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Equation 1 · Part 7 · How Embodied AI Actually Works

Symbol q̇

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

What this part means

q̇ has a dot, marking the rate of change of the underlying indexed quantity with respect to the article’s time variable.

Its job in the formula

q̇ has a dot, marking the rate of change of the underlying indexed quantity with respect to the article’s time variable.

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

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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