Relative Angular Velocity Research Articles

Cooperative pointing control of collinear double-integrators without angular velocity

We deal with the cooperative pointing control problem of collinear double-integrators with unknown rotational inertia in this paper. In particular, we consider the case that the rotational angular velocity information is not available for this coordination task. First, we propose a cooperative pointing control protocol without using the rotational angular velocity measurements. By means of the passivity tool, a distributed estimation scheme is devised to access the relative rotational angular velocity information at each agent via the relative rotational angle information of the agent and its left and respectively right neighbors. Subsequently, we redesign the cooperative pointing control protocol as well as the distributed estimation scheme in the presence of saturated relative rotational angle information. It turns out that, here the unknown rotational inertia does not prevent the coordination task because of the bidirectional interactions. Meanwhile, two local estimation schemes are also presented respectively for the above two control protocols. Besides the rigorous convergence analysis, the effectiveness of our obtained theoretical results is illustrated through numerical simulations.

A Novel Tactile Sensor for Slip Detection Based on Relative Angular Velocity

Object slippage should be prevented as one of the major challenges in robotic manipulation. Applying insufficient grasp force leads to the object slip, whereas a large predetermined grasp force can damage sensitive and fragile objects. The ability to detect slippage in real-time implementations provides required feedback for grasp force regulation, which allows the hand (gripper) to reach the appropriate grasp force and prevent object slip. Predominantly during the slip sensation, high-frequency vibrations are generated due to the relative motion between the object and the fingers. In the present work, a novel tactile slip detection sensor was developed based on the effects of skin vibrations resulting from the slip and by measuring the relative angular velocity between the skin and the rigid parts of the finger. Substantial experimental studies revealed the proposed method can detect slippage events with a 100% success rate and low latency, which reveals merits of the proposed method and the fabricated sensor. Also, the sensor arrangement is designed with an emphasis on minimizing the noise resulting from the actuation motions and vibrations, and increasing the sensitivity to the slippage events.

Optimal planning energy storage for promoting renewable power consumption in the urgent situation of UHV systems

AC/DC hybrid ultra-high voltage (UHV) transmission network is an effective way to deliver large scale renewable energy. Unfortunately, the power transmission capacity is significantly restricted due to guaranteed transient stability. Energy storage systems (ESS) are regarded to be the most flexible means to enhance transient stability. However, optimal planning of ESS for UHV stability is challenge because it involves differential equations. For this, this paper firstly proposes the mathematic formulations for optimal planning of ESS with UHV transient stability. The proposed model considers the DC blocking fault that is simulated by component switching equivalent processing. Mathematically, the proposed model belongs to the nonlinear, mix-integer, discontinuous differential constrained programming. The existing simulation and numerical methods are challenging to solve the proposed model directly. For solving this problem, an effective method is proposed, combining with the methods of implicit trapezoidal integral method, sensitivity analysis method and interior point method. The simulation results show that ESS can enhance the transmission efficiency of UHV transmission lines. From the analysis of delivery capacity, voltage distribution, the generator rotor relative swing angle and angular velocity, the technical benefit can be maximized by optimal planning ESS with the proposed method.

