Control and Stability Analysis of Cooperating Robots
15 Jun 1988-Iss: 25, pp 1382-1386
TL;DR: The work presented here is the description of the control strategy of two cooperating robots, a two-finger hand, which allows for position control of the contact point by one of the robots while the other robot controls the contact force.
Abstract: The work presented here is the description of the control strategy of two cooperating robots. A two-finger hand is an example of such a system. The control method allows for position control of the contact point by one of the robots while the other robot controls the contact force. The stability analysis of two robot manipulators has been investigated using unstructured models for dynamic behavior of robot manipulators. For the stability of two robots, there must be some initial compliancy in either robot. The initial compliancy in the robots can be obtained by a non-zero sensitivity function for the tracking controller or a passive compliant element such as an RCC.
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TL;DR: The derivation of this force distribution and experimental results to corroborate the analytic results are presented, obtained from an experimental cooperating manipulator system developed specifically for use in the application of theo retical control approaches in cooperating hardware systems.
Abstract: Local control schemes using only position and rate errors to generate control forces are widely used for control of open- chain, serial-link robotic mechanisms, When two or more such open chains interact, closed kinematic chain, redundantly actu ated mechanisms are formed. Recent work has shown that the vector of joint forces produced using a local proportional-plus- derivative feedback scheme for the control of a cooperating manipulator system results in a vector of joint torques with a minimum weighted Euclidean norm. The current work presents the derivation of this force distribution and experimental evi dence to corroborate the analytic results. The data presented are obtained from an experimental cooperating manipulator system developed specifically for use in the application of theo retical control approaches in cooperating hardware systems.
9 citations
01 Jan 2000
TL;DR: In this paper, the authors considered the mathematical model and stability of motion of two cooperating manipulators and obtained the domains of stability and non-stability for such parameters of the system as coefficients of gains, stiffness, of force sensors, time delay in the control loop, and mass of load.
Abstract: The mathematical model and stability of motion of two cooperating manipulators is considered. The high order equations of this model make the mathematical analysis of the stability more difficult. By using a symmetrical control scheme with time delay in a feedback loop, we have obtained the domains of stability and non-stability for such parameters of the system as coefficients of gains, stiffness, of force sensors, time delay in the control loop, and mass of load.
3 citations
01 Jan 2004
TL;DR: In this paper, a mathematical model of a manipulator-tool system with time delay present in the feedback loop is analyzed and the minimum possible gain factor necessary for a stable system is obtained.
Abstract: A mathematical model of a manipulator-tool system with time delay present in the feedback loop is analyzed. The drilling process with constant feed force and control of force is the subject of this research. It is shown that the time delay in the control loop is a factor that influences the system’s stability. The minimum possible gain factor necessary for a stable system is obtained. This factor depends on the time delay and the stiffness of the sensor. The theoretically obtained results are compared to experiments.
2 citations
References
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Book•
01 Jan 1978TL;DR: In this article, the authors consider non-linear differential equations with unique solutions, and prove the Kalman-Yacubovitch Lemma and the Frobenius Theorem.
Abstract: Introduction. Non-linear Differential Equations. Second-Order Systems. Approximate Analysis Methods. Lyapunov Stability. Input-Output Stability. Differential Geometric Methods. Appendices: Prevalence of Differential Equations with Unique Solutions, Proof of the Kalman-Yacubovitch Lemma and Proof of the Frobenius Theorem.
3,388 citations
Book•
01 Jan 1975
TL;DR: In this paper, the Bellman-Gronwall Lemma has been applied to the small gain theorem in the context of linear systems and convolutional neural networks, and it has been shown that it can be applied to linear systems.
Abstract: Preface to the Classics edition Preface Acknowledgments Note to the reader List of symbols 1. Memoryless nonlinearities 2. Norms 3. General theorems 4. Linear systems 5. Applications of the small gain theorem 6. Passivity Appendix A. Integrals and series Appendix B. Fourier transforms Appendix C. Convolution Appendix D. Algebras Appendix E. Bellman-Gronwall Lemma References Index.
2,894 citations
"Control and Stability Analysis of C..." refers background or methods in this paper
...The following theorem (Small Gain Theorem) (7, 8 ) states the stability condition of the closed-loop system shown in Figure 4. A corollary is given to represent the size of ~ to guarantee the stability of the system....
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...Definitions 1 to 7 will be used in the stability proof of the closed-loop system (7, 8 )....
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TL;DR: In this paper, the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity.
Abstract: The robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria. Available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity. In particular, robustness results associated with multivariable control systems designed on the basis of linear-quadratic (LQ) and the linear-quadratic Gaussian (LQG) design methodologies are presented.
531 citations
"Control and Stability Analysis of C..." refers background in this paper
...f2- (5,+52)-' (G,e,-G2 e2) ( 5 ) Equation 5 motivates the block diagram of Figure 2 for representation of the contact force in the system where V, and V2 are given by equations 6 and 7....
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01 Dec 1985
TL;DR: In this article, the authors investigate the motion control of robotic manipulators using the recently developed stable factorization approach to tracking and disturbance rejection, and demonstrate the applicability of the linear design techniques and the stability of the closed loop system.
Abstract: In this paper we investigate the motion control of robotic manipulators using the recently developed stable factorization approach to tracking and disturbance rejection. Given a nominal model of the manipulator dynamics, the control scheme consists of an approximate feedback linearizing control followed by a linear compensator design based on the stable factorization approach to achieve optimal tracking and disturbance rejection. Using a multiloop version of the small gain theorem [17], the applicability of the linear design techniques and the stability of the closed loop system are rigorously demonstrated.
83 citations