parameters of the system can be well estimated. The 3h static navigation experiment shows that the position error is less than 0.15nmile/h(CEP) after compensating the error parameters calibrated by the self-calibration strategy, and achieved the expected accuracy of the dual-axis RINS. Finally, it is proved that the calibration strategy has the obvious advantages of short calibration time and simple process, which is of great significance to improve the navigation accuracy of dual-axis RINS.

Inertial and viscous flywheel sensing of nanoparticles

Rotational dynamics often challenge physical intuition while enabling unique realizations, from the rotor of a gyroscope that maintains its orientation regardless of the outer gimbals, to a tennis racket that rotates around its handle when tossed face-up in the air. In the context of inertial sensing, which can measure mass with atomic precision, rotational dynamics are normally considered a complication hindering measurement interpretation. Here, we exploit the rotational dynamics of a microfluidic device to develop a modality in inertial sensing. Combining theory with experiments, we show that this modality measures the volume of a rigid particle while normally being insensitive to its density. Paradoxically, particle density only emerges when fluid viscosity becomes dominant over inertia. We explain this paradox via a viscosity-driven, hydrodynamic coupling between the fluid and the particle that activates the rotational inertia of the particle, converting it into a ‘viscous flywheel’. This modality now enables the simultaneous measurement of particle volume and mass in fluid, using a single, high-throughput measurement.

Neuro-observer based control of double gimbal control moment gyro systems

In this paper, a new third-order nonlinear dynamics solving the mismatched problem is proposed for double gimbal control moment gyros (DGCMGs) affected by friction and coupling torques, unmodeled dynamics, or parameter uncertainties; the new nonlinear dynamics with the control inputs and the disturbances into the same equations should not be linearized and any control method handling multivariate systems with cross-coupling between channels can be then used to design a controller. Secondly, a feed-forward neural network based observer with disturbance rejection ability is proposed to estimate both the exogenous/endogenous disturbances and the states of the system, the number of necessary sensors being decreased. Thirdly, in order to control the rotations of the inner/outer gimbals, compensate the disturbances, enhance the robustness of the control system, and handle the channel interferences, we design, evaluate, and compare two novel control architectures using the Lyapunov theory, the backstepping method or the dynamic inversion control technique. Each of the two control architectures uses two interconnected controllers (an inner gimbal controller and an outer gimbal controller), a neuro-observer, and two reference models to generate the necessary fictive control signals. The simulation results show that the proposed control approaches provide very good angular rate precision of the DGCMG system and successfully handle a wide range of disturbances, parameter uncertainties, and channel interferences. The smaller fluctuations of the rotation angles, angular rates, and angular accelerations in the gimbal channels indicate that the backstepping control provides better ability to reject disturbances, smaller overshoot and convergence time than the dynamic inversion control technique.

Two-axis Gimbal System Stabilization Using Adaptive Feedback Linearization

Background: This paper is devoted to adaptive feedback linearization based stabilization of a two-axis gimbal platform. Methods: A Lyapunov based adaptation mechanism is proposed for stabilization of a two axes gimbal system through a feedback linearized control structure. The uncertainty of the products of inertia is incorporated in the design procedure. Results: The performed computer simulations demonstrate the robust performance of the proposed two-axis gimbal stabilizer considering the cross-coupling effects between inner and outer gimbals. Conclusion: The proposed control structure could be utilized in guided missiles, spacecraft, and navigation systems.

Predictive Functional Control-Based Zenith Pass Controller Design for Roll-Pitch Seeker

A roll-pitch seeker has a wide field of view but suffers from a singularity as the sightline coincides with the outer gimbal (OG) axis. In the vicinity of the singularity, the tracking effectiveness is often degraded or even lost due to the high actuation demand on OG, which is known as the zenith pass problem. To solve this problem, this paper first proposes a novel motion model of sightline to predict the singularity in a receding horizon, where the model parameters are identified using a modified recursive least square estimator. And with the singularity predictions as set points, a predictive functional controller is then designed for the OG position control to minimize the tracking error. This novel combination control scheme is validated in MATLAB/Simulink. Simulation results have confirmed that the proposed scheme can significantly mitigate the zenith pass problem and be applied to the real-time tracking process.

