Kane's Method Research Articles

Linear-parameter-varying-based adaptive sliding mode control with bounded L2 gain performance for a morphing aircraft

Large-scale morphing aircraft can adaptively alter configuration according to the different flight conditions or a variety of missions to ensure the optimal aerodynamic performance. However, this will certainly put forward a higher request to modeling method and controller performance. In this paper, we propose an adaptive sliding mode control strategy with bounded L2 gain performance based on linear-parameter-varying methodology for the robust control of a morphing aircraft with variable span and variable sweep angle. Using the Kane method, the longitudinal dynamic model of the morphing aircraft is derived. Moreover, the linearized linear-parameter-varying model of the aircraft in the wing varying process is formulated for controller synthesis. The adaptive sliding mode control synthesis for this uncertain linear-parameter-varying system consists of two steps. Firstly, based on the full block S-procedure, the sufficient condition in form of linear matrix inequality constrains is derived for the existence of a reduced-order sliding mode dynamics. Then, the synthesized adaptive sliding mode control is proved to drive the linear-parameter-varying system trajectories onto the predefined switching surface without the information of upper bound of external disturbances. The performance and robustness of the proposed controller are verified by the numerical results.

Heel-strike and toe-off motions optimization for humanoid robots equipped with active toe joints

SUMMARYIn this paper, a walking pattern optimization procedure is implemented to yield the optimal heel-strike and toe-off motions for different goal functions. To this end, first, a full dynamic model of a humanoid robot equipped with active toe joints is developed. This model consists of two parts: multi-body dynamics of the robot which is obtained by Lagrange and Kane methods and power transmission dynamic model which is developed using system identification approach. Then, a gait planning routine is presented and consistent parameters are specified. Several simulations and experimental tests are carried out on SURENA III humanoid robot which is designed and fabricated at the Center of Advanced Systems and Technologies located in the University of Tehran. Afterward, a genetic algorithm optimization is adopted to compute the optimal walking patterns for five different goal functions including energy consumption, stability margin, joint velocity, joint torque and required friction coefficient. Also, several parametric analyses are performed to characterize the effects of heel-strike and toe-off angle and toe link mass and length on these five goal functions. Finally, it is concluded that walking pattern without heel-strike and toe-off motions requires less friction coefficient than the pattern with heel-strike and toe-off motions. Also, heavier toe link lowers tip-over instability and slippage occurrence possibility, but requires more energy consumption and joint torque.

Flight Dynamics Modeling and Control of a Novel Catapult Launched Tandem-Wing Micro Aerial Vehicle With Variable Sweep

In this paper, the variable sweep is used as a replacement for the conventional control surfaces for flight control on a tandem-wing micro aerial vehicle (MAV). This configuration allows the MAV to be folded into and launched from a tubular catapult while also retaining an adequately high effectiveness and a simple structure. As new control inputs, the four sweep angles of the MAV are planned as symmetric and asymmetric morphing to eliminate the reactive forces between the airfoils and fuselage during morphing. The aerodynamic characteristics of the MAV are presented through numerical simulations to study the effects of variable sweep morphing. An accurate nonlinear multibody dynamic model of the variable sweep MAV is established using the Kane method. Next, open-loop dynamic responses of sweep morphing based on the nonlinear dynamic model are analyzed and compared with the responses caused by the elevons control mode to examine the control effectiveness. Moreover, a flight control law based on sweep control is designed and verified using a height and yaw tracking simulation with different actuator response rates. The results show that the sweep control mode produces weaker coupling between the longitudinal and lateral dynamics than the elevons control mode and that the innovative approach for flight control is feasible and effective.

Modal Decoupled Dynamics-Velocity Feed-Forward Motion Control of Multi-DOF Robotic Spine Brace

Based on the parallel robotic manipulator, this paper proposes a motion control strategy for the novel robotic spine brace for spinal rehabilitation exercises. However, several shortcomings of this parallel robotic manipulator, such as dynamic coupling in joint space, low response frequency in roll and pitch directions, and bad influence of device’s gravity, result in bad effects on the performance of the robotic spine brace system. For solving these problems of parallel robotic manipulator, a new motion control structure, modal space dynamics-velocity feed-forward (MSDF) motion control strategy, is designed in this paper. A robotic spine brace system model and an actuator dynamic model are expressed using the Kane method. Stability of the robotic system with the MSDF control method is analyzed. For evaluating the performances of the proposed motion control structure, an experimental parallel robotic manipulator is built. Experimental results reveal that the presented MSDF motion control strategy can eliminate those disadvantages efficiently.

