The kinematics of modular spatial hyper-redundant manipulators formed from RPS-type limbs

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Abstract

This study addresses the kinematics, including position, velocity and acceleration analyses, of a modular spatial hyper-redundant manipulator built with a variable number of serially connected identical mechanical modules with autonomous motions. First, the kinematics of the base module, a three-legged in-parallel manipulator, is formulated using the theory of screws. After that, the results thus obtained, are applied recursively for accomplishing the kinematic analyses of the hyper-redundant manipulator at hand. A numerical exampled is included.

Research highlights

► The kinematics of a hyper-redundant manipulator is achieved by means of the screw theory. ► The base module of the robot is a three-legged parallel manipulator. ► The robot under study has a compact topology due to the introduction of compound joints. ► A case study is verified with the aid of a commercially available software.

Introduction

Manipulators can be subdivided into two main groups: parallel and serial. While the first class are more stiff and precise than the second class, they suffer from a limited workspace and a poor manipulability. On the other hand, a Modular Spatial Hyper-Redundant Manipulator (MSHRM), or a modular robot for brevity, is a mechanism which combines harmoniously the mechanical advantages of both types of manipulators. Consider for instance that, due to these merits, MSHRMs have been proposed as self-reconfigurable and self-repairable robot arms.

As it was introduced by Chirikjian [1] “The term hyper-redundant refers to robotic manipulators and mobile robots with a very large, possibly infinite, number of actuable degrees of freedom. These robots are analogous in morphology and operation to snakes, worms, elephant trunks, and tentacles”. It is worth mentioning that the kinematic analysis of such mechanisms is a rather complicated task which has been firstly approached by means of a continuous backbone curve containing essential macroscopic geometric features of the desired motions [2], [3], [4]. Furthermore, modular robots are robotic systems made up of many identical but independent mechatronics modules that can autonomously control its joints [5]. If the modules have the possibility of connecting to, disconnecting from, and relocating to, without external help, then it is said that the robot is self-reconfigurable [6]. These mechanisms, due to an extraordinary number of actuable degrees of freedom, have a high manipulability. Obstacle avoidance ability, sophisticated grasping and robot locomotion are among the most important benefits of such exceptional degree of manipulability. Examples of the performance of hyper-redundant manipulators can be found in nature itself, giving birth to several mechanisms with representative names like snake [7], [8], serpentine [9], tentacle [10] or elephant’s trunk [11]. If the manipulator’s payload is small, it is desirable and convenient to drive it with the minimum number of motors [12]. However, if the load capacity of the manipulator is large, then the number of degrees of freedom is usually the same as the number of motive elements. For instance, it is hard to imagine a powerful mechanical digger, a device with 3-dof, driven by a single piston. On the other hand, it is opportune to mention that in order to improve the manipulability of a general Gough–Stewart platform, it can be transformed into a serial–parallel manipulator with decoupled motions [13], [14], [15]; self-contained modules with autonomous motions is the fundamental idea of a MSHRM.

In [16], the position analysis of hyper-redundant manipulators built with two or more 3-RPS parallel manipulators (where R, P and S stand for Revolute, Prismatic and Spherical, respectively, while the upper asterisk denotes an active joint) assembled in series connection is investigated. Such architecture requires the kinematic assembly of triangular and hexagonal platforms, and more importantly requires the mathematical manipulation of a large number of parameters for the position analysis. A similar manipulator, namely 2(3-SPR) serial–parallel manipulator, was proposed in [17], the comments above mentioned are applicable to this mechanism too. In a previous contribution, Badescu and Mavroidis [18], studied the performance indices to characterize the workspace of reconfigurable hyper-redundant manipulators using combinations of translational and orientational parallel platforms. With this in mind, this study shows how a more compact topology than that proposed in [16], [17] can be obtained by introducing spherical-revolute joints, avoiding the necessity of using different types of platforms and simplifying the position analysis. Furthermore, this work approaches not only the position analysis of the hyper-redundant manipulator, but also the velocity and acceleration analyses which are crucial steps in the design process of any mechanical device.

