Analytical and experimental nonzero-sum differential game-based control of a 7-DOF robotic manipulator

2021 ◽  
pp. 107754632098244
Author(s):  
Mostafa Bagheri ◽  
Peiman Naseradinmousavi
Keyword(s):  
Differential Game ◽  
Equilibrium Solution ◽  
Closed Loop ◽  
Robot Manipulator ◽  
Control Law ◽  
Feedback Nash Equilibrium ◽  
Optimal Control Strategy ◽  
Lagrange System ◽  
Lagrangian Dynamic

We formulate a Nash-based feedback control law for an Euler–Lagrange system to yield a solution to noncooperative differential game. The robot manipulators are broadly used in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler–Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability.

Experimental and Analytical Nonzero-Sum Differential Game-Based Control of a 7-DOF Robotic Manipulator

2020 ◽  
Author(s):  
Mostafa Bagheri ◽  
Alexander Bertino ◽  
Peiman Naseradinmousavi
Keyword(s):  
Differential Game ◽  
Closed Loop ◽  
Robot Manipulator ◽  
Control Law ◽  
Feedback Nash Equilibrium ◽  
Optimal Control Strategy ◽  
Lagrange System ◽  
Lagrangian Dynamic ◽  
Cooperative Differential Game

Abstract We formulate a Nash-based feedback control law for an Euler-Lagrange system to yield a solution to non-cooperative differential game. The robot manipulators are broadly utilized in industrial units on the account of their reliable, fast, and precise motions, while consuming a significant lumped amount of energy. Therefore, an optimal control strategy needs to be implemented in addressing efficiency issues, while delivering accuracy obligation. As a case study, we here focus on a 7-DOF robot manipulator through formulating a two-player feedback nonzero-sum differential game. First, coupled Euler-Lagrangian dynamic equations of the manipulator are briefly presented. Then, we formulate the feedback Nash equilibrium solution in order to achieve perfect trajectory tracking. Finally, the performance of the Nash-based feedback controller is analytically and experimentally examined. Simulation and experimental results reveal that the control law yields almost perfect tracking and achieves closed-loop stability.

scholarly journals Saturating Stiffness Control of Robot Manipulators with Bounded Inputs

2017 ◽  
Vol 27 (1) ◽  
pp. 79-90 ◽  
Author(s):  
María del Carmen Rodríguez-Liñán ◽  
Marco Mendoza ◽  
Isela Bonilla ◽  
César A. Chávez-Olivares
Keyword(s):  
Closed Loop ◽  
Robot Manipulator ◽  
Robot Manipulators ◽  
Contact Forces ◽  
Control Law ◽  
Closed Loop System ◽  
Control Scheme ◽  
Lyapunov Stability Analysis ◽  
Stiffness Control ◽  
Three Degree Of Freedom

AbstractA saturating stiffness control scheme for robot manipulators with bounded torque inputs is proposed. The control law is assumed to be a PD-type controller, and the corresponding Lyapunov stability analysis of the closed-loop equilibrium point is presented. The interaction between the robot manipulator and the environment is modeled as spring-like contact forces.The proper behavior of the closed-loop system is validated using a three degree-of-freedom robotic arm.

A Case Study in Control Methods for Active Magnetic Bearings

2014 ◽  
Author(s):  
Alexander H. Pesch ◽  
Stephen P. Hanawalt ◽  
Jerzy T. Sawicki
Keyword(s):  
Closed Loop ◽  
Controller Design ◽  
Experimental System ◽  
Magnetic Bearings ◽  
Control Law ◽  
Active Magnetic Bearings ◽  
Active Feedback ◽  
Active Feedback Control ◽  
Amb System

Active magnetic bearings (AMBs) provide support to rotating machinery through magnetic forces which are regulated through active feedback control. As AMBs continue to establish themselves as a proven technology, many classical and modern techniques are being employed to address the design of the control law. The current work studies three of the controller design techniques which are common in the literature for AMB applications: PID, LQG, and μ-synthesis. A controller is designed for an AMB system using each of the three techniques. Details of the design processes are given and the resulting controllers are compared. Finally, the controllers are implemented on the experimental system and the closed-loop characteristics are measured and evaluated. This work provides a common case study to demonstrate the strengths and weaknesses of PID, LQG, and μ-synthesis control methodologies as applied to a specific AMB system.

