• Journal of Institute of Control, Robotics and Systems
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• v.4 no.1
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• pp.105-112
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• 1998

Regarding the measure of dexterity of robot manipulators, two geometric tools, manipulability ellipsoids and manipulability polytopes, are examined and compared with each other. Even though the manipulability ellipsoid approach is the most widely used technique, it is shown that the manipulability ellipsoid transforms the inexact joint velocity constraints into task space and so it may fail to give an exact measure of dexterity and optimal direction of motion in task space. After showing that the polytope approach can handle such problems, we propose a practical polytope method which can be applied to 3-dimensional task space in general. The relation between manipulability ellipsoids and manipulability polytopes are also explored for a redundant case and a non-redundant one.

• Journal of Institute of Control, Robotics and Systems
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• v.5 no.3
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• pp.249-256
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• 1999

The conventional robot manipulability is decomposed into linear manipulability and angular manipulability so that they may be analysed and visualized in easy way even in the case of 3 dimensional task space with 6 variables. After the Jacobian matrix is decomposed into linear part and angular part, constraint on joint velocities is transformed into linear task velocity and angular task velocity through the decomposed Jacobian matrices. Under the assumption of redundant robot manipulators, several optimization problems which utilize the redundancy are formulated to be solved by linear programming technique or sequential quadratic programming technique. After deriving the solutions of the optimization problems, we give graphical interpretations for the solutions.

• Proceedings of the IEEK Conference
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• 2003.07c
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• pp.2725-2728
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• 2003

The manipulability of robot provides useful Information for the design and path planning of robots. This paper shows an influence of joint velocities to acceleration of robot end-effector using a dynamic manipulability polytope. The main idea of this paper is that the dynamic manipulability polytope of robot can be divided to three intermediate polytope, the torque-dependant polytope, velocity-dependent polytope, and gravity-dependant polytope. The velocity-dependant polytope is made from the limits of robot joint velocities while the torque-dependant polytope is made from the limits of the joint torques. Combining of these two intermediate polytopes and considering the gravity-dependant polytope, the overall dynamic manipulability polytope of robot is obtained. This investigation will be useful on the field of space robot and high-speed application.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.739-742
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• 1996

Several figures representing velocity transmission from joint space to task space are analyzed and compared with each other. The figures include velocity ellipsoid derived from Jacobian matrix, scaled velocity ellipsoid derived from normalized joint velocities, polytope derived by numerical scaling, and polytopes derived by linear combinations of Jacobian column vectors. The results show that the optimal directions given by the measures are not the same and the conventional velocity ellipsoid is not good choice as optimization measure as far as the moving direction is concerned. Simulation examples for 3 d.o.f. redundant robot manipulators in 2-dimensional task space are given for comparison study.