The paper is organized as follows. In Section 2, a description of the proposed MSHRM is provided. In Section 3, the kinematic analysis of the base module is accomplished using the screw theory. In Section 4, the kinematic analyses, including position, velocity and acceleration analyses, of the proposed MSHRM is presented. Finally, in Section 5 a case study which consists of solving the kinematics of a MSHRM built with four modules is provided.

Section snippets

Description of the modular spatial hyper-redundant manipulator

The conceptual design of a MSHRM requires strategies for simplifying its analysis and operation. For example, a general Gough–Stewart platform is a spatial mechanism whose forward position analysis produces 40 possible solutions [19]. In fact, one of the best solutions presented so far is one in polynomial form [20]. An effective closed-form solution, capable of being expressed as an echelon-form solution, is a difficult endeavor, unrealistic at this time. Therefore, the idea of using this type

Kinematic submodel

In this section, the velocity and acceleration analyses of the base module, a 3-RPS parallel manipulator, are carried out using the theory of screws which is isomorphic to the Lie algebra e(3) also known as motor algebra. For the sake of completeness, the position analysis of a single 3-RPS parallel manipulator is provided in the Appendix.

Kinematics of the modular spatial hyper-redundant manipulator

In this section, the kinematic analysis of the proposed MSHRM, a n(3-RPS) spatial mechanism where n is the number of modules, is provided. The results previously obtained for the kinematics of the three-legged in-parallel manipulator are the basis of this section.

First, consider that the coordinates of the spherical joints attached at the output platform are calculated as [Bi1]=0Tn1[Bin1]i{1,2,3} where Bi=(Xi,Yi,Zi) are the coordinates of the ith point expressed in the reference frame S0

Case study

In this section the forward kinematics of a 4(3-RPS) mechanism is solved applying the theory of screws.

The parameters of the base module, using hereafter SI units, are provided in Table 1.

While the periodical functions shown in Table 2 are chosen as the generalized coordinates.

Thus, the forward position analysis, using Appendix, leads to 65 536 possible solutions,3

Conclusions

In this study, we have proposed a computationally efficient method to realize the kinematic analysis, up to the acceleration analysis, of 3-RPS manipulator modules using the screw theory, and subsequently that of the modular spatial hyper-redundant manipulators built with these modules. The contributions of this study include proposing a manipulator topology leading to a computationally efficient kinematic formulation, and extending the theory of screws to the acceleration analysis of the

Acknowledgement

This work was supported by Dirección General de Educación Superior Tecnológica, DGEST, of México.

Jaime Gallardo received his M.Sc. in Mechanical Engineering in 1989 from the Instituto Tecnológico de Celaya, México, and Ph.D. in Electrical Engineering from the Instituto Tecnológico de la Laguna, México. For several years, Prof. Gallardo worked in prestigious research Institutions founded by the National Council of Science and Technology of México, CONACYT, like IMEC and CIATEQ. In 1993 he joined the Department of Mechanical Engineering of the Instituto Tecnológico de Celaya where he is

References (40)

  • G.S. Chirikjian et al.

    Kinematically optimal hyper-redundant manipulator configurations

    IEEE Transactions on Robotics and Automation

    (1995)
  • J.W. Burdick et al.

    A ‘sidewinding’ locomotion gait for hyper-redundant robots

    Advanced Robotics

    (1995)
  • H. Bojinov et al.

    Emergent structures in modular self-reconfigurable Robots

  • F. Yanqiong et al.

    Modular structure of a self-reconfigurable robot

    Frontiers of Mechanical Engineering in China

    (2007)
  • K.J. Kyriakopoulos et al.

    The NTUA snake: design, planar kinematics, and motion planning

    Journal of Robotic Systems

    (1999)
  • W.I. Clement et al.

