Design of force/position control laws for constrained robots, including effects of joint flexibility and actuator dynamics

Robotica ◽  
1999 ◽  
Vol 17 (1) ◽  
pp. 41-48 ◽  
Author(s):  
Hariharan Krishnan
Keyword(s):  
Feedback Control ◽  
Position Control ◽  
Mathematical Representation ◽  
Control Law ◽  
Differential Algebraic Equation ◽  
Force Output ◽  
End Effector ◽  
Joint Flexibility ◽  
Actuator Dynamics ◽  
Constrained Robot

In this paper, a mathematical representation of constrained robot systems in the form of a differential-algebraic equation model is first considered. This model in modified further to include the joint flexibility between the linkages of the robot, and the actuator dynamics. The objective is to design a feedback control law for the system so that the position output variables (typically the end-effector position) and the force output variables (typically the contact force between the robot's end-effector and the contact surface) of the robot follows the desired position and the desired force trajectories, respectively, despite the presence of joint flexibility and actuator dynamics. A systematic procedure is developed for designing a feedback control law which ensures that the position variables track the desired position trajectories exponentially, and the force variables track the desired force trajectories exponentially. Since the development of the control law is based on the model of a constrained robot system which includes the effects of actuator dynamics and joint flexibility, it is possible to achieve better tracking performance using the force/position control law developed in this paper in cases where such effects are significant.

Task-Space Control Design and Performance Evaluation for a 6DOF Stewart Nanoscale Platform

2008 ◽  
Author(s):  
Chun-Chung Li ◽  
Yung Ting ◽  
Yi-Hung Liu ◽  
Yi-Da Lee ◽  
Chun-Wei Chiu
Keyword(s):  
Feedback Control ◽  
Hybrid Control ◽  
Feedforward Control ◽  
Feedback Controller ◽  
Test Method ◽  
Computation Method ◽  
Task Space ◽  
Force Output ◽  
End Effector ◽  
Control Scheme

A 6DOF Stewart platform using piezoelectric actuators for nanoscale positioning objective is designed. A measurement method that can directly measure the pose (position and orientation) of the end-effector is developed so that task-space on-line control is practicable. The design of a sensor holder for sensor employment, a cuboid with referenced measure points, and the computation method for obtaining the end-effector parameters is introduced. A control scheme combining feedforward and feedback is proposed. The inverse model of a hysteresis model derived by using a dynamic Preisach method is used for the feedforward control. Hybrid control to maintain both the positioning and force output for nano-cutting and nano-assembly applications is designed for the feedback controller. The optimal gain of the feedback controller is searched by using relay feedback test method and genetic algorithm. In experiment, conditions with/without external load employed with feedforward, feedback, and feedforward with feedback control schemes respectively are carried out. Performance of each control scheme verifies the capability of achieving nanoscale precision. The combined feedforward and feedback control scheme is superior to the others for gaining better precision.

scholarly journals Position control for haptic device based on discrete-time proportional integral derivative controller

2022 ◽  
Vol 12 (1) ◽  
pp. 269
Author(s):  
Nguyen Van Tan ◽  
Khoa Nguyen Dang ◽  
Pham Duc Dai ◽  
Long Vu Van
Keyword(s):  
Discrete Time ◽  
Pid Controller ◽  
Position Control ◽  
Haptic Device ◽  
Advanced Technology ◽  
Proportional Integral Derivative ◽  
Force Output ◽  
Kinematic Equation ◽  
End Effector ◽  
Proportional Integral

Haptic devices had known as advanced technology with the goal is creating the experiences of touch by applying forces and motions to the operator based on force feedback. Especially in unmanned aerial vehicle (UAV) applications, the position of the end-effector Falcon haptic sets the velocity command for the UAV. And the operator can feel the experience vibration of the vehicle as to the acceleration or collision with other objects through a forces feedback to the haptic device. In some emergency cases, the haptic can report to the user the dangerous situation of the UAV by changing the position of the end-effector which is be obtained by changing the angle of the motor using the inverse kinematic equation. But this solution may not accurate due to the disturbance of the system. Therefore, we proposed a position controller for the haptic based on a discrete-time proportional integral derivative (PID) controller. A Novint Falcon haptic is used to demonstrate our proposal. From hardware parameters, a Jacobian matrix is calculated, which combines with the force output from the PID controller to make the torque for the motors of the haptic. The experiment was shown that the PID has high accuracy and a small error position.

