Dynamics and control of redundantly actuated parallel manipulators
TL;DR: In this article, a simple scheme for computing the inverse dynamics of a redundant actuation of a parallel manipulator is proposed, and four basic control algorithms, a joint-space proportional derivative (PD), a PD control in generalized coordinates, an augmented PD control, and a computed-torque control, are formulated.
Abstract: It has been shown that redundant actuation provides an effective means for eliminating singularities of a parallel manipulator, thereby improving its performance such as Cartesian stiffness and homogeneous output forces. Based on this concept, several high-performance parallel manipulator prototypes have been designed. A major difficulty that prevents application of the vast control literature developed for the serial counterparts to redundantly actuated parallel manipulators is the lack of an efficient dynamical model for real-time control. In this paper, using the Lagrange-D'Alembert formulation, we propose a simple scheme for computing the inverse dynamics of a redundantly actuated parallel manipulator. Based on this approach, four basic control algorithms, a joint-space proportional derivative (PD) control, a PD control in generalized coordinates, an augmented PD control, and a computed-torque control, are formulated. A two-degrees-of-freedom redundantly acutated parallel manipulator designed for a high-speed assembly task is used to verify the simplicity of the proposed approach and to evaulate the performance of the four control algorithms.
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TL;DR: A robot control/identification scheme to identify the unknown robot kinematic and dynamic parameters with enhanced convergence rate was developed, and the information of parameter estimation error was properly integrated into the proposed identification algorithm, such that enhanced estimation performance was achieved.
Abstract: For parameter identifications of robot systems, most existing works have focused on the estimation veracity, but few works of literature are concerned with the convergence speed. In this paper, we developed a robot control/identification scheme to identify the unknown robot kinematic and dynamic parameters with enhanced convergence rate. Superior to the traditional methods, the information of parameter estimation error was properly integrated into the proposed identification algorithm, such that enhanced estimation performance was achieved. Besides, the Newton–Euler (NE) method was used to build the robot dynamic model, where a singular value decomposition-based model reduction method was designed to remedy the potential singularity problems of the NE regressor. Moreover, an interval excitation condition was employed to relax the requirement of persistent excitation condition for the kinematic estimation. By using the Lyapunov synthesis, explicit analysis of the convergence rate of the tracking errors and the estimated parameters were performed. Simulation studies were conducted to show the accurate and fast convergence of the proposed finite-time (FT) identification algorithm based on a 7-DOF arm of Baxter robot.
321 citations
Cites background from "Dynamics and control of redundantly..."
...Many well-performed robot controllers such as computed torque control [7], augmented proportional-derivative control [8], and impedance control [9] are model-based control and have been successfully implemented in a wide range of robot applications....
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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
TL;DR: A methodology of using scaling factors to determine the force capabilities of non-redundantly and redundantly-actuated parallel manipulators is presented in this paper, which allows the actuator limits to be easily incorporated into the problem of determining force capabilities.
210 citations
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.
180 citations
Additional excerpts
...E.g., the prismatic joint variables as independent coordinates of a Hexapod locally determine its configuration uniquely....
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TL;DR: In this paper, a robust PID controller is proposed for the cable-driven parallel manipulators to ensure that all cables remain in tension and internal force concept is used in the proposed PID control algorithm.
174 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
"Dynamics and control of redundantly..." refers methods in this paper
...The method of Lagrangian equations with constraints in Murray, Li, and Sastry [ 14 ] can also be used to formulate the dynamics of redundantly actuated parallel manipulators....
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...According to [ 14 ], the dynamics of each planar manipulator is given by...
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01 Jun 1989
TL;DR: A general and systematic computational scheme of the inverse dynamics of closed-link mechanisms derived by using d'Alembert's principle and obtained without computing the Lagrange Multipliers is discussed.
Abstract: The authors discuss a general and systematic computational scheme of the inverse dynamics of closed-link mechanisms. It is derived by using d'Alembert's principle and obtained without computing the Lagrange Multipliers. To account for the constraints, only the Jacobian matrix of the passive joint angles in terms of actuated ones is required. Given a nonredundant actuator system, this allows a unique representation of the constraints even for complicated multiloop closed-link mechanisms. The inverse dynamics of closed-link mechanisms that contain redundant actuators and their redundancy optimization are also discussed. For a redundant actuation system that contains N/sub r/ redundant actuators, the passive joint angles are represented by N/sub r/+1 independent ways as functions of actuated joints. Using their Jacobian matrices, the actuation redundancy of a closed-link mechanism is parameterized by an N/sub r/-dimensional arbitrary vector in a linear equation. Numerical examples are given to show the computational efficiency of inverse dynamics computation and the potential of closed-link manipulators with actuation redundancy. >
294 citations
"Dynamics and control of redundantly..." refers background in this paper
...Nakamura [ 12 ] presented a dynamics formulation that could be applied to redundant parallel manipulators, but the result is ambigous....
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...Note that (8) and (9) have the same form as that in Nakamura [ 12 ], but their derivations are much simpler and more straightforward....
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16 May 1998
TL;DR: A novel control scheme that guarantees a lower bound of the end-effector stiffness (LBSC) is presented and is compared with a traditional control scheme for high-speed applications using the minimal 2-norm of actuator torques.
Abstract: A 2-DOF parallel manipulator with actuation redundancy is examined for high-speed and stiffness-controlled operation. Advantages of actuation redundancy are outlined. The kinematics and singularity-free workspace of the manipulator are presented together with a force transmission analysis. Finally, a novel control scheme that guarantees a lower bound of the end-effector stiffness (LBSC) is presented. Simulation results are compared with a traditional control scheme for high-speed applications using the minimal 2-norm of actuator torques.
172 citations
"Dynamics and control of redundantly..." refers background in this paper
...It has been shown that redundant actuation can be an effective mean for eliminating singularities in parallel manipulator designs and thus imporving their performances [2]‐[ 4 ]....
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143 citations
TL;DR: The present method uses a forward recursive scheme to compute velocities and accelerations, the Newton-Euler equation to calculate inertia forces/torque, and the virtual work principle to formulate the dynamic equations of motion.
Abstract: The computational efficiency of inverse dynamics of a manipulator is important to the real-time control of the system. For serial manipulators, the recursive Newton-Euler method has been proven to be the most efficient. However, for more general manipulators, such as serial manipulators with closed kinematic loops or parallel manipulators, it must be modified accordingly and the resultant computational efficiency is degraded. This article presents a computationally efficient scheme based on the virtual work principle for inverse dynamics of general manipulators. The present method uses a forward recursive scheme to compute velocities and accelerations, the Newton-Euler equation to calculate inertia forces/torque, and the virtual work principle to formulate the dynamic equations of motion. This method is equally effective for serial and parallel manipulators. For serial manipulators, its computational efficiency is comparable to the recursive Newton-Euler method. For parallel manipulators or serial manipulators with closed kinematic loops, it is more efficient than the existing methods. As an example, the computations of inverse dynamics (including inverse kinematics) of a general Stewart platform require only 842 multiplications, 511 additions, and 12 square roots.
139 citations