Dynamical analysis and experimental verification of deviation angles caused by rubber dampers deformation in high precision mechanically dithered RLG dual-axis RINS

Abstract Deviation angles between inertial measurement unit (IMU) and turntable in dual-axis rotational inertial navigation system (RINS) degrade the navigation attitude precision seriously. And rubber dampers deformation is an unavoidable and crucial factor in deviation angles when turntable rotates for high precision mechanically dithered ring laser gyroscope (RLG) dual-axis RINS. In this paper, in order to accurately analyze the deviation angles caused by rubber dampers deformation, a novel dynamic analysis and experimental verification method for these deviation angles in dual-axis RINS is proposed. Firstly, a 3-D Voigt model for rubber damper was proposed, and then a 6-DOF dynamic model of mechanically dithered RLG dual-axis RINS was built based on the proposed 3-D Voigt model. Secondly, dynamic equations were derived based on the proposed model for inner gimbal rotation and outer gimbal rotation respectively. Then dynamic equations were solved analytically by decoupling method and the decoupling method was validated by comparing analytic solutions against numerical solutions got by Runge-Kutta method. Afterwards, rotation experiments for turntable were conducted to obtain actual deviation angles caused by rubber dampers deformation. Finally the proposed model and dynamic analysis method were validated by comparing it against the real deviation angles measured by rotation experiments for turntable.

Non-commutative, nonlinear, and non-analytic aspects of the ocular motor plant.

The ocular motor plant, consisting of the globe, extraocular muscles (EOMs), and connective tissue suspension, constitutes an intricate and non-linear actuator of eye movements. The pulley system of the rectus EOMs constitutes a non-linear inner gimbal actuated by the orbital layers of these EOMs that renders the sequence of ocular rotations effectively commutative to the central controller, and can be rotated by the outer gimbal driven by the oblique EOMs. Optic nerve (ON) length is insufficient to permit large angle adduction without tethering by the ON and sheath, creating at and beyond this threshold a large additional load on the medial rectus muscle. Finite element modeling suggests that adduction may eventually cause repetitive strain injury to the ON and glaucomatous optic nerve damage.

Economical High⁻Low Temperature and Heading Rotation Test Method for the Evaluation and Optimization of the Temperature Control System for High-Precision Platform Inertial Navigation Systems.

Inertial navigation systems (INSs) use the temperature control system to ensure the stability of the temperature of the inertial sensors for improving the navigation accuracy of the INSs. That is, the temperature control accuracy affects the performance of the INSs. Thus, the performance of temperature control systems must be evaluated before their application. However, nearly all high-precision INSs are large and heavy and require long-term testing under many different experimental conditions. As a result, conducting an outdoor navigation experiment, which involves high–low temperature and heading rotation tests, is time consuming, laborious, and costly for researchers. To address this issue, an economical high–low temperature and heading rotation test method for high-precision platform INSs is proposed, and an evaluation system based on this method is developed to evaluate the performance of the temperature control systems for high-precision platform INSs indoors. The evaluation system uses an acrylic chamber, exhaust fans, temperature sensors, and an air conditioner to simulate the environment temperature change. The outer gimbals of the platform INSs are utilized to simulate the heading rotation. The temperature control system of a high-precision platform INS is evaluated using the proposed evaluation method. The temperature difference of the gyros is obtained in the high–low temperature test, and the temperature fluctuation of the temperature control system is observed in the rotation test. These tests verify the effectiveness of the proposed evaluation method. Then, the corresponding optimization method for the temperature control system of this high-precision platform INS is put forward on the basis of the test results of the evaluation system. Experimental results show that the maximum temperature differences of the two gyros between high- and low-temperature tests are decreased from 1.51 °C to 0.50 °C, and the maximum temperature fluctuation value of the temperature control system is decreased from 0.81 °C to 0.27 °C after the proposed evaluation and optimization processes. Therefore, the proposed methods are cost effective and useful for evaluating and optimization of the temperature control system for INSs.

