Vibration suppression of collaborative robot based on modified trajectory planning

Aiming at the problem that the vibration of space robot will reduce the dynamic accuracy of robot, a method of vibration suppression of space robot through trajectory planning is proposed. First, the joint was simplified to a linear torsion spring, and the flexible rod was modelled using the finite element method, resulting in a flexible motion model of the robot. Then, a rigid-soft coupled dynamic model that combined the flexible motion model with the Lagrange method was established. Using the dynamic model, the factors influencing the vibration behaviour of space robots were analysed. Finally, the space robot was subjected to vibration suppression through trajectory planning. As verified by experimental analysis, different trajectories and loads affect the excitation force and inherent characteristics of the robot. In the design process, it is necessary to consider the relationship between the excitation force and natural frequency. The trajectory planning method has apparent effects on vibration suppression. The vibration amplitude was significantly reduced, which can improve the positioning accuracy and work efficiency of the robot.

The Delta robot is a high-speed and high-precision parallel robot. When it is in function, the end effector generates residual vibration, which reduces the repeat positioning accuracy and positioning efficiency. The input shaping method has previously been shown to suppress the residual vibration of the robot, but the vibration suppression effect of the single-modal input shaper is not good for the delta robot, which has multiple dominant modes for the residual vibration. To solve this problem, this paper proposes an effective method for residual vibration suppression of Delta robots based on dual-modal input shaping technology. Firstly, the modal analysis of the Delta robot is performed using finite element software, and the dominant modal of its residual vibration is determined. Secondly, six dual-modal input shapers are designed according to the obtained modal parameters. Finally, Simulink is used for simulation analysis to verify the robustness and vibration suppression performance of the designed six dual-modal input shapers and traditional single-modal input shapers. The simulation results show that the designed ZVD-EI dual-modal input shaper has good robustness, can effectively suppress the residual vibration of the Delta robot, and can effectively improve the repetitive positioning accuracy and work efficiency of the Delta robot when it is running at high speed.

High speed motion will bring the residual vibration for palletizing robot with flexible joints, which will affect the dynamic performance of robot. The time-domain motion character of palletizing robot is analyzed based on modal analysis theory, and the residual vibration model is provided. The problem of residual vibration suppression using motion planning method is regarded as functional extreme value problem, and the functional extreme problem is converted to solving the BVP(boundary value problem) of ordinary differential equations based on the Pontryagin maximum principle. The vibration suppression trajectory planning algorithm is designed considering the flexible dynamic model of palletizing robot simultaneously. Simulation results verify the effectiveness of the optimal trajectory planning for the vibration suppression of palletizing robot.

This paper presents a two-impulse input shaping method using off-line learning method to suppress the residual vibration of a flexible joint robot which is considered as perform repetitive tasks. It has been proved that the two-impulse input shaping method has the ability to suppress time-varying or nonlinear residual vibration. However, the parameters of the input shaper are difficult to select. In this paper, a method based on the off-line learning is presented to determine the proper parameters. We found that the torque of the joint can reflect the residual vibration through analysis of relations between the residual vibration and torque of the flexible joint robot. Thus, the torque signal of the joint is used to measure the vibration magnitude and no additional sensors for vibration measurement are required. For the nonmeasurable of the phase of the residual vibration, only the vibration magnitude is used to update the parameters of the input shaper off-line until the minimum vibration is obtained. The initial parameters of the input shaper also are estimated in this paper. Simulations are conducted to suppress residual vibration of a flexible joint robot, thereby demonstrating the effectiveness of the off-learning learning input shaping method.

Trajectory planning and diagonal recurrent neural network vibration control of a flexible manipulator using structural light sensor

Lightweight Delta robot is typical high-speed and high-precision industrial parallel robot. However, under high-speed condition, because of the lightweight components, it will inevitably lead to the vibration of Delta robot, which reduces the position accuracy and positioning efficiency. To solve this problem comprehensively, this article considers the process vibration and residual vibration of Delta robot, and the intelligent shaping vibration suppression control system is designed by using trajectory planning method of improved trapezoidal mode, shaping control method, and fast terminal sliding mode controller, and the detailed experimental analysis is carried out. The experimental results show that the proposed intelligent shaping vibration suppression control method can well suppress the process vibration and residual vibration of Delta robot, which can effectively improve the operation stability, work efficiency, and position accuracy of Delta robot.

The motors and reducers of traditional industrial robots are installed at the joints, which leads to large moment of inertia and difficult to effectively improve the dynamic performance of the robots. In particular, the residual vibration at the end of the robots will significantly reduce its working efficiency and fatigue life. Therefore, this paper proposes a new method to reinstall the motor and reducer near the frame, which can effectively suppress the residual vibration of the robots and simultaneously reduce the moment of inertia. Taking the series industrial robot as the research object, four types of CM robots are designed based on the theory of a multi-DOF controllable mechanism (CM). The motor and reducer of the robot are reinstalled near the frame through different branch chains, and their moments of inertia are calculated and compared. The dynamic equations of residual vibration of the four CM robots considering concentrated mass are established based on the finite element method (FEM) and Timoshenko space beam element (SBE) model, and the correctness of the equations are verified by experiments. The results show that the installation position of motor and reducer has a significant influence on the value of moment of inertia of the robot. The motor and reducer of configuration D are reinstalled near the frame by three branches, which can effectively reduce the attenuation time and amplitude of residual vibration at the end of the robot. The research provides a new idea for improving the dynamic performance of industrial robots.