Kinematics of Hooke’s Joint

Problem. An analysis of the literature has shown that some issues of the kinematics and dynamics of the Hooke’s joint are not fully covered. In particular, this applies to the determination of the kinematic characteristics of the relative movements of the links in the movable joints of the crosspieces and cardan yokes, as well as the acceleration of the crosspiece in the study of the hinge. These kinematic characteristics are the basis for dynamic analysis of the cardan transmission; they are used at research of operation of the bearings of a cardan joint cross; they are necessary to determine the energy expended to overcome the forces of friction in these kinematic pairs; they form the basis for evaluating transmission efficiency. Goal. The goal of this work is to determine the kinematic characteristics of the cross in its absolute and relative motions. Methodology. The research is based on the graphical and analytical method of kinematic analysis of spherical motion of a rigid body. At the initial stage, the calculated dependences for determining the angular velocity of the cross in its absolute and relative motions were obtained. The relative angles of rotation of the links in the movable joints of the crosspiece and cardan yokes were determined by integrating the corresponding differential equations. To determine the angular acceleration of the crosspiece, the theorem on the addition of angular accelerations of a rigid body rotating around two non-parallel axes was used. Results. The study of the kinematics of the cardan joint made it possible to identify and eliminate ambiguities in determining the relative angular velocities of the elements of the kinematic pairs of the cross and cardan yokes. Functional dependences for determination of angular acceleration of a crosspiece in absolute and relative movements, and also relative angles of rotation of links in kinematic pairs of a crosspiece and cardan yokes were received. It was shown that the angular acceleration of the crosspiece is a periodic function of the angle of rotation of the input link. During the operation of the hinge, the crosspiece creates insignificant periodic dynamic loads, which should be taken into account in accurate calculations of high-speed cardan transmissions. Practical value. The work is devoted to the study of the kinematics of the asynchronous hinge, which is the foundation for its dynamic analysis and ultimately aimed at improving the output performance of the cardan transmission. The research method combines mathematical calculations with simplicity and clarity of graphic constructions, which contributes to a deeper understanding of the kinematic features of a hinge of uneven angular velocities. The obtained results can be used in the design and study of motor-transmission units, which include the Hooke’s joint.

Optimal disc brake design for reducing squeal instability using slip-dependent complex eigenvalue analysis

This paper proposes an improved disc brake system optimization method for squeal instability reduction using slip-dependent eigenvalue results. Although complex eigenvalue analysis is widely used for minimizing brake squeal instability, conventional optimization approaches still have the limitation of not being able to reflect slip rate-varying squeal instability characteristics. While relative angular velocity between the pad and disc declines due to braking, disc brake system instability gradually increases up to a specific peak velocity point and decreases until the vehicle stops, which means a maximum instability point exists during the braking process. Therefore, instability optimization should target the prevention of a maximum value during a braking scenario. The proposed optimization formulation is conducted considering maximum instability during full braking. To obtain braking time profiles, a model-based design method is employed and utilized instead of full finite element transient dynamic analysis to reduce computational cost. Kriging surrogate modeling is also used for solving the optimization problem and better express the multi-variable squeal problem. The proposed optimal design method produces minimal squeal instability during the full vehicle braking time range. The effectiveness of the proposed disc brake optimal design is demonstrated via acceleration power value comparison of the structure acceleration with that derived by conventional optimization approach.

Indirect-Neural-Approximation-Based Fault-Tolerant Integrated Attitude and Position Control of Spacecraft Proximity Operations.

In this paper, a neural adaptive fault-tolerant control scheme is proposed for the integrated attitude and position control of spacecraft proximity operations in the presence of unknown parameters, disturbances, and actuator faults. The proposed controller is made up of a relative attitude control law and a relative position control law. Both the relative attitude control law and relative position control law are designed by adopting the neural networks (NNs) to approximate the upper bound of the lumped unknowns. Benefiting from the indirect neural approximation, the proposed controller does not need any model information for feedback. In addition, only two adaptive parameters are required for the indirect neural approximation, and the online calculation burden of the proposed controller is therefore significantly reduced. Lyapunov analysis shows that the overall closed-loop system is ultimately uniformly bounded. The proposed controller can ensure the relative attitude, angular velocity, position, and velocity stabilize into the small neighborhoods around the origin. Lastly, the effectiveness and superior performance of the proposed control scheme are confirmed by a simulated example.

