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The Control of the Hyper-redundant Manipulators by Frequency Criteria

Mircea IVĂNESCU1, Mihaela Cecilia FLORESCU1, Nirvana POPESCU2,
Decebal POPESCU2
1 University of Craiova, România, e-mail: ivanescu@robotics.ucv.ro
2 University “Politehnica” Bucharest, România

Abstract: The control problem of hyper-redundant arms with continuum elements by frequency criteria is discussed. First, there is concern with the dynamic model of the continuum arm for the position control during non-contact operations with the environment. A frequency stability criterion based on the Kalman – Yakubovich – Popov Lemma and P and PD control algorithms is proposed. The control algorithms based on SMA actuators are introduced. Numerical simulations of the arm motion toward an imposed target are presented.

Keywords: Hyper-redundant robot, frequency criterion, SMA actuator.

Mircea Ivănescu received the B. Sc. degrees in Automatic Control in 1965 from the University Politehnica Bucharest. He received the Ph.D. degree in Control Systems in 1975. Now, he is a Professor at the Department of Mechatronics, University of Craiova. His research interests are focused on: Distributed Parameter Systems, Discrete Optimization Problems, Fuzzy Systems, Nonlinear Systems, and Robotics.

Mihaela Cecilia Florescu received the B. Sc. and M. Sc. degrees in Electromechanical Engineering in 1995 and 1996, respectively, from University of Craiova. Now she is Lecturer at the Mechatronics Department, University of Craiova. Her research interests are focused on: Distributed Parameter Systems, Fuzzy Systems, and Robotics.

Nirvana Popescu received her B. Sc. and M. Sc. degrees in Computer Science in 1997 and 1998, respectively, from University Politehnica, Bucharest. She received the Ph.D. degree in Computer Science in 2003 from University Politehnica, Bucharest. Now she is Lecturer at the Computer Department, University Politehnica, Bucharest. Her research interests are focused on: Fuzzy Systems, Digital Circuits, Intelligent Adaptive Systems, Vision Control.

Decebal Popescu received his B. Sc. and M. Sc. degrees in Computer Science in 1997 and 1998, respectively, from University Politehnica, Bucharest. He received his Ph.D. degree in Computer Science in 2003 from University Politehnica, Bucharest. Now he is Lecturer at the Computer Department, University Politehnica, Bucharest. His research interests are focused on: Fuzzy Systems, Digital Circuits, VLSI circuits, and Robotics.

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CITE THIS PAPER AS:
Mircea IVĂNESCU, Mihaela Cecilia FLORESCU, Nirvana POPESCU, Decebal POPESCU, The Control of the Hyper-redundant Manipulators by Frequency Criteria, Studies in Informatics and Control, ISSN 1220-1766, vol. 18 (3), pp. 279-288, 2009.

1. Introduction

The hyper-redundant arms with continuum elements are a special class of robots that perform the grasping function by coiling. This function is often met in the animal world. The elephant trunk, the octopus tentacle or constrictor snakes represent the well-known biological models. The enveloping grasps are superior in terms of restraining objects. As a technical solution, the grasping by wrapping, by coiling is used for restraint, fixturing and dexterous manipulation.

The control of these systems is complex, indeed, and a large number of researchers have tried to cater solutions. In (Gravagne et al., 2000), Gravagne analyzed the kinematic model of “hyper-redundant” robots, known as “continuum” robots. Remarkable results were achieved by Chirikjian and Burdick (Chirikjian et al., 1990, 1993, 1995), who laid the foundations of the kinematic theory of hyper-redundant robots. Their findings are based on a “backbone curve” that captures the robot’s macroscopic geometric features. The inverse kinematics problem is reduced to determining the time varying backbone curve behaviour. New methods of determining “optimal” hyper-redundant manipulator configurations underpinning a continuous formulation of kinematics are developed. Mochiyama investigated the problem of controlling the shape of an HDOF rigid-link robot with two-degree-of-freedom joints using spatial curves (Mochiyama et al., 1998, 1999). In (Robinson et al., 1999), the “state of art” of continuum robots, their areas of application and some control issues are presented. Other papers (Ivanescu et al., 2008, Filip et al., 2009) deal with several technological solutions for actuators used in hyper-redundant structures and with conventional control systems. The artificial intelligence methods in these complex systems are discussed in (Tangour et al., 2008, Dzitac et al., 2009).

The current paper investigates the control problem of a class of hyper-redundant arms with continuum elements that performs the grasping function by coiling. The dynamics of the arm during non-contact or contact operations with the environment are analyzed. The frequency criteria for the stability and control algorithms are also discussed.

The paper is organized as follows: Section II presents technological and theoretical preliminaries; Section III studies the dynamic model for non-contact motions; Section IV presents a frequency criterion and position control law; Section V discusses the dynamics of the arm and load in a grasping function; Section VI presents an extension of the Popov criterion for this class of systems; Section VII verifies the control laws by computer simulation.

6. Conclusions

The paper treats the control problem of a hyper-redundant robot with continuum elements that performs the coil function for grasping. The structure of the arm is given by flexible composite materials, as a layer structure, which ensures the flexibility, the driving and position measuring. First, the dynamic model of continuum arm for the position control during non-contact operations with environment is studied and a frequency stability criterion based on KYP Lemma is introduced. The P and PD control algorithms are proposed. The control algorithms based on SMA actuators are introduced. Numerical simulations of the arm motion toward a imposed target prove the correctitude of the solutions.

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