Worked solutionOne step at a time
A position controller behaves like a spring
It pushes back in proportion to how far the hand is from its target. The constant is the stiffness k.
The stiff case, from the reel
The hand was told to go to where the table should be. The table is 5 mm higher, so the hand stops 5 mm short and the spring stays stretched.
The soft case
Same error, one fortieth of the stiffness.
Answer: B, 5 N
The cost is accuracy. In free air a 5 N disturbance used to move the hand 0.125 mm and now moves it 5 mm. So impedance control makes the spring soft only along the contact direction: the hand yields to the table and still tracks its path sideways.
What the simulation showedSoft in one direction only
The reel has a Kinova Gen3 wipe a table in MuJoCo, with the table 5 mm higher than the robot was told.
- Under stiff position control the 5 mm error turns into about 200 N of downward force, roughly the weight of a 20 kg load on the table.
- With the stiffness lowered along the direction of contact, the press drops to a few newtons.
- The wiping path across the table is unchanged, because the stiffness in those directions was left alone.
Wrong answersWhy each one is tempting
| Pick | What went wrong |
|---|---|
| A · 0.5 N | Slipped a factor of ten converting millimetres to metres. |
| C · 50 N | Used 10,000 N/m. |
| D · 200 N | Reused the stiff controller's answer. |
Follow-ups an interviewer asks nextTry these before opening them
You want the robot to press with 10 N while wiping. What do you command?
With k = 1,000 N/m, set the target 10 mm below the surface: 1,000 × 0.010 = 10 N. Under impedance control you choose force by choosing how far into the surface to aim.
Why not make the arm soft in every direction?
It would sag under its own payload and drift off the path whenever anything brushed it. Softness is only wanted where the arm meets something stiffer than its model says.
What if the table height is off by 5 cm instead of 5 mm?
With k = 1,000 N/m that is 50 N, which may still be too much. Either lower the stiffness further or switch to controlling force directly in that direction.
How is this different from force control?
Force control measures the contact force and regulates it to a target. Impedance control never sets a force: it sets how position error and force relate, and lets the force come out of the contact.