Continuous time-varying feedback control of a robotic manipulator with base vibration and load uncertainty

2020 ◽  
pp. 107754632092759
Author(s):  
Xi Wang ◽  
Baolin Hou
Keyword(s):  
Feedback Control ◽  
Lyapunov Function ◽  
Continuous Time ◽  
Position Control ◽  
Control Method ◽  
Robotic Manipulator ◽  
Control Law ◽  
Time Varying ◽  
Load Uncertainty ◽  
Feedback Control Method

To solve precise and fast position control of a robotic manipulator with base vibration and load uncertainty, a continuous time-varying feedback control method based on the implicit Lyapunov function is studied. This method is proportional–derivative-like in the form of control law, but its proportional and differential coefficients depend on the system Lyapunov function, which are differentiable functions of system error variables. In the motion process of the robotic manipulator, the system performance is influenced by three main nonlinear factors: system friction, balance torque, and base vibration. As the former two factors are available to be modeled and identified through experiments, compensation of the two terms is added to the proposed control law to reduce the effects of system nonlinearities to a certain extent. Experimental results show that the proposed control strategy is robust to base vibration and load uncertainty. Besides, the compensation of system friction and balance torque can shorten the positioning time by 27.3%, from 1.32 s to 0.96 s. Meanwhile, the positioning precision is guaranteed, which verifies the effectiveness of the proposed control scheme.

Adaptive control of rigid-link electrically driven robots with parametric uncertainties in kinematics and dynamics and without acceleration measurements

Robotica ◽  
2014 ◽  
Vol 32 (7) ◽  
pp. 1153-1169 ◽  
Author(s):  
Mahboubeh Ahmadipour ◽  
Alireza Khayatian ◽  
Maryam Dehghani
Keyword(s):  
Motion Tracking ◽  
Jacobian Matrix ◽  
Control Law ◽  
Parametric Uncertainties ◽  
Tracking Errors ◽  
End Effector ◽  
Actuator Dynamics ◽  
Rigid Link ◽  
Control Scheme ◽  
Electrically Driven Robots

SUMMARYIn this paper, the backstepping strategy is used to design an adaptive tracking controller for rigid-link electrically driven robots in the presence of parametric uncertainties in kinematics, manipulator dynamics, and actuator dynamics. To avoid acceleration measurements, two techniques are exploited. One technique adds compensation control terms to the control law signal. The other uses a linear in variable property of the Jacobian matrix. Global asymptotic convergence of the end-effector motion tracking errors is shown via Lyapunov analysis. Simulation results are presented to show the effectiveness of the proposed control scheme.

scholarly journals Force-Free Control for Direct Teaching of a Surgical Assistant Robot End Effector with Wire-Driven Bidirectional Telescopic Mechanism

Sensors ◽  
2021 ◽  
Vol 21 (10) ◽  
pp. 3498
Author(s):  
Youqiang Zhang ◽  
Cheol-Su Jeong ◽  
Minhyo Kim ◽  
Sangrok Jin
Keyword(s):  
Control Algorithm ◽  
Position Control ◽  
Friction Model ◽  
Surgical Instruments ◽  
Control Input ◽  
End Effector ◽  
Motor Current ◽  
Direct Teaching ◽  
End Effectors ◽  
Teaching Operation

This paper shows the design and modeling of an end effector with a bidirectional telescopic mechanism to allow a surgical assistant robot to hold and handle surgical instruments. It also presents a force-free control algorithm for the direct teaching of end effectors. The bidirectional telescopic mechanism can actively transmit force both upwards and downwards by staggering the wires on both sides. In order to estimate and control torque via motor current without a force/torque sensor, the gravity model and friction model of the device are derived through repeated experiments. The LuGre model is applied to the friction model, and the static and dynamic parameters are obtained using a curve fitting function and a genetic algorithm. Direct teaching control is designed using a force-free control algorithm that compensates for the estimated torque from the motor current for gravity and friction, and then converts it into a position control input. Direct teaching operation sensitivity is verified through hand-guiding experiments.

