Reading the documentation, it is not entirely clear to me what are the differences of the joint control modes supported in pybullet.

I try to recap them here, please @erwincoumans feel free to jump in to add more details and address holes in my understanding.

Let's assume that in all cases (excluding torque), the reference error is the following:

error = kp *  (pos_des - pos) + kd * (vel_des - vel)

• VELOCITY_CONTROL: This is a pure proportional control for velocity that by default has kp=0 and kd=1. Gains should be in the range [0, 1].
• POSITION_CONTROL (alias for CONTROL_MODE_POSITION_VELOCITY_PD): Similar to VELOCITY_CONTROL. By default it has kp=1 and kd=0. It allows to optionally specify both the target position and target velocity.
• TORQUE_CONTROL: It should be enabled by disabling the default motorized joints passing a force=0. Later calls using this mode will send directly the torque to the joint.
• PD_CONTROL: Similar to POSITION control but it allows specifying not normalized gains.

Questions:

• Is kp ignored in VELOCITY_CONTROL?
• What is the logic behind the normalized gains in VELOCITY_CONTROL and POSITION_CONTROL?
• Is kd=0 by default in POSITION_CONTROL?
• Is correct that in POSITION_CONTROL if kd=0 and a velocity reference is specified, it has no effect?
• Is the description of PD_CONTROL correct? There's not much information about it.
• Should PD_CONTROL with kp=0 and kd=1 behave as VELOCITY_CONTROL?

I think that a big difference of PD_CONTROL with respect to POSITION and VELOCITY is how the error is treated. I suspect that in the former case a joint force is generated, in the latter ones instead the error is minimized as constraint. Is this correct?

Related issues #2152 #1026