12 volt switching power supply ground and earth ground

I am working on a large robot with an aluminum frame. It has a small gas generator that has an AC outlet so I will be putting 3 of these units (https://www.amazon.com/gp/product/B007K2H0GI) in the robot. Now if I put the ground for the 12 volts out to the frame of the robot and the case of the power supply or any other "earth" connection touches the frame, will there be any issues? Is this the safest way to do this?

Thank you for your help!

You should connect the -ve output from that power supply to the frame. I would not connect the thing with a ground symbol to anything. Then their should be no "issues".

So should I just run N and L through a power cord and not worry about the ground pin to the generator?

If the power cord has a ground then I would use it, to do so would be breaching the safety rules. But don't specifically connect it to the frame.

Here's the NES-350-12 datasheet. In the block diagram, the FG terminal (circled ground symbol) is the Frame Ground of the supply.

Note the opto isolation of the OVP and "detection circuit" and transformer isolation of the PWM control circuit. I don't think it's necessary to connect V- to FG as this will defeat this additional isolation feature.

I would just connect the frame ground of the supply to the aluminum frame of the robot and leave the internal power rails (+V, -V) floating.