Inverse Dynamics of Delta Robot Based on the Principle of Virtual Work

A systematic methodology for solving the inverse dynamics of the Delta robot is presented.First,the inverse kinematics is solved based on the vector method.A new form of the Jacobi matrix formulized by the vectors is obtained so the three types kinematics singularities namely inverse, direct and combined types, can be identified with the physical meaning.Then based on the principle of virtual work, a methodology for driving the dynamical equations of motion is developed.Meanwhile the whole actuating torques, the torques caused by the gravity, the velocity and the acceleration are computed respectively in the numerical example. Results show that torque caused by the acceleration term is much bigger than the other two terms.This approach leads to efficient algorithms since the constraint forces and moments of the robot system have been eliminated from the equations of motion and there is no differential equation for the whole procedure when the principle of virtual work is applied to solving the inverse dynamical problem.

Minimum Time Overtaking Problem of Vehicle Handling Inverse Dynamics Based on Two Kinds of Safe Distances

Overtaking accidents caused by improper operations performed by a driver occur frequently. However, most stud?ies on overtaking safety have neglected research into driver control input. A novel method is proposed to obtain the driver control input during the overtaking process. Meanwhile, to improve the safety of overtaking, two types of safe distances, and the time of the overtaking are considered. Path constraints are established when considering the two types of safe distances. An optimal control model is established to solve the minimum time maneuver under multiple constraints. Using the Gauss pseudospectral method, the optimal control problem is converted into a nonlinear pro?gramming problem, which is then solved through sequential quadratic programming(SQP). In addition, the e ective?ness of the proposed method is verified based on the results of a Carsim simulation. The simulation results show that by adopting an inverse dynamics method to solve the manipulation problem of the vehicle’s minimum overtaking time, the manipulation capability of a vehicle in completing an overtaking safely within the minimum time can be obtained. This method can provide a reference for research into the active safety of manned and unmanned vehicles.

Output Feedback for Stochastic Nonlinear Systems with Unmeasurable Inverse Dynamics

This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.

Real-time trajectory planning for UCAV air-to-surface attack using inverse dynamics optimization method and receding horizon control

This paper presents a computationally efficient real-time trajectory planning framework for typical unmanned combat aerial vehicle （UCAV） performing autonomous air-to-surface （A/S） attack. It combines the benefits of inverse dynamics optimization method and receding horizon optimal control technique. Firstly, the ground attack trajectory planning problem is mathematically formulated as a receding horizon optimal control problem （RHC-OCP）. In particular, an approximate elliptic launch acceptable region （LAR） model is proposed to model the critical weapon delivery constraints. Secondly, a planning algorithm based on inverse dynamics optimization, which has high computational efficiency and good convergence properties, is developed to solve the RHCOCP in real-time. Thirdly, in order to improve robustness and adaptivity in a dynamic and uncer- tain environment, a two-degree-of-freedom （2-DOF） receding horizon control architecture is introduced and a regular real-time update strategy is proposed as well, and the real-time feedback can be achieved and the not-converged situations can be handled. Finally, numerical simulations demon- strate the efficiency of this framework, and the results also show that the presented technique is well suited for real-time implementation in dynamic and uncertain environment.

Analysis and Inverse Substructuring Computation on Dynamic Quality of Mechanical Assembly

Mechanical assembly has its own dynamic quality directly affecting the dynamic quality of whole product and should be considered in quality inspection and estimation of mechanical assembly. Based on functional relations between dynamic characteristics involved in mechanical assembly, the effects of assembling process on dynamic characteristics of substructural components of an assembly system are investigated by substructuring analysis. Assembly-coupling dynamic stiffness is clarified as the dominant factor of the effects and can be used as a quantitative measure of assembly dynamic quality. Two computational schemes using frequency response functions（FRFs） to determine the stiffness are provided and discussed by inverse substructuring analysis, including their applicable conditions and implementation procedure in application. Eigenvalue analysis on matrix-ratios of FRFs before and after assembling is employed and well validates the analytical outcomes and the schemes via both a lumped-parameter model and its analogic experimental counterpart. Applying the two schemes to inspect the dynamic quality provides the message of dynamic performance of the assembly system, and therefore improves conventional quality inspection and estimation of mechanical assembly in completeness.

Dynamic inverse control of feedback linearization in ballistic correction based on nose cone swinging

It is a complicated nonlinear controlling problem to conduct a two-dimensional trajectory correction of rockets.By establishing the aerodynamic correction force mathematical model of rockets on nose cone swinging,the linear control is realized by the dynamic inverse nonlinear controlling theory and the three-time-scale separation method.The control ability and the simulation results are also tested and verified.The results show that the output responses of system track the expected curve well and the error is controlled in a given margin.The maximum correction is about±314 m in the lengthwise direction and±1 212 m in the crosswise direction from the moment of 5 s to the drop-point time when the angle of fire is 55°.Thus,based on the dynamic inverse control of feedback linearization,the trajectory correction capability of nose cone swinging can satisfy the requirements of two-dimensional ballistic correction,and the validity and effectiveness of the method are proved.

