Robot control
Manipulability
Definition
Manipulability describes how a robot configuration maps joint motion into end-effector motion in different directions. It is commonly represented by a Jacobian-based velocity ellipsoid or summarized by a scalar measure.
Also known as: Kinematic manipulability
Updated
Visualizing directional motion capability
Imagine all joint-velocity vectors with the same chosen magnitude. Passing them through the robot Jacobian produces an ellipsoid of end-effector velocities. Its long directions correspond to larger achievable task velocities under that joint-speed normalization.
Modern Robotics illustrates the idea with a planar arm: a circular set of joint velocities maps to an ellipse of tip velocities. Near a kinematic singularity, an axis of the ellipse shrinks.
Different measures answer different questions
The ellipsoid's axis ratio describes directional imbalance. Its volume describes an aggregate motion capability. A smallest-axis measure emphasizes the weakest direction. These quantities are related but are not interchangeable rankings of robot quality.
Manipulability can help compare candidate postures for a task, including alternatives available to a redundant manipulator.
Units and assumptions affect the result
Linear and angular velocities have different units. Modern Robotics therefore discusses separate translational and rotational ellipsoids. Any combined metric needs an explicit scaling choice, especially when comparing mechanisms or mixing revolute and prismatic joints.
A kinematic ellipsoid does not by itself account for collisions, payload, motor torque limits, or control errors. It describes the selected local motion map, not overall task success or dexterity in every operating condition.
Sources
Related terms
Robot Jacobian
A robot Jacobian is a configuration-dependent matrix that maps joint velocities to a chosen task velocity, often an end-effector twist. It describes the local relationship between joint motion and task motion.
Kinematic singularity
A kinematic singularity is a robot configuration where the task Jacobian has lower rank than the maximum it can attain for that mechanism and task. At that configuration the robot loses one or more instantaneous task-motion directions.
Redundant manipulator
A redundant manipulator has more independent joint-motion variables than are needed for its specified end-effector task. This can allow different joint motions or postures to produce the same task result.