A small family service robot system with uncalibrated monocular camera for visual servoing tracking fast moving family targets in short range

Small family service robots are essential applications in service robots, and their accurate tracking of moving targets is the primary condition for robot-human interaction. Compared with long-range target tracking, the limited family space leads to the short distance between the robot and the target, which often leads to the problem of large circumferential relative angular velocity between the robot and the moving target. It dramatically reduces the ability of the robot to track the fast target motion at close range and at different scales. In this paper, a novel family service robot system based on monocular RGB and robot terminal calculation is proposed to track fast-moving targets in close range. Based on the construction of the robot body with two rotation directions, the neural network model is used for visual detection and recognition of the target object. Combined with the historical information of the target, the new relative azimuth information of the target object is calculated to control the changes in the pitch angle and yaw angle of the robot body and realize the servo tracking of the robot vision on the moving target. Experimental results confirm the visual servoing tracking ability of the tiny family service robot system for indoor moving objects, which will positively promote the application of small intelligent service robots.

КЕРУВАННЯ ПРОЦЕСОМ МАНЕВРУВАННЯ ЧОТИРИКОЛІСНОГО СПЕЦІАЛЬНОГО ШАСІ З КОМБІНОВАНОЮ ЕНЕРГЕТИЧНОЮ УСТАНОВКОЮ

Cars with electric and hybrid drive of driving wheels have become widespread in the world in recent years. For a wide class of wheeled vehicles with a combined electromechanical drive, it became possible to make the front axle swivel, which makes it possible to increase their maneuverability. The use of separate control of electric motors of the front swivel drive axle makes it possible to control the turning of machines by creating a difference in tangential reactions on the front wheels. This article analyzes the controllability of a four-wheeled special chassis with a combined power plant when creating a difference in torque on the front wheels. The obtained analytical dependences make it possible to evaluate the controllability of vehicles with a front steering axle. It is determined that the indicators of controllability and turning (angular acceleration and angular velocity) with the front rotary drive axle and the creation of a torque difference on its wheels are higher than in the case of equality of certain moments. The influence of the law of changing the difference of torques on the kinematic parameters of the car turning is investigated. It is determined that for each of the three laws of changing the difference in torques, the relative angular velocity of the car turning increases with time. The proposed steering is a system with two degrees of freedom, since two independent control actions are created at its input - turning the steering wheel and creating a difference in torque on the front wheels. Therefore, the solution of the task was carried out using a complex motion model. It should be said that the rigid wheels of the car were considered. When studying the movement of a car with wheels that are elastic in the lateral direction, it is necessary to use a model of a multicomponent complex movement, consisting of one portable and two relative movements. The second relative movement is the movement due to the deformation of the tires during their lateral withdrawal.

Theoretical and Numerical Analysis of Coupled Axial-Torsional Nonlinear Vibration of Drill Strings

Based on a lumped parameter model with two degrees of freedom, the periodic response of the coupled axial-torsional nonlinear vibration of drill strings is studied by HB-AFT (harmonic balance and alternating frequency/time domain) method and numerical simulations. The amplitude-frequency characteristic curves of axial relative displacement and torsional relative angular velocity are given to reveal the mechanism of bit bounce and stick-slip motion. The stability of periodic response is analyzed by Floquet theory, and the boundary conditions of bifurcation of periodic response are given when parameters such as nominal drilling pressure, angular velocity of turntable, and formation stiffness are varied. The results show that the amplitude of the periodic response of the system precipitates a spontaneous jump and Hopf bifurcation may occur when the angular velocity of the turntable is varied. The variation of parameters may lead to the complex dynamic behavior of the system, such as period-doubling motion, quasiperiodic motion, and chaos. Bit bounce and stick-slip phenomenon can be effectively suppressed by varying the angular velocity of turntable and nominal drilling pressure.

