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Journal ArticleDOI

Internal Preload Control of Redundantly Actuated Parallel Manipulators—Its Application to Backlash Avoiding Control

01 Aug 2005-IEEE Transactions on Robotics (IEEE)-Vol. 21, Iss: 4, pp 668-677
TL;DR: With this formulation a computational efficient open-loop preload control is developed and applied to the elimination of backlash and its simplicity makes it applicable in real-time applications.
Abstract: Redundant actuation of parallel manipulators can lead to internal forces without generating end-effector forces (preload). Preload can be controlled in order to prevent backlash during the manipulator motion. Such control is based on the inverse dynamics. The general solution of the inverse dynamics of redundantly actuated parallel manipulators is given. For the special case of simple overactuation an explicit solution is derived in terms of a single preload parameter. With this formulation a computational efficient open-loop preload control is developed and applied to the elimination of backlash. Its simplicity makes it applicable in real-time applications. Results are given for a planar 4RRR manipulator and a spatial heptapod.
Citations
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Journal ArticleDOI
TL;DR: A mechanics-based model for transforming desired beam configuration to tendon displacements and vice versa is presented and insight as well as performance gains are provided for this increasingly ubiquitous class of manipulators.
Abstract: Continuum robotic manipulators articulate due to their inherent compliance. Tendon actuation leads to compression of the manipulator, extension of the actuators, and is limited by the practical constraint that tendons cannot support compression. In light of these observations, we present a new linear model for transforming desired beam configuration to tendon displacements and vice versa. We begin from first principles in solid mechanics by analyzing the effects of geometrically nonlinear tendon loads. These loads act both distally at the termination point and proximally along the conduit contact interface. The resulting model simplifies to a linear system including only the bending and axial modes of the manipulator as well as the actuator compliance. The model is then manipulated to form a concise mapping from beam configuration-space parameters to n redundant tendon displacements via the internal loads and strains experienced by the system. We demonstrate the utility of this model by implementing an optimal feasible controller. The controller regulates axial strain to a constant value while guaranteeing positive tendon forces and minimizing their magnitudes over a range of articulations. The mechanics-based model from this study provides insight as well as performance gains for this increasingly ubiquitous class of manipulators.

576 citations


Cites background from "Internal Preload Control of Redunda..."

  • ...For redundantly actuated parallel manipulators, Fang et al. [13] minimized the sum of tendon forces and Muller [14] minimized a weighted sum of squares....

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Journal ArticleDOI
TL;DR: In this paper, a planar 3-DOF parallel manipulator with actuation redundancy is considered and a position and force switching control strategy is proposed based on the dynamic model.

258 citations

Journal ArticleDOI
TL;DR: This brief considers the control design problem for a flexible robotic manipulator using an output feedback method to represent a controller to handle the feedback signals that are not able to be measured directly.
Abstract: This brief considers the control design problem for a flexible robotic manipulator. Our control strategies are to: 1) move the manipulator to the certain desired angle; 2) suppress the vibration at the neighborhood of the desired angle; and 3) handle the backlash nonlinearity existing in the practical system. Based on the infinite-dimensional dynamic model, a boundary controller with input backlash is designed to achieve the control aims. An output feedback method is adopted to represent a controller to handle the feedback signals that are not able to be measured directly. The effectiveness of the designed controllers and the stability of the system are demonstrated by theoretical analysis, numerical simulations, and physical experiments.

