Optimal control sequence for underactuated manipulators

Bergerman, Marcel; Xu, Yangsheng

doi:10.1109/robot.1996.509279

Cited by 24 publications

(13 citation statements)

References 6 publications

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“…Consider the single input, single output nonlinear system (6) where and are smooth -dimensional vector fields, and is a smooth, scalar-valued function. It is often possible to choose an input which makes assuming initial conditions are chosen correctly.…”

Section: Interpretation In Terms Of Zero Dynamicsmentioning

confidence: 99%

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Tracking fast inverted trajectories of the underactuated Acrobot

Berkemeier

Fearing

1999

IEEE Trans. Robot. Automat.

144

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The control of underactuated robot manipulators provides a significant challenge to the robotics engineer. The Acrobot is a simple underactuated system consisting of a double pendulum with an actuator at only the second joint. Previous work has shown how linearization methods can achieve the tracking of slow inverted trajectories. In this paper we derive a surprising set of exact trajectories of the nonlinear equations of motion, which involve inverted periodic motions. The trajectories can be made arbitrarily fast by appropriate choice of the Acrobot mass and length parameters. Next, we present a nonlinear control law (which has appeared elsewhere) and show how it can be applied to the Acrobot to track these trajectories. In simulations we compare tracking results for our controller and one based on pseudolinearization. The pseudolinearizing controller produces significant error for a 1 Hz trajectory, while ours produces none. Finally, we present experimental results which demonstrate that the assumptions of the theory were not overly restrictive. In particular, peak-to-peak oscillations of joint 2 as large as 85 were obtained, despite real-world effects, such as joint friction, inexact parameter values, and noisy and delayed joint velocity data.

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Section: Interpretation In Terms Of Zero Dynamicsmentioning

confidence: 99%

“…This was the basis for work by Arai et al [1], [2] and more recently by Bergerman et al [5], [6]. Jain and Rodriguez [13] developed generalized kinematics and dynamics concepts for underactuated manipulators including generalized Jacobian matrices and a computationally efficient approach to finding the equations of motion.…”

Section: Introductionmentioning

confidence: 99%

Tracking fast inverted trajectories of the underactuated Acrobot

Berkemeier

Fearing

1999

IEEE Trans. Robot. Automat.

144

View full text Add to dashboard Cite

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“…As an important part of nonlinear science and engineering, the technique of nonlinear optimal control theories and methods has been widely used in diverse engineering fields, such as chemical engineering [1][2][3], vibration engineering [4][5], robotics [6][7][8] and astrodynamics [9][10][11][12]. It is extremely difficult to analytically solve a nonlinear optimal control problem.…”

Section: Introductionmentioning

confidence: 99%

An hp symplectic pseudospectral method for nonlinear optimal control

Peng

Wang

2017

Communications in Nonlinear Science and Numerical Simulation

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An adaptive symplectic pseudospectral method based on the dual variational principle is proposed and is successfully applied to solving nonlinear optimal control problems in this paper. The proposed method satisfies the first order necessary conditions of continuous optimal control problems, also the symplectic property of the original continuous Hamiltonian system is preserved. The original optimal control problem is transferred into a set of nonlinear equations which can be solved easily by Newton-Raphson iterations, and the Jacobian matrix is found to be sparse and symmetric. The proposed method, on one hand, exhibits exponent convergence rates when the number of collocation points are increasing with the fixed number of sub-intervals; on the other hand, exhibits linear convergence rates when the number of sub-intervals is increasing with the fixed number of collocation points. Furthermore, combining with the hp method based on the residual error of dynamic constraints, the proposed method can achieve given precisions in a few iterations. Five examples highlight the high precision and high computational efficiency of the proposed method.

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“…In [10], the authors have applied an optimal control strategy, wherein the cost function considered is the reciprocal of the coupling index, a measure of the dynamic coupling available between the active and the passive joints of the manipulator. The authors Arai and his co-workers [11,12] have presented a control methodology for underactuated mechanical system with holding brakes on the passive joints.…”

Section: Introductionmentioning

confidence: 99%

Point-to-point control of a 2R planar horizontal underactuated manipulator

Mahindrakar

Rao

Banavar

2006

Mechanism and Machine Theory

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This paper presents a control strategy for a two-link manipulator with revolute joints (2R) with an unactuated second joint, wherein the motion of the system is confined to a horizontal plane. The model takes into account the frictional forces present in the system. The control objective is to move the end-effector from a given position to a target point. The methodology involves two stages. In the first stage a finite-time controller is used to move the passive link to its desired position. In the second stage, the first link is moved to its desired position keeping the second link at rest, using friction as a ''brake'' and subject to the constraint that the cross-coupling torque acting on the second joint does not exceed the static friction.

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Optimal control sequence for underactuated manipulators

Abstract: Abstract

Cited by 24 publications

References 6 publications

Tracking fast inverted trajectories of the underactuated Acrobot

Tracking fast inverted trajectories of the underactuated Acrobot

An hp symplectic pseudospectral method for nonlinear optimal control

Point-to-point control of a 2R planar horizontal underactuated manipulator

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