Modeling and control for ultra-low altitude cargo airdrop

PurposeThe purpose of this paper is to model the aircraft-cargo’s coupling dynamics during ultra-low altitude heavy cargo airdrop and to design the aircraft’s robust flight control law counteracting its aerodynamic coefficients perturbation induced by ground effect and the disturbance from the sliding cargo inside.Design/methodology/approachAircraft-cargo system coupling dynamics model in vertical plane is derived using the Kane method. Trimmed point is calculated when the cargo fixed in the cabin and then the approximate linearized motion equation of the aircraft upon it is derived. The robust stability and robust H∞ optimal disturbance restraint flight control law are designed countering the aircraft’s aerodynamic coefficients perturbation and the disturbance moment, respectively.FindingsNumerical simulation shows the effectiveness of the proposed control law with elevator deflection as a unique control input.Practical implicationsThe model derived and control law designed in the paper can be applied to heavy cargo airdrop integrated design and relevant parameters choice.Originality/valueThe dynamics model derived is closed, namely, the model can be called in numerical simulation free of assuming the values of parachute’s extraction force or cargo’s relative sliding acceleration or velocity as seen in many literatures. The modeling is simplified using Kane method rather than Newton’s laws. The robust control law proposed is effective in guaranteeing the aircraft’s flight stability and disturbance restraint performance in the presence of aerodynamic coefficients perturbation.

Flutter suppression and stability analysis for a variable-span wing via morphing technology

A morphing wing can enhance aerodynamic characteristics and control authority as an alternative to using ailerons. To use morphing technology for flutter suppression, the dynamical behavior and stability of a variable-span wing subjected to the supersonic aerodynamic loads are investigated numerically in this paper. An axially moving cantilever plate is employed to model the variable-span wing, in which the governing equations of motion are established via the Kane method and piston theory. A morphing strategy based on axially moving rates is proposed to suppress the flutter that occurs beyond the critical span length, and the flutter stability is verified by Floquet theory. Furthermore, the transient stability during the morphing motion is analyzed and the upper bound of the morphing rate is obtained. The simulation results indicate that the proposed morphing law, which is varying periodically with a proper amplitude, could accomplish the flutter suppression. Further, the upper bound of the morphing speed decreases rapidly once the span length is close to its critical span length.

Analysis of dynamic response of a restraining system for a powerless advancing ship based on the Kane method

Following general explanations of the working principles of different existing retardation systems to restrain an advancing powerless ship the principles of a new overhead retardation system are presented. A two dimensional simplified model of the activated overhead system is formulated based on Huston’s interpretation of the Kane methodology. Reduced Kane equations are used in the actual simulation, once initial conditions and mechanical analysis of constituent elements have been formulated. Having presented the computational process the various velocity, motion and joint constraint force characteristics of the anchor, the ship and the other elements are monitored in the time domain for the duration of the retardation process. Validation of the Kane based method is established utilising the conservation law and the Lagrangian based formulation of the retardation system within the ADAMS software. The results indicate that a peak value of constraint will occur because of the sudden movement of anchor and this peak is affected significantly by initial ship speed. Variation in anchor chain, overall cable length and its horizontal projected length has little influence upon retardation system performance, whilst the changes of sea bed friction, anchor mass, water depth, initial ship velocity and ship mass will make retardation behaviour different.

