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Journal ArticleDOI

Inverse kinematic solutions with singularity robustness for robot manipulator control

01 Sep 1986-Journal of Dynamic Systems Measurement and Control-transactions of The Asme (American Society of Mechanical Engineers)-Vol. 108, Iss: 3, pp 163-171
About: This article is published in Journal of Dynamic Systems Measurement and Control-transactions of The Asme.The article was published on 1986-09-01. It has received 1096 citations till now. The article focuses on the topics: Inverse kinematics & Parallel manipulator.
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Journal ArticleDOI
TL;DR: The concept of task priority in relation to the inverse kinematic problem of redundant robot manipulators is introduced and the effectiveness of the proposed redundancy control scheme is shown.
Abstract: In this paper, we describe a new scheme for redundancy control of robot manipulators. We introduce the concept of task priority in relation to the inverse kinematic problem of redundant robot manipulators. A required task is divided into subtasks according to the order of priority. We propose to determine the joint motions of robot manipulators so that subtasks with lower priority can be performed utilizing re dundancy on subtasks with higher priority. This procedure is formulated using the pseudoinverses of Jacobian matrices. Most problems of redundancy utilization can be formulated in the framework of tasks with the order of priority. The results of numerical simulations and experiments show the effectiveness of the proposed redundancy control scheme.

933 citations


Cites background from "Inverse kinematic solutions with si..."

  • ...Since pseudoinverse solutions often cause unstable motions near singularities (Nakamura and Hanafusa 1986), the robot manipulator will stop or oscillate before t = 8 s if we...

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Journal ArticleDOI
01 Jun 1997
TL;DR: A new task-priority redundancy resolution technique is developed that overcomes the effects of algorithmic singularities and is applied to a seven-degree-of-freedom manipulator in numerical case studies to demonstrate its effectiveness.
Abstract: Practical application of the task-priority redundancy resolution technique must deal with the occurrence of kinematic and algorithmic singularities. The aim of this paper is twofold. First, the application of existing singularity-robust methods to the case of kinematically redundant arms is studied. Then, a new task-priority redundancy resolution technique is developed that overcomes the effects of algorithmic singularities. Computational aspects of the solutions are also considered in view of real-time implementation of a kinematic control algorithm. The method is applied to a seven-degree-of-freedom manipulator in numerical case studies to demonstrate its effectiveness.

647 citations


Cites background from "Inverse kinematic solutions with si..."

  • ...Computational aspects of the solutions are also discussed in view of real-time implementation of a kinematic control algorithm....

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Proceedings ArticleDOI
19 Jun 1991
TL;DR: A general framework for managing multiple tasks in highly redundant systems is proposed, which derives joint velocity and acceleration solutions which can be used as reference input trajectories to suitable model-based controllers.
Abstract: The exploitation of kinematic redundancies in robotic systems may provide more dexterity and versatility in the execution of complex tasks. When functional constraint tasks are imposed in addition to the end-effector tasks, a task priority strategy is advisable. The authors propose a general framework for managing multiple tasks in highly redundant systems. In particular, they derive joint velocity and acceleration solutions which can be used as reference input trajectories to suitable model-based controllers. They also develop a recursive implementation, and discuss the occurrence of singularities in the Jacobian associated with the generic task. Two case studies illustrate the effectiveness of the algorithm on a snake-like robot. >

614 citations


Cites background from "Inverse kinematic solutions with si..."

  • ...To overcome this drawback, the generalized inverse should rather be a damped least-squares inverse [16,17] that allows to limit joint velocities in the neighborhood of singularities at the expenses of small tracking errors....

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Journal ArticleDOI
TL;DR: A tentatively comprehensive tutorial report of the most recent literature on kinematic control of redundant robot manipulators lends some perspective to the most widely adopted on-line instantaneous control solutions, namely those based on the simple manipulator's Jacobian.
Abstract: 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.

581 citations


Cites methods from "Inverse kinematic solutions with si..."

  • ...In order to overcome this drawback, Wampler (1986) and Nakamura and Hanafusa (1986) independently proposed the use of a damped least-square inverse of the Jacobian matrix in the form of J* = j r ( j j r + 2Zl)-~, corresponding to a modified Jacobian that is nonsingular in the whole workspace....

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Journal ArticleDOI
TL;DR: A new prioritized task-regulation framework based on a sequence of quadratic programs (QP) that removes the limitation of inequality constraints and is implemented and illustrated in simulation on the humanoid robot HRP-2.
Abstract: Redundant mechanical systems like humanoid robots are designed to fulfill multiple tasks at a time. A task, in velocity-resolved inverse kinematics, is a desired value for a function of the robot configuration that can be regulated with an ordinary differential equation (ODE). When facing simultaneous tasks, the corresponding equations can be grouped in a single system or, better, sorted in priority and solved each in the solutions set of higher priority tasks. This elegant framework for hierarchical task regulation has been implemented as a sequence of least-squares problems. Its limitation lies in the handling of inequality constraints, which are usually transformed into more restrictive equality constraints through potential fields. In this paper, we propose a new prioritized task-regulation framework based on a sequence of quadratic programs (QP) that removes the limitation. At the basis of the proposed algorithm, there is a study of the optimal sets resulting from the sequence of QPs. The algorithm is implemented and illustrated in simulation on the humanoid robot HRP-2.

377 citations


Cites background from "Inverse kinematic solutions with si..."

  • ...Of particular interest then is the solution with minimum norm, q̇1 = arg min x 1 2 ‖x‖2 (3) s.t. A1x = b1 (4) with A1 = ∂f1(q)/∂q, b1 = −λf1(q) (the ODE is only reformulated here in the constraint (4) without any modification)....

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