Inverse Dynamics and Kinematics of Multi- Link Elastic Robots: An Iterative Frequency Domain Approach

Bayo, Eduardo; Papadopoulos, Philip M.; Stubbe, James; Serna, Miguel Ángel

doi:10.1177/027836498900800604

Cited by 207 publications

(61 citation statements)

References 14 publications

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“…Frequency domain inversion has been proposed in [3,4] as one of the first solutions to this instability problem. By working in the Fourier domain, this method defines the required open-loop control torque in one step (for linear models of one-link flexible arms) or in few iterations (in multi-link manipulators).…”

Section: S T a B L E I N V E R S I O N C O N T R O Lmentioning

confidence: 99%

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Trajectory control of flexible manipulators

Luca

1998

Lecture Notes in Control and Information Sciences

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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 input-output decoupling and full state linearization. For robots with flexible links, the end-effector trajectory 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 directly on the second-order dynamic equations. I n t r o d u c t i o nModeling robot manipulators as rigid mechanical systems is an idealization that becomes unrealistic when higher performance is requested. Tasks involving fast motion and/or hard contact with the environment are expected to induce deflections in the robot components, eventually exciting an oscillatory behavior. There are two sources of vibration in robot manipulators: joint flexibility, due to the elasticity of motion transmission elements such as harmonic drives, belts, or long shafts [26], and link flezibility, introduced by a long reach and slender/lightweight construction of the arm [6,17]. In order to be able to counteract the negative effects of flexibility, advanced robot control systems should be designed on the basis of a more complete dynamic model of the robot (see, e.g. [27] and [5])In robotic systems with flexible elements, output trajectories are typically defined beyond the structural flexibility, i.e. in terms of link motion for robots with elastic joints or at the level of manipulator tip for robots with link flexibility. We address in this chapter the stable and accurate reproduction of such trajectories using model-based state feedback control. Standard tools for solving trajectory tracking problems in nonlinear systems, such as feedback linearization, input-output decoupling, or inversion control (see, e.g. [19]), are not sufficient in these cases, so that the application of more advanced control techniques should be investigated.

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Section: S T a B L E I N V E R S I O N C O N T R O Lmentioning

confidence: 99%

“…When the system is nonlinear the inversion algorithm is applied repeatedly, using successive linear approximations of the whole flexible manipulator equations around the nominal trajectory [4].…”

Section: E T H O D 2: I T E R a T I V E Inversion In T H E F R E Q mentioning

confidence: 99%

Trajectory control of flexible manipulators

Luca

1998

Lecture Notes in Control and Information Sciences

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“…17 However, the dynamics of multilink articulated exible structuresis more complicated.Some researchershave used a nite element method to numerically construct the dynamic equations. 18 Others have used the assumed modes approach. 19;20 In this paper, the assumed modes method is also used to parameterize the continuous deformation of both exible links.…”

Section: A Forward System Dynamicsmentioning

confidence: 99%

Tip Trajectory Tracking for Multilink Flexible Manipulators Using Stable Inversion

Zhao

Chen

1998

Journal of Guidance, Control, and Dynamics

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The recently developed stable inversion theory for nonminimum phase nonlinear systems is applied to output tracking for multilink exible robot manipulators. The stable inversion theory and a numerical solution to stable inverses are brie y reviewed. Forward dynamics of a two-link exible manipulator with tip position as the output is then given using the assumed modes method. From that, an inverse model is derived and a two-point boundary value condition is set up. This condition guarantees that the inverse solution for a given desired tip trajectory will be stable regardless of the fact that a exible manipulator is a nonminimum-phase system. The stable inverse is incorporated into an output tracking controller that uses only joint-angle feedback. Excellent tracking is achieved with no transient or steady-state errors and no internal vibration buildup.

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“…This cost functions contain various combinations of generalized co-ordinates of relative elastic displacements and their derivatives. Other older investigations in this area include a number of approaches developed for linear flexible systems, which shape the feed forward input such that it does not contain spectral components at system Eigen-frequencies (Bayo et al, 1989). Modifications of such methods have been applied to nonlinear flexible systems (Singh and Vadali, 1993), but they may yield a significant level of residual vibrations (Gorinevsky and Vukovich, 1997).…”

Section: Introductionmentioning

confidence: 99%

Optimal Maneuver of Mechanical System with Internal Degrees of Freedom with State-Variable Constraint

Zakrzhevskii¹

2014

JMSIC

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An effective procedure is presented for the determination of the optimal control input for maneuvers of a mechanical system with internal degrees of freedom such as a slewing of a spacecraft with flexible appendages or a displacement of a reservoir with a liquid for the case of constraint on velocity of the maneuver. The dynamic equations of motion are formulated, allowing taking into account the flexible elements using the quasistatical approach. The problem of optimal reorientation for rest-to-rest maneuvers is formulated using the objective function, which results in the minimal acceleration of the relative motion of the attached flexible elements during the maneuver. The new features and advantages of the proposed approach are the use of a not widely known objective function for the optimal control problem, which has a clear physical interpretation, and analytical solving the constrained optimization problem by the method based on parameterization of the functional for the multi-point boundary value problem. The solution is illustrated graphically. This analytical solution is applicable also for vibrations rejection at shaping the law of deployment of flexible constructions on spacecraft. It is useful for input shaping motion laws of objects of the ground-based transport in the modes of braking and acceleration for minimization of relative accelerations of passengers and goods.

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Inverse Dynamics and Kinematics of Multi- Link Elastic Robots: An Iterative Frequency Domain Approach

Cited by 207 publications

References 14 publications

Trajectory control of flexible manipulators

Trajectory control of flexible manipulators

Tip Trajectory Tracking for Multilink Flexible Manipulators Using Stable Inversion

Optimal Maneuver of Mechanical System with Internal Degrees of Freedom with State-Variable Constraint

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