Maneuver and Active Vibration Suppression of Free-flying Space Robot

This work studies the maneuver control and vibration suppression of a flexible free-flying space robot using variable-speed control moment gyros as actuators. A novel flexible space manipulator is designed. The dynamics of the flexible multibody system is derived by using Kane method. Based on the singular perturbation approach, the dynamics of the flexible manipulator is decoupled into a slow subsystem and a fast subsystem. The slow subsystem is associated with the rigid motion dynamics, and the fast subsystem is related to the link flexible dynamics. A composite control strategy is proposed as a combination of two controllers for these subsystems. An adaptive sliding mode controller is designed for the slow subsystem, and an adaptive controller is designed for the fast subsystem. Uncertainty estimation can be achieved by the adaptive terms of the composite controller. A weighted robust pseudo-inverse steering law is proposed for the variable-speed control moment gyros. Numerical results demonstrate that the proposed composite controller is robust to parameter uncertainties and external disturbances.

Design of LPV-Based Sliding Mode Controller with Finite Time Convergence for a Morphing Aircraft

This paper proposes a finite time convergence sliding mode control (FSMC) strategy based on linear parameter-varying (LPV) methodology for the stability control of a morphing aircraft subject to parameter uncertainties and external disturbances. Based on the Kane method, a longitudinal dynamic model of the morphing aircraft is built. Furthermore, the linearized LPV model of the aircraft in the wing transition process is obtained, whose scheduling parameters are wing sweep angle and wingspan. The FSMC scheme is developed into LPV systems by applying the previous results for linear time-invariant (LTI) systems. The sufficient condition in form of linear matrix inequality (LMI) constraints is derived for the existence of a reduced-order sliding mode, in which the dynamics can be ensured to keep robust stability and L2 gain performance. The tensor-product (TP) model transformation approach can be directly applied to solve infinite LMIs belonging to the polynomial parameter-dependent LPV system. Then, by the parameter-dependent Lyapunov function stability analysis, the synthesized FSMC is proved to drive the LPV system trajectories toward the predefined switching surface with a finite time arrival. Comparative simulation results in the nonlinear model demonstrate the robustness and effectiveness of this approach.

Differential Weighting for Subcomponent Measures of Integrated Clinical Encounter Scores Based on the USMLE Step 2 CS Examination: Effects on Composite Score Reliability and Pass-Fail Decisions.

Medical schools administer locally developed graduation competency examinations (GCEs) following the structure of the United States Medical Licensing Examination Step 2 Clinical Skills that combine standardized patient (SP)-based physical examination and the patient note (PN) to create integrated clinical encounter (ICE) scores. This study examines how different subcomponent scoring weights in a locally developed GCE affect composite score reliability and pass-fail decisions for ICE scores, contributing to internal structure and consequential validity evidence. Data from two M4 cohorts (2014: n = 177; 2015: n = 182) were used. The reliability of SP encounter (history taking and physical examination), PN, and communication and interpersonal skills scores were estimated with generalizability studies. Composite score reliability was estimated for varying weight combinations. Faculty were surveyed for preferred weights on the SP encounter and PN scores. Composite scores based on Kane's method were compared with weighted mean scores. Faculty suggested weighting PNs higher (60%-70%) than the SP encounter scores (30%-40%). Statistically, composite score reliability was maximized when PN scores were weighted at 40% to 50%. Composite score reliability of ICE scores increased by up to 0.20 points when SP-history taking (SP-Hx) scores were included; excluding SP-Hx only increased composite score reliability by 0.09 points. Classification accuracy for pass-fail decisions between composite and weighted mean scores was 0.77; misclassification was < 5%. Medical schools and certification agencies should consider implications of assigning weights with respect to composite score reliability and consequences on pass-fail decisions.

Vibration analysis of rotating pretwisted tapered blades made of functionally graded materials

This paper presents a new structural dynamic model with which vibration characteristics of rotating blades made of functionally graded materials (FGMs) can be investigated. The equations of motion of a rotating pretwisted tapered blade made of FGM are derived using the Rayleigh-Ritz assumed mode method along with the Kane's method. After converting the equations of motion into dimensionless forms, dimensionless natural frequencies are obtained by solving the modal formulation of the dimensionless equations. Various dimensionless geometric parameters like pretwist angle, taper ratios, hub radius ratio and width-to-thickness ratio as well as continuous variation of material properties along the blade thickness are considered to obtain the new structural dynamic model. The accuracy and efficiency of the proposed model are verified through a comparison study first. Then, effects of the volume fraction index, Young's modulus ratio, hub radius ratio, pretwist angle, taper ratios, width-to-thickness ratio and angular speed upon the dimensionless natural frequencies of the FG blade are investigated using the proposed model. In addition, an algebraic condition under which dimensionless natural frequencies can be minimized is obtained.

