Equation 2 · How Embodied AI Actually Works
What does this equation mean?
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the desired joint position. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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subscript
subscript
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.
How to interpret it
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What the article says around this equation
Here and q are the desired and measured joint positions, and set how stiff and how damped that virtual spring-and-damper is, and 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 : 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 and q are the desired and measured joint positions, and set how stiff and how damped that virtual spring-and-damper is, and 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 : 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.
Sources cited in the article section
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