Developing a Cutting Edge, Closed-Loop Organics-to-Energy Project – Roseville Case Study

2018 ◽  
Vol 2018 (7) ◽  
pp. 5417-5435
Author(s):  
Alison Nojima ◽  
Adam Ross ◽  
Ken Glotzbach ◽  
Todd Jordan ◽  
George Hanson
Keyword(s):  
Closed Loop ◽  
Cutting Edge

scholarly journals Software Sensor to Enhance Online Parametric Identification for Nonlinear Closed-Loop Systems for Robotic Applications

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3653
Author(s):  
Lilia Sidhom ◽  
Ines Chihi ◽  
Ernest Nlandu Kamavuako
Keyword(s):  
Degrees Of Freedom ◽  
Closed Loop ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
Parametric Identification ◽  
Recursive Least Squares ◽  
Unknown Parameters ◽  
Closed Loop Identification ◽  
Input Variables ◽  
Robotic Applications

This paper proposes an online direct closed-loop identification method based on a new dynamic sliding mode technique for robotic applications. The estimated parameters are obtained by minimizing the prediction error with respect to the vector of unknown parameters. The estimation step requires knowledge of the actual input and output of the system, as well as the successive estimate of the output derivatives. Therefore, a special robust differentiator based on higher-order sliding modes with a dynamic gain is defined. A proof of convergence is given for the robust differentiator. The dynamic parameters are estimated using the recursive least squares algorithm by the solution of a system model that is obtained from sampled positions along the closed-loop trajectory. An experimental validation is given for a 2 Degrees Of Freedom (2-DOF) robot manipulator, where direct and cross-validations are carried out. A comparative analysis is detailed to evaluate the algorithm’s effectiveness and reliability. Its performance is demonstrated by a better-quality torque prediction compared to other differentiators recently proposed in the literature. The experimental results highlight that the differentiator design strongly influences the online parametric identification and, thus, the prediction of system input variables.

A Digital Algorithm for Near-Minimum-Time Control of Robot Manipulators

1987 ◽  
Vol 109 (4) ◽  
pp. 320-327 ◽  
Author(s):  
C. K. Kao ◽  
A. Sinha ◽  
A. K. Mahalanabis
Keyword(s):  
Control Algorithm ◽  
State Feedback ◽  
Closed Loop ◽  
Robot Manipulator ◽  
Minimum Time ◽  
State Feedback Control ◽  
Final States ◽  
Closed Loop System ◽  
Time Control ◽  
Digital Algorithm

A digital state feedback control algorithm has been developed to obtain the near-minimum-time trajectory for the end-effector of a robot manipulator. In this algorithm, the poles of the linearized closed loop system are judiciously placed in the Z-plane to permit near-minimum-time response without violating the constraints on the actuator torques. The validity of this algorithm has been established using numerical simulations. A three-link manipulator is chosen for this purpose and the results are discussed for three different combinations of initial and final states.

Industrial compliant robot bases in interaction tasks: a force tracking algorithm with coupled dynamics compensation

Robotica ◽  
2016 ◽  
Vol 35 (8) ◽  
pp. 1732-1746 ◽  
Author(s):  
Loris Roveda ◽  
Nicola Pedrocchi ◽  
Federico Vicentini ◽  
Lorenzo Molinari Tosatti
Keyword(s):  
Closed Loop ◽  
Control Law ◽  
Light Weight ◽  
Mobile Platforms ◽  
Control Laws ◽  
Assembly Task ◽  
Base Position ◽  
Force Tracking ◽  
Compliant Robot ◽  
Target Force

SUMMARYLight-weight manipulators are used in industrial tasks mounted on mobile platforms to improve flexibility. However, such mountings introduce compliance affecting the tasks. This work deals with such scenarios by designing a controller that also takes into account compliant environments. The controller allows the tracking of a target force using the estimation of the environment stiffness (EKF) and the estimation of the base position (KF), compensating the robot base deformation. The closed-loop stability has been analyzed. Observers and the control law have been validated in experiments. An assembly task is considered with a standard industrial non-actuated mobile platform. Control laws with and without base compensation are compared.

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