Dynamic analysis, simulation, and control of a 6-DOF IRB-120 robot manipulator using sliding mode control and boundary layer method

Because of its ease of implementation,a linear PID controller is generally used to control robotic manipulators.Linear controllers cannot effectively cope with uncertainties and variations in the parameters;therefore,nonlinear controllers with robust performance which can cope with these are recommended.The sliding mode control(SMC)is a robust state feedback control method for nonlinear systems that,in addition having a simple design,efficiently overcomes uncertainties and disturbances in the system.It also has a very fast transient response that is desirable when controlling robotic manipulators.The most critical drawback to SMC is chattering in the control input signal.To solve this problem,in this study,SMC is used with a boundary layer(SMCBL)to eliminate the chattering and improve the performance of the system.The proposed SMCBL was compared with inverse dynamic control(IDC),a conventional nonlinear control method.The kinematic and dynamic equations of the IRB-120 robot manipulator were initially extracted completely and accurately,and then the control of the robot manipulator using SMC was evaluated.For validation,the proposed control method was implemented on a 6-DOF IRB-120 robot manipulator in the presence of uncertainties.The results were simulated,tested,and compared in the MATLAB/Simulink environment.To further validate our work,the results were tested and confirmed experimentally on an actual IRB-120 robot manipulator.

Guidance and Control for UAV Aerial Refueling Docking Based on Dynamic Inversion with L_1 Adaptive Augmentation

The guidance and control for UAV aerial refueling docking based on dynamic inversion with L1 adaptive augmentation is studied.In order to improve the tracking performance of UAV aerial refueling docking,aguidance algorithm is developed to satisfy the tracking requirement of position and velocity,and it generates the UAV flight control loop commands.In flight control loop,based on the 6-DOF nonlinear model,the angular rate loop and the attitude loop are separated based on time-scale principle and the control law is designed using dynamic inversion.The throttle control is also derived from dynamic inversion method.Moreover,an L1 adaptive augmentation is developed to compensate for the undesirable effects of modeling uncertainty and disturbance.Nonlinear digital simulations are carried out.The results show that the guidance and control system has good tracking performance and robustness in achieving accurate aerial refueling docking.

An Improved Nonlinear Dynamic Inversion Method for Altitude and Attitude Control of Nano Quad-Rotors under Persistent Uncertainties

Nonlinear dynamic inversion(NDI)has been applied to the control law design of quad-rotors mainly thanks to its good robustness and simplicity of parameter tuning.However,the weakness of relying on accurate model greatly restrains its application on quad-rotors,especially nano quad-rotors(NQRs).NQRs are easy to be influenced by uncertainties such as model uncertainties(mainly from complicated aerodynamic interferences,strong coupling in roll-pitch-yaw channels and inaccurate aerodynamic prediction of rotors)and external uncertainties(mainly from winds or gusts),particularly persistent ones.Therefore,developing accurate model for altitude and attitude control of NQRs is difficult.To solve this problem,in this paper,an improved nonlinear dynamic inversion(INDI)method is developed,which can reject the above-mentioned uncertainties by estimating them and then counteracting in real time using linear extended state observer(LESO).Comparison with the traditional NDI(TNDI)method was carried out numerically,and the results show that,in coping with persistent uncertainties,the INDI-based method presents significant superiority.

NONLINEAR DYNAMIC INVERSION CONTROL WITH ADAPTIVE COMPENSATION FOR FLIGHT CONTROL SYSTEM

A type of nonlinear dynamic inversion control with adaptive compensation is proposed in order to overcome its over sensitivity to parameter uncertainty and disturbance for flight control system using nonlinear dynamic inversion. This control strategy is different from the general strategy of a nonlinear adaptive control by taking into consideration both parameter uncertainty and external disturbance, the two major uncertain forms in flight control. Finally, an analysis of the stabilily of this control structure is given.

A new method for dynamic inversion of anisotropic equations

A new dynamic inversion method, which can simultaneously use many waves and multicomponent observation data and is suitable for directly inversing elastic parameters and density of media or wave velocities, is developed based on dynamic equations in anisotropic media. Because full wave field information is utilized as much as possible in the method, the inversion results are more reliable than that of kinematic inversion. Based on the qSH wave equation in the transversely isotropic medium and started from different initial models, seismic wave velocities are inversed by using this method, so that the validity of the method is affirmed and its suitable range is obtained. It shows that the inversion results are still very precise when the perturbational deviation of initial model parameters arrives to 12.3 percent. Besides, vectorized and parallelized calculations of the method can be easily implemented because of its special construction.

