Spatial Flexible Manipulators Research Articles

Modeling spatial multi-link flexible manipulator arms based on system modes

Modeling spatial multi-link flexible manipulator arms based on system modes

Trajectory planning of a spatial flexible manipulator for vibration suppression

Vibration decreases operational accuracy and productivity of flexible manipulators, and trajectory planning is an effective way to suppress vibration. However, the existing trajectory planning methods can only suppress vibration of planar flexible manipulators. In this paper, a trajectory planning method is proposed to suppress vibration of spatial flexible manipulators. Firstly, the dynamic models of each link of the flexible manipulator are established separately. Then with the constraint equations, the dynamic model of the flexible manipulator is established as a Differential Algebraic Equation (DAE). Secondly, the trajectory functions are designed as quintic polynomials, and the conditions are deduced to satisfy acceleration limits of each joint. Finally, the trajectory planning problem is transferred to an optimal problem. Particle Swam Optimization (PSO) is adopted to solve the optimal problem. Numerical simulation is conducted to demonstrate the good performance of the proposed method.

Recursive Formulation for Dynamic Modeling and Simulation of Multilink Spatial Flexible Robotic Manipulators

The dynamics for spatial manipulator arms consisting of n flexible links and n flexible joints is presented. All the transversal, longitudinal, and torsional deformation of flexible links are considered. Within the total longitudinal deformation, the nonlinear coupling term, also known as the longitudinal shortening caused by transversal deformation, also is considered here. Each flexible joint is modeled as a linearly elastic torsional spring, and the mass of joint is considered. Lagrange's equations are adopted to derive the governing equations of motion of the system. The algorithmic procedure is based on recursive formulation using 4 × 4 homogenous transformation matrices where all the kinematical expressions as well as the final equations of motion are suited for computation. A corresponding general-purpose C++ software package for dynamic simulation is developed. Several examples are simulated to illustrate the performance of the algorithm.

Dynamic analysis of multi-link spatial flexible manipulator arms with dynamic stiffening effects

The dynamics for multi-link spatial flexible manipulator arms is investigated. The system considered here is an N-flexible-link manipulator driven by N DC-motors through N revolute flexible-joints. The flexibility of each flexible joint is modeled as a linearly elastic torsional spring, and the mass of the joint is also considered. For the flexibility of the link, all of the stretching deformation, bending deformation and the torsional deformation are included. The complete governing equations of motion of the system are derived via the Lagrange equations. The nonlinear description of the deformation field of the flexible link is adopted in the dynamic modeling, and thus the dynamic stiffening effects are captured. Based on this model, a general-purpose software package for dynamic simulation of multi-link spatial flexible manipulator arms is developed. Several illustrative examples are given to validate the algorithm presented in this paper and to indicate that not only dynamic stiffening effects but also the flexibility of the structure has significant influence on the dynamic performance of the manipulator.

Recursive Lagrangian dynamic modeling and simulation of multi-link spatial flexible manipulator arms

The dynamics for multi-link spatial flexible manipulator arms consisting of n links and n rotary joints is investigated. Kinematics of both rotary-joint motion and link deformation is described by 4 × 4 homogenous transformation matrices, and the Lagrangian equations are used to derive the governing equations of motion of the system. In the modeling the recursive strategy for kinematics is adopted to improve the computational efficiency. Both the bending and torsional flexibility of the link are taken into account. Based on the present method a general-purpose software package for dynamic simulation is developed. Dynamic simulation of a spatial flexible manipulator arm is given as an example to validate the algorithm.

Vibration Mechanism of Constrained Spatial Flexible Manipulators.

For free motions, vibration suppression of flexible manipulators has been one of the hottest research topics. However, for constrained motions, a little effort has been devoted for vibration suppression control. Using the dependency of elastic deflections of links on contact force under static conditions, vibrations for constrained planar two-link flexible manipulators have been suppressed successfully by controlling the contact force. However, for constrained spatial multi-link flexible manipulators, the vibrations cannot be suppressed by only controlling the contact force. So, the aim of this paper is to clarify the vibration mechanism of a constrained, multi-DOF, flexible manipulator and to devise the suppression method. We apply a concise hybrid position/force control scheme to control a flexible manipulator modeled by lumped-parameter modeling method. Finally, a comparison between simulation and experimental results is presented to show the performance of our method.

Spatial Flexible Manipulator Trajectory Control Through Solving the Inverse Kinematics

Abstract In this paper, the inverse kinematics of a spatial flexible link manipulator which is the most fundamental issue in Cartesian space trajectory control, is investigated. First, based on some rational assumptions, an approximate solution in the sense that the problem is solved not fully dynamically, is found by a numerical method. Next, a numerical iterative learning approach is presented to further reduce the end-effector's position errors remained in the approximate solution. Convergence analysis for both methods are also conducted. Numerical simulation and real experiment are carried out on a laboratory manipulator with two flexible links and three rigid revolute type joints. Results are shown to validate the proposed methods.