Fast steering and quick positioning of large field-of-regard, two-axis, four-gimbaled sight

Fast steering and quick positioning are prime requirements of the current electro-optical tracking system to achieve quick target acquisition. A scheme has been proposed for realizing these features using two-axis, four-gimbaled sight. For steering the line of sight in the stabilization mode, outer gimbal is slaved to the gyro stabilized inner gimbal. Typically, the inner gimbals have direct drives and outer gimbals have geared drives, which result in a mismatch in the acceleration capability of their servo loops. This limits the allowable control bandwidth for the inner gimbal. However, to achieve high stabilization accuracy, high bandwidth control loops are essential. This contradictory requirement has been addressed by designing a suitable command conditioning module for the inner gimbals. Also, large line-of-sight freedom in pitch axis is required to provide a wide area surveillance capacity for airborne application. This leads to a loss of freedom along the yaw axis as the pitch angle goes beyond 70 deg or so. This is addressed by making the outer gimbal master after certain pitch angle. Moreover, a mounting scheme for gyro has been proposed to accomplish yaw axis stabilization for 110-deg pitch angle movement with a single two-axis gyro.

Research on six degrees of freedom compound control technology for improving photoelectric pod pointing accuracy

High line-of-sight (LOS) pointing precision is a prerequisite for improving the laser confrontation capability of a photoelectric interference pod. In a traditional photoelectric pod, the time delay in TV tracking reduces the system phase margin, system stability and LOS pointing precision. In view of this deficiency, a normalized LMS algorithm is introduced to compensate for the TV camera delay in the inner gimbal position loop of a two-axis and four-gimbal structure, which can allow a pod to avoid system phase margin reduction. Meanwhile, a fast steering mirror (FSM) system is used to improve the LOS pointing precision. First, this paper proposes a normalized LMS algorithm. Second, a compound control structure, with an outer gimbal analog controller and an inner gimbal lag–lead controller, is designed. Finally, the FSM beam control precision is analyzed. The experimental results show that the normalized LMS algorithm yields almost no delay; moreover, the azimuth and pitch beam control accuracies are greater by a factor of 15 and 3, respectively, compared with those of a conventional photoelectric pod.

可変速2軸ジンバルCMGの特異点の回避／通過則について

Attitude control of a spacecraft using a variable-speed double-gimbal control moment gyro is considered in this paper. A steering law of this type of actuator has singular points where the rotation axis of the wheel coincides with that of the outer gimbal. Either the avoidance or passage of the singular states can be adopted in the steering law. In this paper, the steering law that selects the avoidance or passage of the singular states from the outer gimbal motion in the vicinity of the singular states is proposed. The usefulness of the steering law is examined by the ground experiments as well as the numerical simulations.

The Coupling Characteristic Investigation of Double-Gimbal Magnetically Suspended Control Moment Gyro Used on Agile Maneuver Spacecraft

Double-gimbal magnetically suspended CMG is a novel attitude control actuator for the agile maneuver spacecraft. Taking the double-gimbal magnetically suspended control moment gyro used on agile maneuver spacecraft as the research object, the dynamic model of the magnetically suspended rotor, the inner gimbal, and the outer gimbal of double-gimbal magnetically suspended control moment gyro is built. The nonlinear coupling characteristic between the rotor, the gimbal, and the spacecraft is given. It can be seen that the motion of magnetically suspended rotor does not only rely on magnetic bearing force but also suffer from the influence of gimbal servo system and spacecraft motion. The coupling torque includes the gyro coupling torque and the inertial coupling torque. The work in this paper provides the foundation for further studies.

The Simulation and analysis of a strapdown antenna platform in kinetic interception progress

A six-degree-of-freedom simulation of kinetic interceptors and modeling of a strapdown antenna platform have been worked out in Matlab Simulink to analyze the implication of nonlinear factors and the cross-coupling effect for the strapdown antenna platform. From the results of the simulation, the cross-coupling effect, which is between the inner gimbal and outer gimbal of the strapdown antenna platform, has less implication on the angular speed output. When the nonlinear factor was introduced, both the cross-coupling effect between the inner gimbal and outer gimbal and that between a missile body and antenna platform were increased. The results provide a theoretical foundation and simulation model for further research on the strapdown antenna platform.

