Manipulability ellipsoid
The manipulability ellipsoid is a concept in robotics that represents the manipulability of a robotic system in a graphical form. Here, the manipulability of a robot 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[1]
[math]\displaystyle{ \{ \xi : \xi^\operatorname{T} (J(q) J^\operatorname{T}(q)) \xi \le 1 \} }[/math]
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.[1][2]
References
- ↑ 1.0 1.1 Spong, M.W.; Hutchinson, Seth; Vidyasagar, M. (2005). Robot Modeling and Control. Wiley. Wiley. ISBN 9780471765790. https://books.google.de/books?id=muCMAAAACAAJ.
- ↑ "5.4. Manipulability – Modern Robotics". Northwestern University. https://modernrobotics.northwestern.edu/nu-gm-book-resource/5-4-manipulability/.
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