An efficient gradient projection optimization scheme for a seven-degree-of-freedom redundant robot with spherical wrist

Dubey, Rajiv; Euler, J.A.; Babcock, S.M.

doi:10.1109/robot.1988.12019

Cited by 67 publications

(22 citation statements)

References 12 publications

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“…choosing ~10 = (Oh/Oq) r. Notice that any differentiable cost function may be used as long as the function can be reduced to an expression in terms of the joint variables only. Examples of cost functions can be found in Li6geois (1977) for the avoidance of mechanical joint limits, in Yoshikawa (1985a,b) for the maximization of kineto-static and dynamic manipulability measures respectively, and in Dubey, Euler and Babcock (1988) for the maximization of various criteria. Yet another solution based on proper bounds for the rate of change of the Jacobian to be optimized has been proposed by Mayorga and Wong (1988).…”

Section: Gradient Projection Methodsmentioning

confidence: 99%

Kinematic control of redundant robot manipulators: A tutorial

Siciliano

1990

J Intell Robot Syst

534

299

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In this paper, we present a tentatively comprehensive tutorial report of the most recent literature on kinematic control of redundant robot manipulators. Our goal is to lend some perspective to the most widely adopted on-line instantaneous control solutions, namely those based on the simple manipulator+s Jacobian, those based on the local optimization of objective functions in the null space of the Jacobian, those based on the task space augmentation by additional constraint tasks (with task priority), and those based on the construction of inverse kinematic functions.

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Section: Gradient Projection Methodsmentioning

confidence: 99%

Kinematic control of redundant robot manipulators: A tutorial

Siciliano

1990

J Intell Robot Syst

534

299

View full text Add to dashboard Cite

show abstract

“…Since the _ q þ k vector can also be used to execute some objective function wðq k Þ, such as obstacle avoidance, it is also possible to use the gradient projection scheme. 22 This method permits the projection of the gradient of a specific objective function rwðq k Þ (calculated in joint space) into Jacobian null space, as shown below…”

Section: Redundancy Resolution For a Single Manipulatormentioning

confidence: 99%

Redundancy analysis of cooperative dual-arm manipulators

Freddi

Longhi

Monteriù

et al. 2016

International Journal of Advanced Robotic Systems

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This paper presents the redundancy analysis of two cooperative manipulators, showing how they can be considered as a single redundant manipulator through the use of the relative Jacobian matrix. In this way, the kinematic redundancy can be resolved by applying the principal local optimization techniques used in the single manipulator case. We resolve the redundancy by using the Jacobian null space technique, which permits us to perform several tasks with different execution priority levels at the same time; this is a useful feature, especially when the manipulators are to be mounted on and cooperate with a mobile platform. As an illustrative example, we present a case study consisting of two planar manipulators mounted on a smart wheelchair, whose degrees of redundancy are employed to move an object along a predefined path, while avoiding an obstacle in the manipulator's workspace at the same time.

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“…Equation (6) requires fewer floating-point operations for a general than (2)- (5) with . When , (6) is similar in concept to the dual projection method [30] and the projection methods given in [31] for one degree of redundancy and [32] and [33] for general redundancy. Though somewhat faster, it is comparable with these in its computational cost.…”

Section: Computational Costsmentioning

confidence: 99%

On the implementation of velocity control for kinematically redundant manipulators

English¹,

Maciejewski

2000

IEEE Trans. Syst., Man, Cybern. A

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Abstract-The velocity control of kinematically redundant manipulators has been addressed through a variety of approaches. Though they differ widely in their purpose and method of implementation, most are optimizations that can be characterized by Liégeois's method. This characterization is used in this article to develop a single framework for implementing different methods by simply selecting a scalar, a function of configuration, and a joint-rate weighting matrix. These quantities are used to form a fully constrained linear system by row augmenting the manipulator Jacobian with a weighted basis of its nullspace and augmenting the desired hand motion with a vector function of the nullspace basis. The framework is shown to be flexible, computationally efficient, and accurate.

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An efficient gradient projection optimization scheme for a seven-degree-of-freedom redundant robot with spherical wrist

Cited by 67 publications

References 12 publications

Kinematic control of redundant robot manipulators: A tutorial

Kinematic control of redundant robot manipulators: A tutorial

Redundancy analysis of cooperative dual-arm manipulators

On the implementation of velocity control for kinematically redundant manipulators

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