    Design of a snake-like manipulator

    Robotics and Autonomous Systems

    (1990)
  • E. Paljug, T. Ohm, S. Hayati, The JPL serpentine robot: a 12-DOF system for inspection, in: Proceedings of the IEEE...
  • J.S. Pettinato, H.E. Stephanou, Manipulability and stability of a tentacle based robot manipulator, in: Proceedings of...
  • M.W. Hanan et al.

    Kinematics and the implementation of an elephant’s trunk manipulator and other continuum style robots

    Journal of Robotic Systems

    (2003)
  • L. Yanming et al.

    Design and study of a novel hyper-redundant manipulator

    Robotica

    (2003)
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    Jaime Gallardo received his M.Sc. in Mechanical Engineering in 1989 from the Instituto Tecnológico de Celaya, México, and Ph.D. in Electrical Engineering from the Instituto Tecnológico de la Laguna, México. For several years, Prof. Gallardo worked in prestigious research Institutions founded by the National Council of Science and Technology of México, CONACYT, like IMEC and CIATEQ. In 1993 he joined the Department of Mechanical Engineering of the Instituto Tecnológico de Celaya where he is currently a full time Professor. He is member of the National System of Researchers, SNI; of México and his research fields include spatial kinematics and dynamics, more specifically kinematics and dynamics of robotic systems using the screw theory, development of software engineering and machine theory. Dr. Gallardo had authored/co-authored more than 30 regular papers published in several journals, approaching these topics.

    Raúl Lesso received his Bachelor in Mechanical Engineering in 1991, and M.Eng. in Mechanical Engineering in 1993, both from the Universidad de Guanajuato, Mexico, and his M.Sc. in Finite Element Method from the Universidad de Educación a Distancia UNED, Spain. For many years Prof. Lesso worked for different companies and prestigious research Institutions of Mexico. In 1994 he joined the Department of Mechanical Engineering of the Instituto Tecnológico de Celaya where he is currently a full time Professor. His main interests cover finite element methods, biomechanics and computer aided design.

    José M. Rico received his Bachelor in Mechanical Engineering in 1974 from the Instituto Tecnológico de Celaya, México; his M.Eng. in 1977 from the Instituto Tecnológico y de Estudios Superiores de Monterrey Campus Monterrey, México; and his Ph.D. in Mechanical Engineering from the University of Florida in 1988. He spent some years in postdoctoral stays in the University of Florida, the Arizona State University and the University of California at Davis. He is a member of the National System of Researchers of México, the IFToMM, and the American Society of Mechanical Engineers, where he is an Associate Editor of the ASME Journal of Mechanical Design. After more than twenty years of productive work, in 2006 Dr. Rico decided to retire from Instituto Tecnológico de Celaya and joined the Department of Mechanical Engineering of FIMEE of the Universidad de Guanajuato, where he is currently a full time Professor. His main research interests include the kinematics and dynamics of spatial chains, theoretical and applied robot kinematics, as well as mechanical vibrations. Prof. Dr. Rico had authored/co-authored more than 40 regular papers and chapters published in several journals and books.

    Gürsel Alici received his B.Sc. degree with high honours from Middle East Technical University, Gaziantep, Turkey, in 1988 and his M.Sc. degree from Gaziantep University in 1990 (both degrees in mechanical engineering); and his Ph.D degree in Robotics from Oxford University, UK, in 1993. He is currently an Associate Professor at the School of Mechanical, Materials and Mechatronic Engineering in the University of Wollongong, Australia, where he leads Mechatronic Engineering. His research interests are in the areas of mechanics, optimum design, control and calibration of mechanisms/robot manipulators/parallel manipulators, micro/nano manipulation systems, and modelling, analysis and characterisation of conducting polymer actuators and sensors for use in functional biomimetic and robotic devices. These researches have generated more than 100 fully-refereed international journal and conference papers.

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