Large deformation modeling of flexible manipulators to determine allowable load

This paper presents a finite-element (FE) model of a manipulator with a flexible link and flexible joint as well as embedded PZT actuators and proposes a corrected rebuilt reduced model (CRRM) to make its dynamic characteristics more consistent with reality and facilitate control design. The CRRM considers the holding torque of the manipulator driving motor and eliminates the response divergence induced by a fault of the mass matrix of the FE model. In order to reduce the dimensions and maintain the precision of the model, an iterated improved reduction system (IIRS) method is adopted. Additionally, a LQR controller is designed based on the output function of the improved model. The simulation results demonstrate that the CRRM is consistent with reality and the active controller has good performance in suppressing vibration of the manipulator with both the flexible link and the flexible joint.

Due to excessive maneuverability, mobile manipulators which consist of one or more manipulators mounted on a mobile base have attracted much of interest. Tipping-over is one of the most important problems in such systems especially when manipulating heavy objects, also during maneuvers in unknown environment or in rugged terrains. Therefore, estimation and evaluation of dynamic stability with appropriate easy-computed measure throughout the motion of such systems is a challenging task. In this study, various dynamic stability measures are investigated and compared with each other. Next, a new effective measure named as Moment-Height Stability (MHS) measure is presented for wheeled mobile manipulators. The proposed metric is physically meaningful based on principal concepts, and can be implemented with limited low computational effort. The suggested MHS measure can be effectively used for both legged robots and mobile manipulators. Finally, a few case studies are presented to compare the new MHS measure with the main existing measures. The obtained simulation results show the merits of the new proposed MHS measure, in terms of prediction the exact time of instability occurrence, without additional precautions of the other measures which may confine the maneuverability of the system and its operation.

The under actuated model of a smart space manipulator with flexible links and joints is established based on the Lagrange equation and assumed model method. Afterwards, using singular perturbation method, the system is decomposed into a slow subsystem and a fast subsystem, which describe the rigid-body motion and flexible vibration, respectively. Then, a modified computed torque controller based on the under actuated model is put forward to realize trajectory tracking of joints. In the meantime, the joint flexibility is compensated real-timely by the motors while the real-time suppression of the link vibration is realized by the embedded piezoelectric actuators. Finally, the simulation results indicate that the proposed composite control strategy can realize the trajectory tracking rapidly and in the same time suppress the vibration caused by flexible joints and links efficiently.

Human finger joints are conventionally simplified as rigid joints in robotic hand design and biomechanical hand modelling, due to their anatomic and morphologic complexity. However, our understanding of the effect of the finger joint configuration on the resulting hand performance is still primitive. In this study, we systematically investigate the grasping performance of the hands with the conventional rigid joints and the biomechanical flexible joints based on a computational human hand model. The measured muscle electromyography (EMG) and hand kinematic data during grasping are used as inputs for the grasping simulations. The results show that the rigid joint configuration currently used in most robotic hands leads to large reductions in hand contact force, contact pressure and contact area, compared to the flexible joint configuration. The grasping quality could be reduced up to 40% and 36% by the rigid joint configuration in terms of algebraic properties of grasping matrix and finger force limit respectively. Further investigation reveals that these reductions are caused by the weak rotational stiffness of the rigid joint configuration. This study implies that robotic/prosthetic hand performance could be improved by exploiting flexible finger joint design. Hand contact parameters and grasping performance may be underestimated by the rigid joint simplification in human hand modelling.

SUMMARYPresent study on industrial manipulator control either completely neglects structural flexibility or only considers manipulator link flexibility. Ignoring joint flexibility may cause significant errors in gross motion control if the joint elastic effect is predominant. This paper presents an effective control scheme which can compensate for the motion errors generated by simultaneous existence of both link and joint flexibility. The manipulator dynamics is formulated comprehensively by a superposition of two models, namely, an assumed modes of vibration model for links and a torsional spring model.for joints. Then, a nonlinear feedback rate servo control system is developed that compensates for the gross motion errors introduced by both joint elasticity and link flexibility. Motion simulation results show that the proposed formulation can effectively describe the dynamic behavior of a flexible-link, elastic-joint robot. They also verify that the proposed controller is robust in that it can satisfactorily suppress the manipulator end oscillations and yield an accurate gross motion.

Mathematical modeling and trajectory planning of mobile manipulators with flexible links and joints

In this paper, we propose a novel design for a pectoral fin joint of a robotic fish. This joint uses a flexible part to enable the rowing pectoral fin to feather passively and thus reduce the hydrodynamic drag in the recovery stroke. On the other hand, a mechanical stopper allows the fin to maintain its motion prescribed by the servomotor in the power stroke. The design results in net thrust even when the fin is actuated symmetrically for the power and recovery strokes. A dynamic model for this joint and for a pectoral fin-actuated robotic fish involving such joints is presented. The pectoral fin is modeled as a rigid plate connected to the servo arm through a pair of torsional spring and damper that describes the flexible joint. The hydrodynamic force on the fin is evaluated with blade element theory, where all three components of the force are considered due to the feathering degree of freedom of the fin. Experimental results on robotic fish prototype are provided to support the effectiveness of the design and the presented dynamic model. We utilize three different joints (with different sizes and different flexible materials), produced with a multi-material 3D printer, and measure the feathering angles of the joints and the forward swimming velocities of the robotic fish. Good match between the model predictions and experimental data is achieved, and the advantage of the proposed flexible joint over a rigid joint, where the power and recovery strokes have to be actuated at different speeds to produce thrust, is demonstrated.

