robot kinematics Robot kinematics applies geometry to the study of the movement of multi-degree of freedom kinematic chains that form the structure of robotic systems. The emphasis on geometry means that the links of the robot are modeled as rigid bodies and i ...

, 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

\

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 In linear algebra, the singular value decomposition (SVD) is a Matrix decomposition, factorization of a real number, real or complex number, complex matrix (mathematics), matrix into a rotation, followed by a rescaling followed by another rota ...

of the robot Jacobian.

References

External links

Interactive demonstration of manipulability ellipsoid of a robot arm
{{robotics-stub Robot control Geometry Ellipsoids