Modeling of flexible-link manipulators with prismatic joints

The axially translating flexible link in flexible manipulators with a prismatic joint can be modeled using the Euler-Bernoulli beam equation together with the convective terms. In general, the method of separation of variables cannot be applied to solve this partial differential equation. In this paper, we present a nondimensional form of the Euler-Bernoulli beam equation using the concept of group velocity and present conditions under which separation of variables and assumed modes method can be used. The use of clamped-mass boundary conditions lead to a time-dependent frequency equation for the translating flexible beam. We present a novel method to solve this time-dependent frequency equation by using a differential form of the frequency equation. We then present a systematic modeling procedure for spatial multi-link flexible manipulators having both revolute and prismatic joints. The assumed mode/Lagrangian formulation of dynamics is employed to derive closed form equations of motion. We show, using a model-based control law, that the closed-loop dynamic response of modal variables become unstable during retraction of a flexible link, compared to the stable dynamic response during extension of the link. Numerical simulation results are presented for a flexible spatial RRP configuration robot arm. We show that the numerical results compare favorably with those obtained by using a finite element-based model.

Precise Lumped-Parameter Modeling of Flexible Manipulator Dynamics.

In this paper, we discuss the modeling of flexible manipulators, for which there are two approaches: one based on distributed-parameter modeling and the other on lumped-parameter modeling. The former has been applied to control and analysis of simple manipulators requiring precision, while the latter has been applied to multilink spatial manipulators, because of the model's simplicity. We have already proposed a lumped-parameter modeling method for multilink spatial flexible manipulators. In this paper, we apply our lumped-parameter modeling method to a simple manipulator, and investigate what degree of precision we can obtain using the model. Experiments and simulations are performed and, based on comparison of the results, the approximation performance of our modeling method is discussed.

Trajectory tracking of a spatial flexible link manipulator using an inverse dynamics method

Discussed in this paper is the problem of trajectory tracking of a spatial flexible link manipulator. To solve this problem, an inverse dynamics method is proposed, based on which computed joint torques can be determined and used to drive the endpoint of a spatial flexible link manipulator to follow its given trajectory.

Vibration suppression control of spatial flexible manipulators

In spatial 3D flexible manipulators, some parameters change, depending upon the arm's configuration. The relationship between vibrations and actuators might be configuration-dependent. Therefore, such configuration dependency has to be considered in the control of 3D spatial flexible manipulators. Linear quadratic regulator (LQR) would be one of the solutions. However, state feedback gains must be computed at various configurations and the gain table would be quite large in the case of multi-DOF manipulators. In this paper, a configuration-dependent variable-gain vibration-suppression control strategy for 3D spatial flexible manipulator is discussed. The vibration control scheme computes the link deflection feedback gain depending upon the current configuration during each sampling period. Thus, no large gain table is needed, and the scheme would be effective in the case of multi-DOF 3D spatial manipulators. The control scheme is examined in the case of a 2-link 7-joint type manipulator through experiments. The stability of the control scheme is also discussed.

Comparison of the Assumed Modes and Finite Element Models for Flexible Multilink Manipulators

The objective of this paper is to compare two discretization models—namely, the assumed modes and finite element mod els—to efficiently represent the link flexibility of robot manip ulators. We present a systematic modeling procedure based on homogeneous transformation matrices for spatial multilink flexible manipulators with both revolute and prismatic joints. The Lagrangian formulation of dynamics and computer algebra are employed to derive closed-form equations of motion. We show that fewer mathematical operations are required for in ertia matrix computation in the finite element model compared with the assumed modes formulation; however, because the number of state space equations are more, the numerical sim ulation time may be greater for finite element models. Use of the finite element model to approximate flexibility usually gives rise to overestimated stiffness matrix. We analytically show that overestimation of structure stiffness may lead to unstable closed-loop response of the original manipulator system, using a model-based control law. We illustrate the complexity owing to the time-dependent frequency equation of the assumed modes model arising in a prismatic jointed flexible link with payload and in manipulators with more than one link with revolute joints. We describe a novel method based on the differential form of the frequency equation to simulate such systems. A model-based decoupling control law is used to compare the dynamic responses of the manipulator system. The results are illustrated by numerical simulation of a flexible spatial RRP configuration robot.

Vibration suppression control of spatial flexible manipulators

In spatial 3D flexible manipulators, some parameters change depending upon the arm’s configuration. The relationship between vibrations and actuators might be configuration dependent. Therefore, such configuration dependency has to be considered in the control of 3D spatial flexible manipulators. Linear quadratic regulator (LQR) would be one of the solutions. However, state feedback gains must be computed at various configurations and the gain table would be quite large in the case of multi-DOF manipulators. In this paper, a configuration dependent variable gain vibration suppression control strategy for 3D spatial flexible manipulator is discussed. The vibration control scheme computes the link deflection feedback gain depending upon the current configuration during each sampling period. Thus, no large gain table is needed, and the scheme would be effective in the case of multi-DOF 3D spatial manipulators. The control scheme is examined in the case of 2-link 7-joint type manipulator through experiments. Stability of the control scheme is also discussed.

加速度指令による三次元フレキシブルマニピュレータの振動抑制制御

In this paper, we discuss the control of a 3D (3-dimensional) spatial flexible manipulator. In the 3D spatial flexible manipulator, object parameters for the control change depending on the arm configuration. Therefore, gains in the controller for the vibration suppression have to be changed configuration-dependently. In this paper, we propose a configuration-dependent adaptive controller in which the joint accelerations are used as commands to suppress the vibration. We discuss two configuration-dependent control schemes. One is a scheme which adds damping to the vibration system. We call this scheme as ‘active damping control.’ The other is a scheme which uses the optimal regulator. These schemes are combined to be implemented on a 3D flexible manipulator. Experimental results show the effectiveness of the control schemes. In the experiment, we find discontinuous gains of the optimal regulator for some arm configurations. Also the plausible reasons for discontinuity are briefly discussed.