Life Extending Control of Helicopter Based on Dynamic Inversion

The purpose of using life extending control for Black Hawk UH-60 helicopter is to make a trade-off between the handling qualities and the service life of critical components. An increase in service life span results in enhanced safety and the reduction in maintenance costs. This paper presents a design methodology of life extending control for structural durability and high performance of mechanical system, which is based on an explicit dynamic inversion control scheme. A real-time nonlinear fatigue crack growth model is built to predict fatigue damage resulting from the impact of cyclic bending stress on rotor shaft, which serves as an indicator of service life. The 4-axis gainscheduled flight controller, whose gains are adjusted as a function of damage and flight velocity, is designed to regulate roll attitude, pitch attitude, vertical velocity and yaw rate. The nonlinear system simulation results show that the responses can meet the requirements on ADS-33 Level 1 handling qualities and that the 4-axis decoupling control is realized. As the damage increases, the tracking performance is slightly degraded, which results in smaller transients in bending moment response.

Dynamic inversion of the rupture parameters on fault system with complex geometry:A GPU parallel genetic algorithm based on BIEM

In this study,we attempted to perform an earthquake source dynamic inversion to obtain dynamic parameters on fault system with complex geometry.The forward modeling of the spontaneous rupture process is carried out using a boundary integral equation method(BIEM)based on unstructured meshing,and the inversion method is implemented by a genetic algorithm based on a parallel acceleration of the GPU.The source model in this study is a branched fault,which is described by two physical parameters,the initial stress T0 and the critical slip-weakening distance Dc.We investigated the effect of the inherited parameters on the accuracy and convergence of the inversion simulation.Numerical results showed that if a set of parameters are assigned properly,the inversion of rupture parameters is accurate and converges fast.It is easy to converge to a local optimal solution during the inversion process if inappropriate inherited parameters are selected.Compared with T0,D。has better convergence and accuracy in.the inversion process.

Position Control of Flexible Joint Carts Using Adaptive Generalized Dynamics Inversion

This paper presents the design and implementation of Adaptive Generalized Dynamic Inversion(AGDI)to track the position of a Linear Flexible Joint Cart(LFJC)system along with vibration suppression of the flexible joint.The proposed AGDI control law will be comprised of two control elements.The baseline(continuous)control law is based on principle of conventional GDI approach and is established by prescribing the constraint dynamics of controlled state variables that reflect the control objectives.The control law is realized by inverting the prescribed dynamics using dynamically scaledMoore-Penrose generalized inversion.To boost the robust attributes against system nonlinearities,parametric uncertainties and external perturbations,a discontinuous control law will be augmented which is based on the concept of sliding mode principle.In discontinuous control law,the sliding mode gain is made adaptive in order to achieve improved tracking performance and chattering reduction.The closed-loop stability of resultant control law is established by introducing a positive define Lyapunov candidate function such that semi-global asymptotic attitude tracking of LFJC system is guaranteed.Rigorous computer simulations followed by experimental investigation will be performed on Quanser’s LFJC system to authenticate the feasibility of proposed control approach for its application to real world problems.

Civil aircraft fault tolerant attitude tracking based on extended state observers and nonlinear dynamic inversion

For the problem of sensor faults and actuator faults in aircraft attitude control,this paper proposes a fault tolerant control(FTC)scheme based on extended state observer(ESO)and nonlinear dynamic inversion(NDI).First,two ESOs are designed to estimate sensor faults and actuator faults respectively.Second,the angular rate signal is reconstructed according to the estimation of sensor faults.Third,in angular rate loop,NDI is designed based on reconstruction of angular rate signals and estimation of actuator faults.The FTC scheme proposed in this paper is testified through numerical simulations.The results show that it is feasible and has good fault tolerant ability.

Application of a parameter-shifted grey wolf optimizer for earthquake dynamic rupture inversion

Global optimization is an essential approach to any inversion problem.Recently,the grey wolf optimizer(GWO)has been proposed to optimize the global minimum,which has been quickly used in a variety of inv-ersion problems.In this study,we proposed a parameter-shifted grey wolf optimizer(psGWO)based on the conven-tional GWO algorithm to obtain the global minimum.Com-pared with GWO,the novel psGWO can effectively search targets toward objects without being trapped within the local minimum of the zero value.We confirmed the effectiveness of the new method in searching for uniform and random objectives by using mathematical functions released by the Congress on Evolutionary Computation.The psGWO alg-orithm was validated using up to 10,000 parameters to dem-onstrate its robustness in a large-scale optimization problem.We successfully applied psGWO in two-dimensional(2D)synthetic earthquake dynamic rupture inversion to obtain the frictional coefficients of the fault and critical slip-weakening distance using a homogeneous model.Furthermore,this alg-orithm was applied in inversions with heterogeneous dist-ributions of dynamic rupture parameters.This implementation can be efficiently applied in 3D cases and even in actual earthquake inversion and would deepen the understanding of the physics of natural earthquakes in the future.

