Manipulability ellipsoid
{{short description|Graphical representation of the ease with which a robotic arm can move its end effector}}
In robot kinematics, the manipulability ellipsoid represents the manipulability of a robotic system in a graphical form. Here, the manipulability of a robot arm refers to its ability to alter the position of the end effector based on the joint configuration. A higher manipulability measure signifies a broader range of potential movements in that specific configuration. When the robot is in a singular configuration the manipulability measure diminishes to zero.
Definition
The manipulability ellipsoid is defined as the set{{Cite book |author=Spong |first1=M.W. |url=https://books.google.com/books?id=muCMAAAACAAJ |title=Robot Modeling and Control |last2=Hutchinson |first2=Seth |last3=Vidyasagar |first3=M. |publisher=Wiley |year=2005 |isbn=9780471765790 |series=Wiley}}
where q is the joint configuration of the robot and J is the robot Jacobian relating the end-effector velocity with the joint rates.
Geometric Interpretation
A geometric interpretation of the manipulability ellipsoid is that it includes all possible end-effector velocities normalized for a unit input at a given robot configuration. The axis of the ellipsoid can be computed by using the singular value decomposition of the robot Jacobian.{{cite web |title=5.4. Manipulability – Modern Robotics |url=https://modernrobotics.northwestern.edu/nu-gm-book-resource/5-4-manipulability/ |access-date=18 October 2023 |website=modernrobotics.northwestern.edu |publisher=Northwestern University}}
References
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External links
- [https://demonstrations.wolfram.com/ManipulabilityEllipsoidOfARobotArm Interactive demonstration of manipulability ellipsoid of a robot arm]
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