외부짐발 선구동에 의한 EOTS의 기동성 개선

An EOTS (Electro-Optical Tracking System) provides stabilized images while tracking a moving target. This paper presents a novel concept of driving the outer gimbal first for improving the maneuverability of an EOTS, contrary to the conventional inner gimbal mode. It has the advantages of faster positioning performance and stable operation in Nadir-point. Analysis of frequency responses reveal that the present scheme results in a wider control bandwidth and larger gain margin, compared to those of the previous one. The actual experimental results confirm that the maneuvering is stable although the input command has a large angular acceleration.

Investigations of an integrated angular velocity measurement and attitude control system for spacecraft using magnetically suspended double-gimbal CMGs

This paper presents an integrated angular velocity measurement and attitude control system of spacecraft using magnetically suspended double-gimbal control moment gyros (MSDGCMGs). The high speed rotor of MSDGCMG is alleviated by a five-degree-of-freedom permanent magnet biased AMB control system. With this special rotor supported manner, the MSDGCMG has the function of attitude rate sensing as well as attitude control. This characteristic provides a new approach to a compact light-weight spacecraft design, which can combine these two functions into a single device. This paper discusses the principles and implementations of AMB-based angular velocity measurement. Spacecraft dynamics with DGMSCMG actuators, including the dynamics of magnetically suspended high-speed rotor, the dynamics of inner gimbal and outer gimbal, as well as the determination method of spacecraft angular velocity are modeled, respectively. The effectiveness of the proposed integrated system is also validated numerically and experimentally.

Mathematical model of stabilization system for data-measuring complex on moving base

The paper is devoted to actual problem of measuring-data system stabilization. The trend of the modern measuring-data development is improvement of their accuracy. For measuring-data systems mounted at the moving base the further progress of this tendency is impossible without system stabilization. The paper represents mathematical model of the stabilization system which controls position of data-measuring system mounted at platform in the gimbals with three degrees of freedom. In its turn stabilized platform with stabilized data-measuring system is mounted at the base which carries out angular motion. Using of such platforms provides high accuracy of the stabilization. Mathematical model includes both dynamic and kinematic descriptions of the gimballed platform. In the paper the important obtained results are represented such as expressions for control moments applied to outer gimbal, inner gimbal and platform. Another important result is determination of stabilization speeds and corresponding algorithm of these speeds determination. Efficiency of suggested approach is proved by the represented simulation results. The obtained results may be applied in area of wide class measuring devices stabilization.

Fast Model Predictive Control of the Nadir Singularity in Electro-Optic Systems

RECISION pointing and stabilization of the sightline are vital capabilities in all airborne electro-optic (EO) equipment. In traditional control theoryterminology,the pointingtask isatracking requirement,eitherofadynamictargetorsomeotherspecialpointof interest, and stabilization refers to the disturbance rejection capability of the sightline controller; typical disturbances are a combinationofownshipmotionandbearingfriction. Therelativeimportance between the pointing and stabilization tasks is a function of the intendedoperationoftheEOsystem;forexample,long-rangetargetingrequiresprecisestabilization,butanagilesightlineisessentialfor directed infrared countermeasures (DIRCM) systems [1], although both pointing and stabilization loops should be optimized for all systems. A DIRCM engagement occurs when the host platform is attacked by a surface-to-air missile, usually a shoulder-launched Man-Portable Air Defence missile, which is defeated when the DIRCM system positions a jamming signal onto the missile seeker. Obviously, accurate target tracking is essential over a full hyperhemispherical field of regard (FOR), as any tracking deficiencies are sure to be exploited by future missile guidance systems and tactics. Given the particular threat of global terrorism to the airline industry, future DIRCM systems should be small, lightweight, and costeffective for inclusion on commercial aircraft, which invariably limits the number of available axes for sightline control. A minimum of two axes are necessary to attain full hyperhemispherical FOR. The outer gimbal (OG) axis is usually constrained to rotate with respect to the platform z axis (through azimuth angle � ) and the inner gimbal (IG) with respect to the OG y axis (through elevation angle ). This is shown in Fig. 1. When the outerandinneraxesareorthogonal,thesightlinecanbepositionedto any orientation in space, as the IG and OG axes form an ideal orthogonal basis. However,whenthe innergimbal angleapproaches the nadir (defined as �� 90 deg) (i.e., the sightline becomes aligned with the axis of rotation of the outer gimbal), the pointing system experiences the loss of a degree of freedom known as gimbal