Redundant manipulator

Extra freedom is relative to a task#

A seven-joint arm can have redundancy for a six-dimensional hand-pose task. A three-joint planar arm can be redundant for controlling only its tip's two-dimensional position, even if all three joints are needed when tip orientation is also specified.

Modern Robotics uses these examples to explain Jacobians with more columns than task dimensions. Redundancy is therefore a relationship between a mechanism and a task, not a fixed synonym for a particular joint count.

Moving the elbow while holding the hand#

Some joint velocities can change internal posture while producing zero instantaneous hand velocity. These velocities lie in the task Jacobian's null space. They can provide freedom to choose a preferred posture alongside the main task.

MIT's manipulation notes use a secondary objective that draws the joints toward a nominal configuration while tracking the desired hand motion.

Extra joints do not remove constraints#

Redundancy does not eliminate kinematic singularities, travel limits, or collisions. Secondary objectives can conflict with constraints or with the primary task. The useful freedom depends on the current configuration and the tasks already imposed, so an additional contact or orientation requirement can consume redundancy that was previously available.