Control of redundant manipulators for task compatibility

Chiu, S.

doi:10.1109/robot.1987.1087795

Cited by 79 publications

(48 citation statements)

References 4 publications

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“…Alternative formulations for instantaneously optimizing a secondary criterion by augmenting the Jacobian matrix have also been presented [1], [5]. Some of the secondary criteria that have been applied include joint range availability [12], singularity avoidance [16], [18], various measures of dexterity [6], [7], [10], [19], [20], and obstacle avoidance [14], [18]. The homogeneous solution can also be used to optimize secondary criteria defined in Cartesian space, either to impose a priority to the manipulation variables [17] or to avoid obstacles [14], by using where x is an m-dimensional vector specifying the end effector velocity, iJ is an n-dimensional vector denoting the joint velocities, and J is the m by n Jacobian matrix.…”

Section: Kinetic Limitations On the Use Of Redundancy In Robotic Manimentioning

confidence: 99%

“…Under these conditions, there will in general be an acceleration at the end effector due to the rate of change of J as given by (5). The resulting joint angle acceleration required to maintain the desired configuration of the end effector is given by (6), which if one assumes that there is to be no acceleration along the homogeneous solution results in Unfortunately, because this is only a local minimization technique, it has been shown that the joint acceleration given by (10) can induce large joint velocities that may require physically unrealizable joint torques in order to maintain the desired end effector trajectory.…”

Section: Kinetic Effects Of a Homogeneous Solutionmentioning

confidence: 99%

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Kinetic limitations on the use of redundancy in robotic manipulators

Maciejewski

1991

IEEE Trans. Robot. Automat.

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where the C, are matrices of Coriolis and centrifugal coefficients. If T is used to denote the torque due to the minimum norm acceleration, then T can be obtained by substituting the first term of (6), i.e., the pseudoinverse solution, into (7), which results in where T is the vector of joint torques, H is the inertia matrix, C is a vector of torques due to Coriolis and centrifugal effects, and g is the gravity vector. The elements of the vector c can be written in quadratic form, so that It has been shown [8] that one can sacrifice the minimum norm acceleration in order to locally minimize the norm of the torque by using a solution of the form which uses a homogeneous acceleration term in a manner analogous to that of (4). The value of this minimum torque can beThe dynamic equations of a manipulator can be written in closed form aswhich has been simplified by taking advantage of the fact that the projection operator is Hermetian and idempotent [14].In all of the above techniques, the specified end effector trajectory is the implicit primary criterion. Unfortunately, the specification of an arbitrary homogeneous joint velocity may result in unrealistic demands on manipulator performance. These difficulties were first illustrated in [11] where the dynamic performance of a redundant manipulator showed significant end effector tracking errors when a secondary criterion was imposed. A more dramatic difficulty with using homogeneous solutions is the instability illustrated in [8] when redundancy is resolved at the acceleration level to instantaneously minimize joint torque. In this case, the joint acceleration is related to the end effector acceleration by differentiating (1) to obtain where once again the general solution is expressed in the form where the subscript 2 refers to the secondary criterion. The overall solution is then given by substituting (3) into (2) to obtain (2) (1)where + denotes the pseudoinverse, (l -J+ J) is a projection operator onto the null space of J, and ci > is an arbitrary vector in iJ space. The second term in (2) is the homogeneous solution to(1) since it results in no end effector velocity and will be denoted here by iJH' This homogeneous solution is frequently used to optimize some secondary criterion under the constraint of the specified end effector velocity by choosing cP to be the gradient of some function of (J [13]. Alternative formulations for instantaneously optimizing a secondary criterion by augmenting the Jacobian matrix have also

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Section: Kinetic Limitations On the Use Of Redundancy In Robotic Manimentioning

confidence: 99%

Section: Kinetic Effects Of a Homogeneous Solutionmentioning

confidence: 99%

Kinetic limitations on the use of redundancy in robotic manipulators

Maciejewski

1991

IEEE Trans. Robot. Automat.

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“…It is well known that by varying the posture of a robot, we can change the optimal directions for generating motion or applying specific forces. This has direct implications in hybrid control, since the controller capability can be fully realized when the optimal directions for controlling velocity and force coincide with those dictated by the task [4]. In this context, the so-called manipulability ellipsoid [23] serves as a geometric descriptor that indicates the ability to arbitrarily perform motion and exert a force along the different task directions in a given joint configuration.…”

Section: Introductionmentioning

confidence: 99%

Geometry-aware Tracking of Manipulability Ellipsoids

Jaquier

Rozo

Calinon

2018

Robotics: Science and Systems XIV

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Abstract-Body posture can greatly influence human performance when carrying out manipulation tasks. Adopting an appropriate pose helps us regulate our motion and strengthen our capability to achieve a given task. This effect is also observed in robotic manipulation where the robot joint configuration affects not only the ability to move freely in all directions in the workspace, but also the capability to generate forces along different axes. In this context, manipulability ellipsoids arise as a powerful descriptor to analyze, control and design the robot dexterity as a function of the articulatory joint configuration. This paper presents a new tracking control scheme in which the robot is requested to follow a desired profile of manipulability ellipsoids, either as its main task or as a secondary objective. The proposed formulation exploits tensor-based representations and takes into account that manipulability ellipsoids lie on the manifold of symmetric positive definite matrices. The proposed mathematical development is compatible with statistical methods providing 4th-order covariances, which are here exploited to reflect the tracking precision required by the task. Extensive evaluations in simulation and two experiments with a real redundant manipulator validate the feasibility of the approach, and show that this control formulation outperforms previously proposed approaches.

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“…Within the robotics literature, the issues of tool dexterity, endoscopic viewpoint, and workspace limits can be related to robot dexterity [4][5][6][7][8][9][10] . Many of the reported dexterity measures have been proposed to measure endpoint dexterity for multilink robots.…”

Section: Introductionmentioning

confidence: 99%

<title>Dexterity optimization by port placement in robot-assisted minimally invasive surgery</title>

et al. 2002

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A computer-based algorithm has been developed which uses preoperative images to provide a surgeon with a list of feasible port triplets ranked according to tool dexterity and endoscopic view quality at each surgical site involved in a procedure. A computer simulation allows the surgeon to select from among the proposed port locations. The procedure selected for the development of the system consists of a coronary artery bypass graft (CABG). In this procedure, the interior mammary artery (IMA) is mobilized from the interior chest wall, and one end is attached to the coronary arteries to provide a new blood supply for the heart. Approximately 10-20 cm is dissected free, using blunt dissection and a harmonic scalpel or electrocautery. At present, the port placement system is being evaluated in clinical trials.

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Control of redundant manipulators for task compatibility

Cited by 79 publications

References 4 publications

Kinetic limitations on the use of redundancy in robotic manipulators

Kinetic limitations on the use of redundancy in robotic manipulators

Geometry-aware Tracking of Manipulability Ellipsoids

<title>Dexterity optimization by port placement in robot-assisted minimally invasive surgery</title>

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