An advanced multipole model for (216) Kleopatra triple system

Aims.To interpret adaptive-optics observations of (216) Kleopatra, we need to describe an evolution of multiple moons orbiting an extremely irregular body and include their mutual interactions. Such orbits are generally non-Keplerian and orbital elements are not constants.Methods.Consequently, we used a modifiedN-body integrator, which was significantly extended to include the multipole expansion of the gravitational field up to the orderℓ= 10. Its convergence was verified against the ‘brute-force’ algorithm. We computed the coefficientsCℓm,Sℓmfor Kleopatra’s shape, assuming a constant bulk density. For Solar System applications, it was also necessary to implement a variable distance and geometry of observations. Ourχ2metric then accounts for the absolute astrometry, the relative astrometry (second moon with respect to the first), angular velocities, and silhouettes, constraining the pole orientation. This allowed us to derive the orbital elements of Kleopatra’s two moons.Results.Using both archival astrometric data and new VLT/SPHERE observations (ESO LP 199.C-0074), we were able to identify the true periods of the moons,P1= (1.822359 ± 0.004156) d,P2= (2.745820 ± 0.004820) d. They orbit very close to the 3:2 mean-motion resonance, but their osculating eccentricities are too small compared to other perturbations (multipole, mutual), meaning that regular librations of the critical argument are not present. The resulting mass of Kleopatra,m1= (1.49 ± 0.16) × 10−12M⊙or 2.97 × 1018kg, is significantly lower than previously thought. An implication explained in the accompanying paper is that (216) Kleopatra is a critically rotating body.

Hand-Finger Pose Estimation Using Inertial Sensors, Magnetic Sensors and a Magnet

Hand-finger motion tracking based on inertial and magnetic measurement units (IMMUs) has become a well-accepted method in many applications such as rehabilitation and virtual reality. However, existing systems require an IMMU on each segment of the whole hand and known length of each segment, which is hard to achieve for users. Therefore, we proposed a small sensor configuration with three IMMUs and a magnet to estimate poses of interested fingertips relative to the hand. The relative orientations were estimated by integrating relative angular velocity and fused with relative orientation estimation during time intervals when the whole hand moved or rotated as one object. The relative positions were estimated by using a magnetic dipole model of the magnet and prior estimated relative orientations. The performance has been demonstrated in multiple experiments. For whole hand rotation and functional grasping or writing experiments, the estimated errors of index fingertip position and orientation relative to the hand were 8.0~9.8 mm and 5.7° ~11.2°. For index finger flexion and pinching, the estimated errors of index fingertip position and orientation relative to the hand were 16.2~25.2 mm and 20.6° ~ 21.7°.

A study of factors affecting torque transmission in permanent magnet-based magnetorheological fluid clutch

In this article, the study of several factors affecting the torque transmission capability of a permanent magnet-based, drum-type magnetorheological fluid (MRF) clutch is presented. These factors are: number of magnetic poles in the magnet assembly, material of the clutch, MRF layer thickness, and relative rotational velocity between the input and output stages of the clutch. For this purpose, a special single-MRF layer clutch was designed and fabricated, one which allows the convenient assembly and disassembly to reduce preparation time for testing. The average transmitted torque of this clutch under several combinations of the aforementioned factors was recorded and analyzed. Additionally, several magnetostatic simulations of the clutch were carried out, and both the magnetic flux density and transmittable torque calculated from the results of these simulation were compared against experimental measurements. It was found that magnet assemblies with lower number of magnetic poles resulted in higher torque outputs, however, the effectiveness of the utilized torque variation mechanism was reduced due to magnetic saturation of the components of the clutch. The material of the clutch was found to have a significant effect at low relative rotational velocities, resulting in a nonlinear relationship between transmitted torque and relative angular velocity. This nonlinear effect was more significant when aluminum was used in the components which interact directly with the MR fluid whereas the use of ferromagnetic components reduced this effect. Finally, the thickness of the MRF layer was found to have a significant effect on the transmitted torque of the MRF clutch, although not according to what magnetostatic simulations predict.

