← All parts of this equation

Equation 1 · Part 12 · How Embodied AI Actually Works

subscript

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

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

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…

Read this part in the article →

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.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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