The effects of flexible joints on the dynamic response and control of robot are studied in this paper. Firstly, the spatial robot model consisting of $n$ flexible joints and $n$ flexible links is built, and the dynamic equations of the robot system are derived via the Lagrangian's equations. The tensile deformation, bending deformation, torsional deformation, and nonlinear coupling deformation of the flexible link are considered. Furthermore, the effects of the flexible joint are also considered in order to provide an important theoretical basis for the research of the vibration suppression and control of robots. The flexible joint is simplified as a linear torsion spring with damping, and the mass effect of the flexible joint is also considered in the model. Secondly, the dynamic simulations of the spatial manipulators are done to explore the effects of the joint stiffness and damping on the dynamic response of the robot system. The results show that as the stiffness coefficient increases, the amplitude of dynamic response of the flexible robot decreases, and the vibration frequency of the system becomes larger. As the damping coefficient increases, the dynamic response of the flexible robot decreases, and the dynamic response decays faster. The vibration of the flexible robot can be suppressed by adjusting the values of the stiffness and damping of the flexible joint. Finally, in order to study the effects of the flexibility of the joint on the control system, the rigid-joint manipulator and flexible-joint manipulator are made to move under the same circular motion. Then the joint torques of the two system are obtained respectively by solving the inverse dynamics equations, and the influence of the flexibility of the joint on the dynamics control is studied. The results show that the actuating torques required in the flexible-joint system are reduced compared to that required in the rigid-joint system.

Redundant robot manipulators with joint and link flexibility—II. Residual vibration decreasing

This paper considers a portal frame with rigid members and flexible joints. The stability and postbuckling characteristics are derived analytically. The optimum frame to raise a load to a given height is trapezoidal in shape, with only the top two joints heavily strengthened.

BackgroundThe paper presents vibration analysis of dynamic models of systems with flexible mechanical components, friction modeled and subjected to position and kinematic programmed constraints, which can be imposed as control goals, work or service task demands.MethodsThe constrained dynamics is derived using an automated computational procedure dedicated to constrained systems. The procedure was successfully implemented to rigid system models. A class of systems composed of flexible parts and subjected to programmed motions is considered in the paper. Their motion analysis has to be accompanied by vibration inspection. The novelty of the presented approach is in the possibility of analyzing system motions and vibrations that can be induced by the presence of programmed constraints.ConclusionsThe constrained motion is examined by the example of a crane model equipped with a flexible link, e.g. a jib, friction modeled in its joints and subjected to programmed constraints. The example delivers a realistic work situation, in which the crane carries loads and moves according to the programmed constraint put on motion.

This paper describes a mechanics–based framework for virtual prototyping of soft robots, i.e. robots with deformable bodies and flexible joints. The framework builds on top of the screw theory, and uses geometrically exact nonlinear beam models for describing the behavior of deformable bodies, as well as the finite element method for space discretization. The computer implementation of this framework results in SimSOFT, a physics engine for soft robots. The capabilities of the framework are illustrated with one general example, an articulated chain of rigid and soft links connected through rigid and flexible joints. Furthermore, several case studies are shown for industrial and medical applications.

In this paper, an innovative method of controlling the endpoint precision of a single-link flexible manipulator has been presented. The flexibility of the link has been stiffened by using a pair of strings while retaining its advantage of being lightweight. The flexible link is modeled as an Euler-Bernoulli beam. Dynamic analyses of the string-stiffened single-link flexible manipulator (SSSLFM) with flexible joint have been carried out using Euler-Lagrange’s formulation with the assumed mode method. The effects of string-stiffening on tip deflection of the link have been found. Coupling effects of string vibration on tip deflection of the link as well as on the joint of the manipulator have also been investigated. It has been observed that by the stiffening of the flexible link with a pair of strings, tip deflection of the link has been reduced significantly. Residual vibrations have been controlled by applying robust proportional-integral and derivative (PID) control.

In space and surgical robotics applications, the desire is to use thin and lightweight manipulators and cable-driven end-effectors. This, however, introduces joint and/or link flexibility in the slave robot of a master-slave teleoperation system, reducing the effective stiffness of the slave and the transparency of teleoperation. Here, we analyze teleoperation transparency and stability under slave joint and link flexibility (tool flexibility) and evaluate the added benefits of using extra sensors at the tip of the flexible slave. One of the results of this paper is that tip velocity feedback can eliminate the display of joint or link flexibility to the user during a hard contact task.

The singular perturbation approach has been shown to be successful in controlling both flexible link manipulators and flexible joint manipulators. In this paper, the technique is extended to control both link and joint flexibility of a multilink manipulator simultaneously while a desired trajectory is being tracked. A comprehensive, closed-form, Euler-Lagrange, assumed-mode model of a multilink manipulator has been formulated in which the effects of the link and joint flexibility are incorporated. This is then converted into a two-time-scale, state-space, singular perturbation model where the slow subsystem involves the link angles and the fast subsystem consists of the joint deflection and the link deflection variables. A composite controller is designed based on the two-time-scale model of the flexible link and joint manipulator. Numerical simulation results confirm that the proposed controller satisfactorily suppresses the tip deflection and joint flexibility of the manipulator while very good trajectory tracking is achieved.