182 citations

Journal ArticleDOI
TL;DR: These two indices provide tight upper bounds to the end-effector rotation and point-displacement sensitivity under a unit-magnitude array of actuated-joint displacements and are thought to be clear and definite to the designer of a robotic manipulator.
Abstract: Numerous performance indices have been proposed to compare robot architectures based on their kinematic properties. However, none of these indices seems to draw a consensus among the robotics community. The most notorious indices, which are manipulability and dexterity, still entail some drawbacks, which are mainly due to the impossibility to define a single invariant metric for the special Euclidean group. The natural consequence is to use two distinct metrics, i.e., one for rotations and one for point displacements, as has already been proposed by other researchers. This is the approach used in this paper, where we define the maximum rotation sensitivity and the maximum point-displacement sensitivity. These two indices provide tight upper bounds to the end-effector rotation and point-displacement sensitivity under a unit-magnitude array of actuated-joint displacements. Therefore, their meaning is thought to be clear and definite to the designer of a robotic manipulator. Furthermore, methods for the computation of the proposed indices are devised, some of their properties are established and interpreted in the context of robotic manipulator design, and an example is provided.

133 citations


Cites background from "Internal Preload Control of Redunda..."

  • ...Further information on the control of redundantly actuated manipulators may be found in [27], for example, where a redundant Gough–Stewart platform is also studied....

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Journal ArticleDOI
TL;DR: Primary advantages of PKM redundancy include workspace enlargement, singularity elimination/ avoidance, and improved joint-torque distribution, in contrast to the main challenges redundant mechanisms present, such as in motion planning and control, and calibration.
Abstract: Parallel kinematic mechanisms (PKM) have received particular attention due to their higher stiffness, increased payload capacity, and agility, when compared to their serial counterparts. Despite these significant advantages, however, most PKM designs, typically, yield limited workspace, problematic singularities, and configuration-dependent stiffness. In response, mechanism redundancy has emerged as an effective tool to address these and other problems. In this paper, we present an in-depth discussion of past research on PKM redundancy. The methodical review of the pertinent literature, first, introduces the concept of redundancy based on the number of actuators and the number of degrees of freedom required to perform a task and, then, discusses the two main types of redundancy according to the mobility of the mechanism, i.e., kinematic and actuation redundancy. Subsequently, research on the design aspects of redundant PKMs, including the various criteria used for design optimization is detailed. Primary advantages of PKM redundancy include workspace enlargement, singularity elimination/ avoidance, and improved joint-torque distribution. In this paper, these advantages are discussed in contrast to the main challenges redundant mechanisms present, such as in motion planning and control, and calibration. Other issues of PKM redundancy, briefly, presented herein for completeness are fault-tolerance, reconfigurability, cable-driven and hyper-redundant PKMs.

78 citations

References
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Book
22 Mar 1994
TL;DR: In this paper, the authors present a detailed overview of the history of multifingered hands and dextrous manipulation, and present a mathematical model for steerable and non-driveable hands.
Abstract: INTRODUCTION: Brief History. Multifingered Hands and Dextrous Manipulation. Outline of the Book. Bibliography. RIGID BODY MOTION: Rigid Body Transformations. Rotational Motion in R3. Rigid Motion in R3. Velocity of a Rigid Body. Wrenches and Reciprocal Screws. MANIPULATOR KINEMATICS: Introduction. Forward Kinematics. Inverse Kinematics. The Manipulator Jacobian. Redundant and Parallel Manipulators. ROBOT DYNAMICS AND CONTROL: Introduction. Lagrange's Equations. Dynamics of Open-Chain Manipulators. Lyapunov Stability Theory. Position Control and Trajectory Tracking. Control of Constrained Manipulators. MULTIFINGERED HAND KINEMATICS: Introduction to Grasping. Grasp Statics. Force-Closure. Grasp Planning. Grasp Constraints. Rolling Contact Kinematics. HAND DYNAMICS AND CONTROL: Lagrange's Equations with Constraints. Robot Hand Dynamics. Redundant and Nonmanipulable Robot Systems. Kinematics and Statics of Tendon Actuation. Control of Robot Hands. NONHOLONOMIC BEHAVIOR IN ROBOTIC SYSTEMS: Introduction. Controllability and Frobenius' Theorem. Examples of Nonholonomic Systems. Structure of Nonholonomic Systems. NONHOLONOMIC MOTION PLANNING: Introduction. Steering Model Control Systems Using Sinusoids. General Methods for Steering. Dynamic Finger Repositioning. FUTURE PROSPECTS: Robots in Hazardous Environments. Medical Applications for Multifingered Hands. Robots on a Small Scale: Microrobotics. APPENDICES: Lie Groups and Robot Kinematics. A Mathematica Package for Screw Calculus. Bibliography. Index Each chapter also includes a Summary, Bibliography, and Exercises

