Equation 1 · Part 3 · How Embodied AI Actually Works

Symbol q_d

\tau = K_p (q_d - q) + K_d (\dot{q}_d - \dot{q}) + \tau_{ff}

q_d

What this part means

the desired joint position.

Its job in the formula

$q_d$ is one of the signed contributions combined to compute the quantity on the left.

Full expressionSymbol q_dArticle meaning

Where the article explains it

Here $q_d$ and q are the desired and measured joint positions, $K_p$ and $K_d$ set how stiff and how damped that virtual spring-and-damper is, and $\tau_{ff}$ is a feedforward term — gravity compensation, or a reaction-force term handed down from a higher-level controller — added on top.

The passage around this formula

…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: $\tau = K_p (q_d - q) + K_d (\dot{q}_d - \dot{q}) + \tau_{ff}$ . Here $q_d$ and q are the desired and measured joint positions, $K_p$ and $K_d$ set how stiff and how damped that virtual spring-and-damper is, and $\tau_{ff}$ is a feedforward term — gravity compensation, or a reaction-force term handed down from a higher-level controller — added on top. The learned policy’s…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

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Sources cited in the article section

[12] Safe Physical Human-Robot Interaction through Variable Impedance Control based on ISO/TS 15066 ↗

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