Analysis of Dynamic Variations of Crustal Density in the Longmenshan Area before the Wenchuan M_S8.0 Earthquake

Based on the repeated gravity observation data from 1996 to 2007 from the Longmenshan gravity network, which has been dealt with by adjustment processing, the benchmark interference removal and impact of elevation changes removal, and by using the 3-D inversion method to reflect underground density, we analyze the characteristics of Longmenshan regional dynamic crustal density at depths of 25km, 20km and 15kin. The results show that in the Wenchuan earthquake preparation process, the regional density field showed marked characteristics both in time and space distribution. From the point of time process, the density change trend in the ten years before the earthquake presents a periodic change pattern： steady phase, dramatic stage, slow reducing phase and slow increase phase. The degree of density changes is from large to small, which means that earthquake gestation has reached the final stage. From the point of space distribution, density change distribution has a tendency of ＂dispersion--relative concentration＂, this shows that before the earthquake, the entropy of the underground density field was decreased. In addition, dramatic density changes often occur in the Longmenshan fault zone and western Sichuan plateau. Also, with the increase of depth, the trend of density change is more and more obvious. Through comparative analysis, the influence of density change on gravity is much bigger than that from height change.

Analysis of Channeling-Path Phenomena in a Complex Fault-Block Reservoir with Low Recovery Factor and High Water-Cut Ratio

Current methods for the analysis of channeling-path phenomena in reservoirs cannot account for the influence of time and space on the actual seepage behavior.In the present study,this problem is addressed considering actual production data and dynamic characteristic parameters quantitatively determined in the near wellbore area by fitting the water-cut curve of the well.Starting from the dynamic relationship between injection and production data,the average permeability is determined and used to obtain a real-time quantitative characterization of the seepage behavior of the channeling-path in the far wellbore area.For the considered case study(Jidong oilfield),it is found that the seepage capacity of the channeling-path in the far wellbore area is far less(10 times smaller)than that of the channeling-path in the near wellbore area.The present study and the proposed model(combining near wellbore area and far wellbore area real-time data)have been implemented to support the definition of relevant adjustment measures to ultimately improve oil recovery.

NEURAL NETWORK REALIZATION OF STRUCTURAL VIBRATION CONTROL USING MR DAMPER

Magnetorheological (MR) dampers are one of the most promising new devices for civil infrastructural vibration control applications. However, due to their highly nonlinear dynamic behavior, it is very difficult to obtain of a mathematical model of inverse MR damper that has an explicit relationship between the desired damper force and the command signal (voltage). This force voltage relationship is especially required for the structural vibration control design and simulation using MR dampers. This paper focuses on using a neural network (NN) technique to emulate the inverse MR damper model. The output of the neural network can be used to command the MR damper for generating desired forces. Numerical simulations are also presented to illustrate the effectiveness of this inverse model in semi active vibration control using MR dampers.

Inertia Match of a 3-RRR Reconfigurable Planar Parallel Manipulator

Inertia match of the parallel manipulator means the ratio of the inertial load of the parallel manipulator converted to each actuator shaft and the moment of inertia of the actuator is kept within a reasonable range. Currently there are many studies on parallel manipulators, but few mention inertia parameters and inertia match of parallel manipulators. This paper focuses on the inertia characteristics of the 3-RRR reconfigurable planar parallel manipulator. On the basis of the inverse dynamic formulations deduced with the principle of virtual work, the inertia matrix of the 3-RRR planar parallel manipulator in the actuator space is obtained in algebraic form. Then, by unifying the dimension and averaging diagonal elements of the inertia matrix, the equivalent inertia of the parallel manipulator, which is the inertial load of the parallel manipulator converted to each actuator shaft, is determined. By transforming the inertia problem of the 3-RRR parallel manipulator into that of the serial multi-bar manipulator, the practicality of the equivalent inertia deduced by inverse dynamics is demonstrated. According to the physical meaning of the inertia equation, the manipulator is divided in to three parts. Further analysis is carried out on the contribution of each part to the equivalent inertia and their distributions in the required workspace, revealing that the passive links cannot ignored in calculating the equivalent inertia of the parallel manipulator. Finally, the inertia match for the 3-RRR reconfigurable parallel manipulator under three configurations is accomplished, and reducers are selected. The equivalent inertia calculation and the inertial match results illustrate that the inertia math is a necessary step to the design of the parallel manipulator, and inertia parameters dramatically affect dynamic performances of parallel manipulators. Besides, the equivalent inertia and inertial match principles, proposed in the paper, can be widely applied in the dynamic analysis and servomotors selecting for the parallel manipulator.