6,592 citations


"Internal Preload Control of Redunda..." refers background in this paper

  • ...1552-3098/$20.00 © 2005 IEEE According to the IFToMM terminology [7] a PM is a manipulator in which the end-effector (EE) is controlled by means of at least two kinematic chains going from the base to the EE....

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  • ...The vector of the remaining joint variables of passive joints is denoted with , so that ....

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  • ...The first approach yields an explicit formulation of the preload parameter as a function of time, while the second only yields its numerical values at specific time instants....

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Book
06 Apr 1990
TL;DR: The controlled Invariant Submanifolds and Nonlinear Zero Dynamics and the Disturbance Decoupling problem are studied.
Abstract: Contents: Introduction.- Manifolds, Vectorfields, Lie Brackets, Distributions.- Controllability and Observability, Local Decompositions.- Input-Output Representations.- State Space Transformation and Feedback.- Feedback Linearization of Nonlinear Systems.- Controlled Invariant Distribution and the Disturbance Decoupling Problem.- The Input-Output Decoupling Problem: Geometric Considerations.- Local Stability and Stabilization of Nonlinear Systems.- Controlled Invariant Submanifolds and Nonlinear Zero Dynamics.- Mechanical Nonlinear Control Systems.- Controlled Invariance and Decoupling for General Nonlinear Systems.- Discrete-Time Nonlinear Control Systems.- Subject Index.

2,573 citations


"Internal Preload Control of Redunda..." refers background in this paper

  • ...…kinematic and dynamic constraints are EE-constraints Closure constraints (8) It shall be emphasized that the kinematic basic functions (Jacobians) , the constraint Jacobian and their partial derivatives of any order can be given explicitly and algebraically in terms of screw products [3], [19]....

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Journal ArticleDOI
TL;DR: In this article, a performance index for the kinematic optimization of robotic manipulators is presented based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the joint and Cartesian spaces.
Abstract: In this paper, a novel performance index for the kinematic optimization of robotic manipulators is presented. The index is based on the condition number of the Jacobian matrix of the manipulator, which is known to be a measure of the amplification of the errors due to the kinematic and static transformations between the joint and Cartesian spaces. Moreover, the index proposed here, termed global conditioning index (CGI), is meant to assess the distribution of the aforementioned condition number over the whole workspace. Furthermore, the concept of a global index is applicable to other local kinematic or dynamic indices. The index introduced here is applied to a simple serial two-link manipulator, to a spherical three-degree-of-freedom serial wrist, and to three-degree-of-freedom parallel planar and spherical manipulators. Results of the optimization of these manipulators, based on the GCI, are included.

884 citations


"Internal Preload Control of Redunda..." refers background in this paper

  • ...The vector of the remaining joint variables of passive joints is denoted with , so that ....

    [...]

Journal ArticleDOI
TL;DR: A theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom, is presented and controlability and stabilizability results are derived.
Abstract: This paper presents a theoretical framework for the dynamics and control of underactuated mechanical systems, defined as systems with fewer inputs than degrees of freedom. Control system formulation of underactuated mechanical systems is addressed and a class of underactuated systems characterized by nonintegrable dynamics relations is identified. Controllability and stabilizability results are derived for this class of underactuated systems. Examples are included to illustrate the results; these examples are of underactuated mechanical systems that are not linearly controllable or smoothly stabilizable.

511 citations

Journal ArticleDOI
TL;DR: A tailored simultaneous solution strategy based on multiple shooting and reduced SQP is presented, which allows an efficient and robust solution of multistage optimal control and design optimization problems for large, sparse DAE process models of index one.

414 citations