Optimization approach to the constrained regulation problem for linear continuous-time fractional-order systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Xindong Si ◽  
Hongli Yang
Keyword(s):  
Feedback Control ◽  
Fractional Order ◽  
State Feedback Control ◽  
Invariant Sets ◽  
Linear Feedback ◽  
Control Law ◽  
Optimization Approach ◽  
Fractional Order Systems ◽  
Linear Feedback Control ◽  
Computational Point

AbstractThis paper deals with the Constrained Regulation Problem (CRP) for linear continuous-times fractional-order systems. The aim is to find the existence conditions of linear feedback control law for CRP of fractional-order systems and to provide numerical solving method by means of positively invariant sets. Under two different types of the initial state constraints, the algebraic condition guaranteeing the existence of linear feedback control law for CRP is obtained. Necessary and sufficient conditions for the polyhedral set to be a positive invariant set of linear fractional-order systems are presented, an optimization model and corresponding algorithm for solving linear state feedback control law are proposed based on the positive invariance of polyhedral sets. The proposed model and algorithm transform the fractional-order CRP problem into a linear programming problem which can readily solved from the computational point of view. Numerical examples illustrate the proposed results and show the effectiveness of our approach.

scholarly journals Proposal of a Decoupled Structure of Fuzzy-PID Controllers Applied to the Position Control in a Planar CDPR

Electronics ◽  
2021 ◽  
Vol 10 (6) ◽  
pp. 745
Author(s):  
Marco Carpio ◽  
Roque Saltaren ◽  
Julio Viola ◽  
Cristian Calderon ◽  
Juan Guerra
Keyword(s):  
Position Control ◽  
Control Structure ◽  
Parallel Robot ◽  
Pid Controllers ◽  
Fuzzy Pid ◽  
End Effector ◽  
Robot Systems ◽  
Decoupled Control ◽  
The Mathematical Model ◽  
Decoupled Structure

The design of robot systems controlled by cables can be relatively difficult when it is approached from the mathematical model of the mechanism, considering that its approach involves non-linearities associated with different components, such as cables and pulleys. In this work, a simple and practical decoupled control structure proposal that requires practically no mathematical analysis was developed for the position control of a planar cable-driven parallel robot (CDPR). This structure was implemented using non-linear fuzzy PID and classic PID controllers, allowing performance comparisons to be established. For the development of this research, first the structure of the control system was proposed, based on an analysis of the cables involved in the movement of the end-effector (EE) of the robot when they act independently for each axis. Then a tuning of rules was carried out for fuzzy PID controllers, and Ziegler–Nichols tuning was applied to classic PID controllers. Finally, simulations were performed in MATLAB with the Simulink and Simscape tools. The results obtained allowed us to observe the effectiveness of the proposed structure, with noticeably better performance obtained from the fuzzy PID controllers.

Design, Modelling and Simulation of a Rotational Robotic Arm

2020 ◽  
Author(s):  
Bin Wei
Keyword(s):  
Angular Velocity ◽  
3D Model ◽  
Modelling And Simulation ◽  
Robotic Arm ◽  
Forward Kinematics ◽  
Position Vector ◽  
Control Law ◽  
Model Design ◽  
End Effector ◽  
Design And Optimization

Abstract In this paper, a rotational robotic arm is designed, modelled and optimized. The 3D model design and optimization are conducted by using SolidWorks. Forward kinematics are derived so as to determine the position vector of the end effector with respect to the base, and subsequently being able to calculate the angular velocity and torque of each joint. For the goal positioning problem, the PD control law is typically used in industry. It is employed in this application by using virtual torsional springs and frictions to generate the torques and to keep the system stable.

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