Dynamics: Theory and Application of Kane's Method

Dynamics: Theory and Application of Kane's Method

연결된 세 보 구조를 갖는 다모드 압전 에너지 하베스터의 전기-역학적 모델링 및 해석

Electromechanical model for analyzing a multimodal piezoelectric energy harvester comprising three connected beams is presented in this paper. This system consists of three beams which are connected alternately. The piezoelectric layer is only attached to the middle beam. With this special structural configuration, the first, second, and third natural frequencies are congregated so that the energy harvester can generate meaningful amount of power consistently when the main frequency component of the excitation varies around the lowest three natural frequencies of the harvester. To investigate the dynamic and electric response of the piezoelectric energy harvester, an electromechanical model is developed using the Kane's method and the accuracy of the model is validated by comparing the results obtained with the model with those obtained with the commercial software ANSYS. The results show that the piezoelectric energy harvester comprising three connected beams has much broader power generating frequency range than that of the conventional piezoelectric energy harvester.

Dynamic modeling and control of a 6-DOF micro-vibration simulator

A micro-vibration simulator with multiple degrees of freedom is required for performance testing of sensitive instruments in a micro-vibration environment on-board spacecraft before launch. In this study, a novel 6-DOF micro-vibration simulator (6-MVS) is proposed, which can reproduce a micro-vibration environment with a wide bandwidth of disturbance frequencies. The complete inverse dynamic equations of the proposed 6-MVS are derived using the Kane method, which is very suitable for processing by computer. The validity of the derived dynamic equations is then verified by co-simulation. The structural performance of the 6-MVS is investigated using the finite element method. Based on this dynamic model, a robust proportional-integral (PI) control scheme is then performed. The control performance of the proposed controller is evaluated by co-simulation. The analysis and simulation results show that the proposed robust PI controller has excellent robustness and stability and the 6-MVS can exactly produce the required micro-vibration spectrum.

Prototype design, modeling, and experimental research of a novel lower limb powered exoskeleton

In this paper, a new type of lower limb powered exoskeleton is presented, which is based on a screw-nut actuated mechanism to help paraplegics to stand, walk and accomplish activities of daily living. The Denavit–Hartenberg method and the Kane method are adopted to establish a kinematic and dynamic model of novel lower limb powered exoskeleton to analyze the workspace and the control strategy simulation. A double-closed loop control strategy is proposed to ensure precision, and its effectiveness is validated. The results of prototype gait control and patient experiments show that the new type of lower limb powered exoskeleton can enable patients to realize stable and smooth walking.

纵列式航模直升机建模与分析

根据纵列式双旋翼直升机具有的不同于单旋翼带尾桨直升机的特点，提出建立纵列式直升机数学模型的方法。将纵列式双旋翼直升机看作3个刚体(机体和前后两副旋翼)，利用分析力学的Kane方法建立直升机的动力学模型，并对模型进行分析。在适当的条件下将数学模型进行简化，导出简化的平移方程和转动方程，在MATLAB/Simulink界面进行仿真，对仿真结果进行分析，为控制器的设计提供依据。 Based on the difference between tandem helicopters and single rotor helicopters, the tandem helicopter was modeled as three rigid bodies: fuselage and two tail rotors. The dynamical model was deduced by Kane method. The mathematical model was simplified to develop simpler translational and rotational equations. The model was simulated in the environment of MATLAB/Simulink. It would provide the basis for the control system of the unmanned tandem helicopter.