Relative Position and Attitude Estimation of Non-cooperative Spacecraft Based on Stereo Camera and Dynamics

The relative position and attitude estimation of non-cooperative spacecraft is essential to high-precision guidance, navigation, and control systems. This paper mainly proposes a method to measure the relative position, velocity and attitude of non-cooperative spacecrafts using stereo camera and dynamics. First, using stereo camera observe the spacecraft, and extract the feature points of images. Then, calculate the 3D position of the feature points, and match the relationship between the feature points to obtain geometric constraint information between frames. Based on this, the relative position, velocity, attitude and angular velocity of the target spacecraft are calculated. According to relative orbit dynamics and relative attitude dynamics model, design extended Kalman filter to update the measurement results. The simulation results show that the estimation accuracy is better than 0.01m, the relative velocity accuracy is better than 0.001m/s, and the relative attitude accuracy is better than 0.01°. This method can provide technical support for the relative navigation of non-cooperative spacecraft.

Robust neural-network-based quasi-sliding-mode control for spacecraft-attitude maneuvering with prescribed performance

This paper investigates the robust tracking control problem for spacecraft attitude maneuvering with prescribed performance. Firstly, a control scheme is studied based on a quasi-sliding-mode approach which can simultaneously restrict the convergence speed and the steady-state error of both Euler angle and relative angular velocity. Then, to reduce actuators' energy consumption, a three-layer back-propagation neural network is combined with the above control law to auto-tune the control gains. Finally, the performance and effectiveness of the control approach are demonstrated by numerical simulation.

A Sliding-Mode Control Algorithm to Enhance In-Hand Motion Capabilities

Abstract This article reports a method for regulating the internal forces during in-hand manipulation of an unknown shaped object with soft robotic fingers. The internal forces ensure that the object does not move between the robotic fingers, thus improving the grip. It is shown that if soft fingers show bounded conformity and the finger–object interface have bounded relative slip, then the relative angular velocity between the object and the fingertip coordinate frame in contact is bounded. Detailed derivation of the proof is presented. The proof is later used to define a new metric of relative slip. The metric is used to design a sliding mode control algorithm that results in an efficient grip, which is robust toward uncertainty in object shape. The robotic fingers are assumed to be under virtual rigidity constraint, that is, the distance between the fingertips do not change. The control algorithm is attractive as it skirts requirement of information of the shape of the object or to solve optimization problems. The grip with the robust control algorithm is shown to be finite-time stable through Lyapunov’s method. The methodology is demonstrated using simulations.

Mathematical Model of Satellite-Inertial Mobile Computational Gravimetry

The article proposes a mathematical model of a hybrid system installed on board of a moving object and represented by an inertial sensor of the vector of specific forces — a three-component newtonometer with orthogonal sensitivity axes and a network of receivers of a navigation satellite system (HSS). The purpose of this hybrid system is the temporal estimations of the nearEarth gravitational field on the trajectory of the object. Within the Newtonian mechanics the possibility of choosing an inertial reference system with a beginning at the center of mass of the Earth is assumed; сomplementary to the PZ-90 (Russia) and WGS-84 (USA) standards, the following are introduced: 1) an ellipsoidal (geodesic) coordinate system, rigidly connected with the solid Earth; 2) two movable accompanying right-angled trihedrals with a common origin as a point whose movement forms the trajectory of the object; the instrument one, is rigidly connected with the object as a solid body, and is thus freely oriented, other one are geographic, and permanently oriented to the cardinal points (East, North, Zenith). In the presentation of kinematics, attention is drawn to the fact that the variability of the absolute linear velocity in inertial space explained by the motion of an object relative to solid Earth and its own rotation is characterized by rotational vectors of relative and portable velocities which identify the vectors of relative and portable angular rotational velocities of the undeformable geographic trihedron and are represented projections on its axis. The causality of the trajectory is determined by Newton’s second law; in projections on the axis of the moving geographic trihedron, component-wise recording of the equations of dynamics is performed, which are resolved with respect to the components of the strength of the gravitational field. It is noted that the previous article by the authors is devoted to the problem of a high-precision estimate of the kinematic parameters of motion equations. In such a context it is indicated that direct calculation of the gravitational field strength requires the convertting of Newtonometer measurements from the instrument trihedron to the geographic one. The required linear transformation for this is constructed considering the possibilities of multiposition of the NSS object. A computational experiment is described and some of its results are presented.

