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Equation 5 · How Embodied AI Actually Works

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KdK_d

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KdK_d

Symbol K_d

KdK_d is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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subscript

subscript

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Here qdq_d and q are the desired and measured joint positions, KpK_p and KdK_d set how stiff and how damped that virtual spring-and-damper is, and τff\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 contribution to this equation is qdq_d : a target, updated at whatever rate the policy runs. Everything else in the equation runs at a much higher rate, underneath the policy, and it is what actually decides how the robot responds to unexpected resistance in the interval between two policy decisions. Lower the gains and the joint yields to contact instead of fighting it; that yielding, not any…
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Here qdq_d and q are the desired and measured joint positions, KpK_p and KdK_d set how stiff and how damped that virtual spring-and-damper is, and τff\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 contribution to this equation is qdq_d : a target, updated at whatever rate the policy runs. Everything else in the equation runs at a much higher rate, underneath the policy, and it is what actually decides how the robot responds to unexpected resistance in the interval between two policy decisions. Lower the gains and the joint yields to contact instead of fighting it; that yielding, not any property of the learned policy, is most of what keeps a light unexpected collision from becoming a hard one.

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