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Published equation contexts

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

Why this formula appears here

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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q˙d\dot{q}_d

Symbol q̇_d

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

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q˙\dot{q}

Symbol q̇

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

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τff\tau_{ff}

Symbol tau_ff

a feedforward term — gravity compensation, or a reaction-force term handed down from a higher-level controller — added on top.

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Published contexts (1)

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

Equation 1 · Robotics & Embodied AI

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

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…

Meanings in this article

  • qdq_d: the desired joint position.
  • qq: the measured joint position.
  • τff\tau_{ff}: a feedforward term — gravity compensation, or a reaction-force term handed down from a higher-level controller — added on top.
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