Kp / Kd Parameter Description

In Simulation (Isaac Gym)

PD Controller:

\[\tau = K_p e_p + K_d e_v\]

• \(K_p\): Stiffness
• \(K_d\): Damping
• \(e_p\): Position error
• \(e_v\): Velocity error

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On Real Robot Actuators

PID Controller:

\[I = P_p P_v e_p + P_v e_v\]

\[\tau' = g I K_t = g(P_p P_v K_t e_p + P_v K_t e_v)\]

• \(P_p\): Position loop proportional gain
• \(P_v\): Velocity loop proportional gain
• \(g\): Gear ratio
• \(K_t\): Torque constant

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Sim-to-Real Parameter Alignment

When \(\tau = \tau'\), the relationship between simulation and real-robot parameters is as follows:

\[K_p = g P_p P_v K_t\]

\[K_d = g P_v K_t\]

Derived real-robot configuration parameters:

\[P_v = \frac{K_d}{K_t \cdot g}\]

\[P_p = \frac{K_p}{K_d}\]

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Joint Logic Code Snippet