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Operational Space (or Task-Space) Control

A control method where the robot's hand (end-effector) is treated as if it's attracted to a goal position by a virtual force (like a magnet pulling it toward a target). Instead of calculating exact joint angles, the system lets the robot naturally find its own path to reach the target.


How it works:

  1. Define a goal position in 3D space (where you want the hand to be)
  2. Create a virtual force field — The system calculates an invisible "pull" toward that goal
  3. Apply forces to joints — The control system translates this spatial force into torques on each joint
  4. Robot responds naturally — Each joint moves to follow the virtual force, and the hand drifts toward the target

The key difference:


Instead of: "Calculate exact joint angles → Command motors to those angles"

You get: "Apply virtual force to end-effector → Let dynamics naturally solve which joints move"


Why it's called "operational space":


The control happens in the operational/task space (where the hand actually works) rather than joint space. The Jacobian matrix translates forces from hand-space back to joint-space.


Advantages:

  1. Natural motion — The robot moves smoothly and intuitively, like a living creature responding to forces
  2. Obstacle handling — If something blocks the path, the robot naturally adapts around it
  3. Compliance — The robot can be "soft" and responsive to external forces (human pushes, collisions)
  4. Elegant math — Uses physics-based principles rather than abstract angle calculations
  5. Human-like behavior — Moves more naturally than rigid joint-by-joint control

Disadvantages:

  1. More complex — Requires deeper understanding of dynamics and control theory
  2. Computationally intensive — Real-time force calculations on all joints
  3. Tuning required — Virtual force strength, damping, and stiffness must be carefully tuned
  4. Less predictable paths — The exact trajectory depends on dynamics, not pre-planned geometry

Practical example:

Imagine your hand is magnetically attracted to a cup on a table:

  1. You don't calculate "shoulder rotate 45°, elbow bend 90°"
  2. Instead, you feel pulled toward the cup—your arm naturally bends however needed
  3. If something blocks your path, you instinctively go around it
  4. Your hand finds the most efficient, natural way to reach the cup

Common applications:

  1. Collaborative robots — Safe interaction with humans (soft, force-responsive)
  2. Manipulation tasks — Picking, pushing, assembly with natural compliance
  3. Robotic surgery — Delicate, adaptive movements
  4. Human-robot collaboration — The robot "feels" external forces and adapts


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