Kane Method Based Dynamics Modeling and Control Study for Space Manipulator Capturing a Space Target

Dynamics modeling and control problem of a two-link manipulator mounted on a spacecraft (so-called carrier) freely flying around a space target on earth’s circular orbit is studied in the paper. The influence of the carrier’s relative movement on its manipulator is considered in dynamics modeling; nevertheless, that of the manipulator on its carrier is neglected with the assumption that the mass and inertia moment of the manipulator is far less than that of the carrier. Meanwhile, we suppose that the attitude control system of the carrier guarantees its side on which the manipulator is mounted points accurately always the space target during approaching operation. The ideal constraint forces can be out of consideration in dynamics modeling as Kane method is used. The path functions of the manipulator’s end-effector approaching the space target as well as the manipulator’s joints control torque functions are programmed to meet the soft touch requirement that the end-effector’s relative velocity to the space target is zero at touch moment. Numerical simulation validation is conducted finally.

Robot-musculoskeletal dynamic biomechanical model in robot-assisted diaphyseal fracture reduction.

A number of issues that exist in common fracture reduction surgeries can be mitigated by robot-assisted fracture reduction. However, the safety of patients and the performance of the robot, which are closely related to the muscle forces, are important indexes that restrict the development of robots. Though researchers have done a great deal of work on the biomechanics of the musculoskeletal system, the dynamics of the musculoskeletal system, particularly the aspects related to the function of the robot, is not well understood. For this reason, we represent the complex biological system by establishing a dynamic biomechanical model based on the Hill muscle model and the Kane method for the robot that we have developed and the musculoskeletal system. We analyzed the relationship between the motion and force of the bone fragments and the robot during a simulation of a robot-assisted fracture reduction. The influence of the muscle force on the robot system was predicted and managed. The simulation results provide a basis for a fracture reduction path plan that ensures patient safety and a useful reference for the mechanical design of the robot.

Dynamics and Trajectory Planning for Reconfigurable Space Multibody Robots

A free-floating space robot equipped with multiple reconfigurable manipulators is designed and investigated in this paper. Lockable passive cylindrical joints (PCJs) are utilized to make the manipulator have the ability of changing its length and twisted angle. Each cylindrical joint, connecting two adjacent rigid links, has no embedded actuators but a brake mechanism. Normally, the mechanism is locked during the operation. When in the reconfiguration stage, two manipulators grasp each other to form a closed loop. Then one PCJ is unlocked, whose relative rotation and translation can be changed by the active torques at other joints. This system is a typical space multibody system. The dynamics of the space robot with unlocked cylindrical joints and a closed structural loop is investigated. The equations of motion are derived through Maggi–Kane's method. The obtained mathematical model is free of multipliers, which makes it suitable for controller design. A trajectory planning algorithm capable of avoiding the configuration singularity of the manipulators is proposed. A slide mode controller embedded with an extended state observer (ESO) is designed for the trajectory tracking control. Numerical simulations demonstrate the effectiveness of the trajectory planning and control strategy for the reconfiguration process.

Analytical Dynamic Modelling of Heel-off and Toe-off Motions for a 2D Humanoid Robot

The main objective of this article is to optimize the walking pattern of a 2D humanoid robot with heel-off and toe-off motions in order to minimize the energy consumption and maximize the stability margin. To this end, at first, a gait planning method is introduced based on the ankle and hip joint position trajectories. Then, using these trajectories and the inverse kinematics, the position trajectories of the knee joint and all joint angles are determined. Afterwards, the dynamic model of the 2D humanoid robot is derived using Lagrange and Kane methods. The dynamic model equations are obtained for different phases of motion and the unknowns, including ground reactions, and joint torques are also calculated. Next, the derived dynamic model is verified by comparing the position of the ZMP point based on the robot kinematics and the ground reactions. Then, the obtained trajectories have been optimized to determine the optimal heel-off and toe-off angles using a genetic algorithm (GA) by two different objective functions: minimum energy consumption and maximum stability margin. After optimization, a parametric analysis has been adopted to inspect the effects of heel-off and toe-off motions on the selected objective functions. Finally, it is concluded that to have more stable walking in high velocities, small angles of heel-off and toe-off motions are needed. Consequently, in low velocities, walking patterns with large angles of heel-off and toe-off motions are more stable. On the contrary, large heel-off and toe-off motions lead to less energy consumption in high velocities, while small heel-off and toe-off motions are suitable for low velocities. Another important point is that for the maximum stability optimization, compared to minimum energy consumption optimization, more heel-off and toe-off motions are needed.