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Equation 1 · Part 9 · How Embodied AI Actually Works

=

τ=Kp(qd−q)+Kd(q˙d−q˙)+τff\tau = K_p (q_d - q) + K_d (\dot{q}_d - \dot{q}) + \tau_{ff}
=

What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

The dominant scheme for the last stage is impedance control rather than pure position control, and the distinction matters for exactly the reason a robot has to touch things. A pure position controller tries to force a joint to a commanded angle regardless of what resists it, which is dangerous the instant the arm meets an object, a surface, or a person, because the controller will keep applying more torque to fight the very contact it should be responding to. An impedance controller instead makes the joint behave like a programmable spring and damper around the commanded target: τ=Kp(qd−q)+Kd(q˙d−q˙)+τff\tau = K_p (q_d - q) + K_d (\dot{q}_d - \dot{q}) + \tau_{ff}. Here qdq_d and q are the desired and measured joint positions, KpK_p and KdK_d set how stiff and…

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

Open the illustrated equality: what the equals sign claims guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.