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redundancy (in kinematics)

A situation where multiple joint configurations can achieve the same end-effector position. Like how you can reach for a coffee cup with your elbow high or low—both work. This creates computational complexity because there’s no single “correct” answer.


Key insight:


To reach a point in 3D space, you theoretically need only 6 degrees of freedom (3 for position, 3 for orientation). But many robots have 7 or more joints, creating redundancy—extra "flexibility" that allows multiple solutions.

Real-world example:

Imagine reaching for a coffee cup on a table:

  1. Elbow high approach — Shoulder bent up, elbow high, wrist angled down
  2. Elbow low approach — Shoulder less bent, elbow low, wrist angled up
  3. Both reach the exact same cup

Your arm is redundant because you have 7 degrees of freedom but only need 6 to reach the target.


Why robots have redundancy:

  1. Obstacle avoidance — Extra joints let the arm route around obstacles
  2. Dexterity — More configurations mean better positioning for delicate tasks
  3. Reach extension — Access hard-to-reach spaces

The computational problem:


When solving inverse kinematics, redundancy creates a nightmare:

  1. Instead of one solution, there are infinite solutions (a whole continuum of valid configurations)
  2. The algorithm must choose which solution to use—but based on what criteria?
  3. This adds significant computational complexity and requires additional decision-making logic

How it's handled:


Engineers add secondary objectives like:

  1. "Choose the solution closest to the current pose" (smooth movement)
  2. "Avoid joint limits and singularities" (stay away from dangerous configurations)
  3. "Minimize energy consumption"


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