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Flexible Multibody Dynamics: Review of Past and Recent Developments
 Journal of Multibody System Dynamics
, 1997
"... Abstract. In this paper, a review of past and recent developments in the dynamics of flexible multibody systems is presented. The objective is to review some of the basic approaches used in the computer aided kinematic and dynamic analysis of flexible mechanical systems, and to identify future direc ..."
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Cited by 71 (5 self)
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Abstract. In this paper, a review of past and recent developments in the dynamics of flexible multibody systems is presented. The objective is to review some of the basic approaches used in the computer aided kinematic and dynamic analysis of flexible mechanical systems, and to identify future directions in this research area. Among the formulations reviewed in this paper are the floating frame of reference formulation, the finite element incremental methods, large rotation vector formulations, the finite segment method, and the linear theory of elastodynamics. Linearization of the flexible multibody equations that results from the use of the incremental finite element formulations is discussed. Because of space limitations, it is impossible to list all the contributions made in this important area. The reader, however, can find more references by consulting the list of articles and books cited at the end of the paper. Furthermore, the numerical procedures used for solving the differential and algebraic equations of flexible multibody systems are not discussed in this paper since these procedures are similar to the techniques used in rigid body dynamics. More details about these numerical procedures as well as the roots and perspectives of multibody system dynamics are discussed in a companion review by Schiehlen [79]. Future research areas in flexible multibody dynamics are identified as establishing the relationship between different formulations, contact and impact dynam
Robot Dynamics: Equations and Algorithms
 IEEE Int. Conf. Robotics and Automation
, 2000
"... This paper reviews some of the accomplishments in the field of robot dynamics research, from the development of the recursive NewtonEuler algorithm to the present day. Equations and algorithms are given for the most important dynamics computations, expressed in a common notation to facilitate their ..."
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Cited by 68 (4 self)
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This paper reviews some of the accomplishments in the field of robot dynamics research, from the development of the recursive NewtonEuler algorithm to the present day. Equations and algorithms are given for the most important dynamics computations, expressed in a common notation to facilitate their presentation and comparison. 1
Underactuated Mechanical Systems
 Control Problems in Robotics and Automation
, 1998
"... In this paper we discuss the control of underactuated mechanical systems. Underactuated mechanical systems have fewer control inputs than degrees of freedom and arise in applications, such as space and undersea robots, mobile robots, flexible robots, walking, brachiating, and gymnastic robots. The L ..."
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Cited by 58 (1 self)
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In this paper we discuss the control of underactuated mechanical systems. Underactuated mechanical systems have fewer control inputs than degrees of freedom and arise in applications, such as space and undersea robots, mobile robots, flexible robots, walking, brachiating, and gymnastic robots. The Lagrangian dynamics of these systems may contain feedforward nonlinearities, nonminimum phase zero dynamics, nonholonomic constraints, and other properties that place this class of systems at the forefront of research in nonlinear control [21, 13]. A complete understanding of the control of these systems is therefore lacking. We will discuss the application of geometric nonlinear control, as well as methods based on passivity and energy for stabilization and tracking control. We will survey some of the existing results and point to open research problems. 1 Introduction A mechanical system may be "underactuated" in several ways. The most obvious way is from intentional design as in the brac...
Modeling, Design and Control of Flexible Manipulator Arrns: A Tutorial Review
 Proceedings of the 2 P Conference on Decision, Control and Dynamics
, 1996
"... The desire for higher performance manipulators has lead to dynamic behavior in which the flexibility is an essential aspect. This paper first examines the mathematical representations commonly used in modeling flexible arms and arms with flexible drives. Then design considerations directly arising f ..."
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Cited by 17 (3 self)
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The desire for higher performance manipulators has lead to dynamic behavior in which the flexibility is an essential aspect. This paper first examines the mathematical representations commonly used in modeling flexible arms and arms with flexible drives. Then design considerations directly arising from the flexible nature of the arm are discussed. Finally, controls of joints for general and tip motion are discussed. MODELING FLEXIBLE ~ Models are used for simulation, analysis, and synthesis. In robotics, models may be used directly in the control algorithm with the computed torque technique. We will first look at the representation
Inverse dynamics and kinematics of multilink elastic robots: An iterative frequency domain approach
 Int. J. Robotics Research
, 1989
"... A technique is presented and experimentally validated for solving the inverse dynamics and kinematics of multilink flexible robots. The proposed method finds the joint torques necessary to produce a specified endeffector motion. Since the inverse dynamic problem in elastic manipulators is closely ..."