Stereovision‐based initial pose estimation relative to non‐cooperative space target

Initial relative parameters are of great importance as inputs of the subsequent filter process based on the stereovision system. The relative dynamic model is approximated to estimate the initial relative state. Firstly, the error distribution property of feature point captured using cameras can be approximately regarded to be zero-mean Gaussian distribution when the measurement error of pixel is assumed to be the same. Furthermore, the cofactor matrix can be derived to describe the error distribution property. Built on what is mentioned above, the weighted total least square is adopted to compute the relative angular velocity. To analyse the estimation precision of the algorithm, the Cramer-Rao low bound is also exploited to calculate the theoretical precision trend with the number of the feature point. The relative position estimation uses the particle swarm optimisation algorithm to seek optimal solution due to the fact that the corresponding coefficient matrix is not full rank. Finally, three groups of simulation experiments are conducted to verify its effectiveness. The experiment results show that this algorithm can be utilised to estimate the initial relative state.

Simulation of Brain Response to Noncontact Impacts Using Coupled Eulerian-Lagrangian Method.

Finite element (FE) method has been widely used for gaining insights into the mechanical response of brain tissue during impacts. In this study, a coupled Eulerian-Lagrangian (CEL) formulation is implemented in impact simulations of a head system to overcome the mesh distortion difficulties due to large deformation in the cerebrospinal fluid (CSF) region and provide a biofidelic model of the interaction between the brain and skull. The head system used in our FE model is constructed from the transverse section of the human brain, with CSF modeled by Eulerian elements. Spring connectors are applied to represent the pia-arachnoid connection between the brain and skull. Validations of the CEL formulation and the FE model are performed using the experimental results. The dynamic response of brain tissue under noncontact impacts and the brain regions susceptible to injury are evaluated based on the intracranial pressure (ICP), maximum principal strain (MPS), and von Mises stress. While tracking the critical MPS location on the brain, higher likelihood of contrecoup injury than coup injury is found when sudden brain-skull motion takes place. The accumulation effect of CSF in the ventricle system, under large relative brain-skull motion, is also identified. The FE results show that adding relative angular velocities, to the translational impact model, not only causes a diffuse high strain area, but also cause the temporal lobes to be susceptible to cerebral contusions since the protecting CSF is prone to be squeezed away at the temporal sites due to the head rotations.

Leader-follower formation control of nonholonomic mobile robots with bearing-only measurements

This paper investigates the leader-follower formation control problem of nonholonomic vehicles. An estimator is first developed to estimate the relative position in its local coordinate system with bearing measurements, to avoid directly using positions or relative positions in the global reference frame. A control law is then proposed for the follower vehicle to follow the leader based on the estimated relative position. It is shown that the estimation error converges to zero, if some conditions on the relative angular velocity between the leader and the follower are satisfied. It is also shown that the stability of the closed loop system involving both the estimator and the controller is guaranteed if some mild conditions on the trajectory of the leader are satisfied. Extension to the case of multiple followers is also considered. Simulation results of numerical examples verify the effectiveness of the proposed control scheme.

Lubrication modeling and wear calculation in artificial hip joint during the gait

Abstract In the framework of Total Hip Replacement (THR), the aim of this paper was to propose a novel 3D contact-lubrication model for the in-silico prosthetic wear calculation during the gait. The approach is based on the Reynolds equation and in-vivo loads were selected for the simulations. The hip relative angular velocities were calculated by a commercial musculoskeletal software. In the considered conditions, by using the Archard wear theory, the model allows the determination of the unsteady fluid film pressure and the volumetric wear rate prediction. With reference to a Ceramic on Polyethylene hip prosthesis, the volumetric wear rate was calculated showing a good agreement with the values obtained by other Authors as a result of FEM approaches or in-vitro tests.