(preferably a physics simulator library, not an entire framework)
idk there is plenty of universities that have robotics labs.. Probably the best value is to apply for masters etc if you are interested in that..
Good off-the-shelf arms are low thousands last time I looked. You can DIY for $1-2k https://www.anninrobotics.com/robot-kits
It becomes expensive when you want an robot arm with high dexterity and torque-sensors, which is often a requirement for some tasks, but position-based control can be done on cheaper models.
Quadruped with an arm for <$1000 would be a steal. Got any recommendations?
It runs on Raspberry Pi which is a big +, as version 1 was running on custom hardware. People had to plug a Jetson Nano or other device to run their code (such as this [2]). It comes with their own App, connected via bluetooth, for simple commands too.
I (and most kickstart backers) funded/bought it for either hobby or research purpose (some backers were from labs) so if you're looking for *practical* application this one might be a bit too weak.
But version 1&2 did come with a processing power that could run YOLO detection so there's enough power to test things out and learn.
[1] https://www.robotshop.com/products/xgo-mini-2-quadruped-robo... [2] https://www.youtube.com/watch?v=xqfwCwu4-Rc
Does it has servos feedback too ?