Manipulability Ellipsoid of a Robot Arm
Manipulability Ellipsoid of a Robot Arm
Manipulability of a robot is the capacity to change the end effector's position as a function of the joint configuration [1]. A larger manipulability measure indicates a greater range of possible motions at that configuration. The manipulability measure reduces to zero when the robot is in a singular configuration and cannot generate velocities in at least one direction.
The manipulability ellipsoid includes all possible velocities normalized for a unit input at a given robot configuration. These velocities are calculated using the robot’s velocity Jacobian.
In this Demonstration, you can adjust a three-link elbow manipulator’s configuration to see how the joint configuration affects the manipulability. For singular configurations, the Jacobian loses rank, causing the manipulability ellipsoid to lose dimensions to either an ellipse or a line.