Frog-leg robots are widely used for wafer-handling in semiconductor manufacturing. A typical frog-leg robot uses a magnetic coupler to achieve contactless transmission of motion between its driving motors, which operate at atmospheric pressure, and its end effector (blade) which operates within a vacuum chamber. However, the magnetic coupler is a low-stiffness transmission element that induces residual vibration during fast motions of the robot. Excessive residual vibration can cause collisions between the fragile wafer carried by the robot and cassette, hence damaging the wafer. While this problem could be solved by slowing down the robot, it comes at the cost of reduced productivity, which is undesirable. Therefore, this paper reports a preliminary investigation into input shaping (a popular vibration compensation technique) as a tool to reduce residual vibration of a frog-leg robot during high-speed motions. Two types of motions of the robot are considered: rotation and extension. A standard input shaper is shown to be very effective for mitigating residual vibration caused by rotational motion but is much less effective for extensional motion. The rationale is that the resonance frequencies of the robot are constant during rotation but they vary significantly during extension, hence reducing the effectiveness of standard input shaping. This necessitates the use of more advanced input shapers that can handle varying resonance frequencies to mitigate residual vibration during extensional motion in future work.

Aiming at the problem that the rigid flexible coupling manipulator generates elastic vibration during movement, which reduces the positioning accuracy and work efficiency, we propose a method of end vibration suppression based on cosine function superposition and multi population genetic algorithm. First, we get the relationship between the elastic vibration of the flexible arm and the joint trajectory motion according to the dynamic model of the system. Then, the cosine function superposition is used as the basis function to construct motion parameters of joints and the minimum residual vibration amplitude at the end of the flexible arm is used as the objective function. The undetermined coefficients in the basis function are optimized by multi population genetic algorithm to obtain the optimal trajectory. Finally, the simulation and experiment results show that the residual vibration amplitude is reduced by 60.6%. The proposed method can suppress the residual vibration at the end of the flexible arm and improve the work efficiency.

Residual vibration after point-to-point motion is one of the main factors affecting the working performance and service life of flexible link manipulators. In this paper, a trajectory planning method based on the transfer matrix method of multibody system (MSTMM) is proposed to suppress the residual vibration of a two-link rigid-flexible manipulator. Firstly, the dynamic model of the system is established by MSTMM. Secondly, the boundary value of the joint trajectory and the system dynamics model are used as constraints to construct an objective function, which is the average minimum value of the tip deformation of the flexible connecting rod after the point-to-point movement of the manipulator. Finally, the particle swarm optimization (PSO) algorithm is used to solve the trajectory optimization. Numerical simulation is used to verify the effectiveness of the proposed method. The method proposed in this paper uses MSTMM to describe the dynamic characteristics of the manipulator, which not only effectively improves the efficiency of trajectory optimization, but also provides theoretical support for the vibration suppression of the spatial multi-flexible link manipulator.

Research on vibration suppression and trajectory tracking control strategy of a flexible link manipulator

This brief studies a novel residual vibration suppression problem arising in a high-speed macromicromanipulator system designed for various precision positioning tasks. First, the dynamic of the macromicrosystem is mathematically modeled by a nonlinear partial differential equation (PDE). Subsequently, a new nonlinear vibration suppression and trajectory planning problem governed by a couple of ordinary differential equations (ODEs) are successfully formulated by using the assumed mode method (AMM) and Hamilton’s principle. Based on the developed model, an optimal switching time control strategy combined with control parameterization is proposed to realize the residual vibration suppression by trajectory planning. The gradients of the cost functional with respect to the unknown control variables and switching time variables are derived analytically by the sensitivity analysis method. Both numerical simulations and real experiments in the laboratory verify that the proposed method is superior to the classical fifth-order polynomial (FOP) approach for the vibration suppression problem.

As described in this paper, we specifically examine a point-to-point motion task of a rigid robot manipulator attached to a flexible link and present an optimal trajectory planning technique for suppressing residual vibrations of the flexible link. Soft computing methods are used in the trajectory planning method, in which radial basis function networks and a particle swarm optimization algorithm are adopted. Suppression of residual vibration can be accomplished by rotating the joint along the generated trajectory. The proposed control scheme is an open-loop control that does not require sensors to measure unwanted vibrations. Results obtained from simulations and experiments demonstrate the effectiveness of the proposed trajectory planning method for suppressing residual vibration.

Modified ADRC based on optimized repetitive control for low-frequency vibration and harmonic disturbance suppression: Design and application to inertially stabilized platforms

In sampled-data positioning control systems, the vibrations caused by the mechanical resonances around a sampling frequency are not only the difficult to observe but readily excited by the control input in transient-state characteristics. To address this problem, we developed a control method that can suppress the zero-order-hold induced residual vibration in the sampled-data positioning control system. The study is on a shock response spectrum (SRS) analysis that handles the transient-state characteristics of mechanical resonances. The control method uses multi-rate notch filters that modify the acceleration input signals beyond the Nyquist frequency. We designed the notch filter based on the SRS analysis because the frequency response on the Bode diagram was not suitable for analyzing transient characteristics. The results of SRS analyses showed that the multi-rate notch filter was able to decrease the amplitude of residual vibrations caused by the mechanical resonances around the sampling frequency. To demonstrate the validity of the proposed method, simulations were conducted on a sampled-data positioning control system.