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Cited by 16 (0 self)
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A technique is presented and experimentally validated for solving the inverse dynamics and kinematics of multilink flexible robots. The proposed method finds the joint torques necessary to produce a specified endeffector motion. Since the inverse dynamic problem in elastic manipulators is closely coupled to the inverse kinematic problem, the solution of the first also renders the displacements and rotations at any point of the manipulator, including the joints. Furthermore the formulation is complete in the sense that it includes all the nonlinear terms due to the large rotation of the links. The Timoshenko beam theory is used to model the elastic characteristics, and the resulting equations of motion are discretized using the finite element method. An iterative solution scheme is proposed that relies on local linearization of the problem. The solution of each linearization is carried out in the frequency domain. The performance and capabilities of this technique are tested, first through simulation analysis, and second through experimental validation using feedforward control. Results show the potential use of this method not only for openloop control, but also for incorporation in feedback control strategies. 1.
S.: An Iterative Scheme for Learning Gravity Compensation in Flexible Robot Arms
 Automatica
, 1994
"... Abstract. Mimicking the case of rigid robot arms, the setpoint regulation problem for manipulators with flexible links moving under gravity can be solved by either modelbased compensation or PID control. The former cannot be applied if an unknown payload is present or when model parameters are poo ..."
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Cited by 8 (1 self)
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Abstract. Mimicking the case of rigid robot arms, the setpoint regulation problem for manipulators with flexible links moving under gravity can be solved by either modelbased compensation or PID control. The former cannot be applied if an unknown payload is present or when model parameters are poorly estimated, while the latter requires fine and lengthy tuning of gains in order to achieve good performance on the whole workspace. Moreover, no global convergence proof has been yet given for PID control of flexible robot arms. In this paper, a simple iterative scheme is proposed for generating exact gravity compensation at the desired set point, without the knowledge of rigid or flexible dynamic model terms. The control law starts with a PD action on the error at the joint level, updating at discrete instants an additional feedforward term. Global convergence of the scheme is proved under a mild condition on the proportional gain and a structural property on the arm stiffness, which is usually satisfied in practice. Experimental results are presented for a twolink robot with a flexible forearm moving on a tilted plane.
An efficient calculation of the flexible manipulator inverse dynamics
 International Journal of Robotics Research
, 1998
"... This article presents an efficient recursive computation of the inverse dynamics of flexible manipulators. The algorithm is equivalent to the nonlinear computed torque law offlexible manipulators. The computation method is based on the generalized NewtonEuler model of flexible manipulators and ca ..."
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Cited by 7 (4 self)
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This article presents an efficient recursive computation of the inverse dynamics of flexible manipulators. The algorithm is equivalent to the nonlinear computed torque law offlexible manipulators. The computation method is based on the generalized NewtonEuler model of flexible manipulators and can be considered as a generalization of the computed torque control algorithm of rigid robots proposed by Luh, Walker, and Paul for executing joint trajectories. The given algorithm is programmed using Mathematica to get automatically an efficient customized symbolic model with a reduced number of operations. 1.
Spatial Dynamics of Deformable Multibody Systems with Variable Kinematic Structure: Part2Velocity Transforma tion
 ASME Journal of Mechanical Design
, 1990
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Trajectory Control of Flexible Manipulators
 Control Problems in Robotics and Automation
, 1997
"... We present some feedback control techniques recently developed for the exact solution of trajectory tracking problems for manipulators with flexible elements. Two classes are considered: i) robots with rigid links but with elastic transmissions, in which flexibility is concentrated at the joints, a ..."
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Cited by 5 (0 self)
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We present some feedback control techniques recently developed for the exact solution of trajectory tracking problems for manipulators with flexible elements. Two classes are considered: i) robots with rigid links but with elastic transmissions, in which flexibility is concentrated at the joints, and ii) robots with lightweight and/or long arms, where flexibility is distributed along the links. For robots with elastic joints, we introduce a generalized inversion algorithm for the synthesis of a dynamic feedback control law that gives inputoutput decoupling and full state linearization. For robots with flexible links, the endeffector t ajectory tracking problem is solved based on the iterative computation of the link deformations associated with the desired output motion, combined with a state trajectory regulator. For both robot models, the control design is performed irectly on the secondorder dynamic equations. 1. In t roduct ion Modeling robot manipulators as rigid mechanical systems is an idealization
Dynamic modeling of structurallyflexible planar parallel manipulator
"... This paper presents a dynamic model of a planar parallel manipulator including structural flexibility of several linkages. The equations of motion are formulated using the Lagrangian equations of the first type and Lagrangian multipliers are introduced to represent the geometry of multiple closed l ..."
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Cited by 3 (1 self)
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This paper presents a dynamic model of a planar parallel manipulator including structural flexibility of several linkages. The equations of motion are formulated using the Lagrangian equations of the first type and Lagrangian multipliers are introduced to represent the geometry of multiple closed loop chains. Then, an active damping approach using a PZT actuator is described to attenuate structural vibration of the linkages. Overall dynamic behavior of the manipulator, induced from structural flexibility of the linkage, is well illustrated through simulations. This analysis will be used to develop a prototype parallel manipulator.