An excellent SIGGRAPH 2018 paper using Bullet Physics to simulate physics based character locomotion, by Xue Bin Peng, Pieter Abbeel, Sergey Levine, Michiel van de Panne.

See https://xbpeng.github.io/projects/DeepMimic/index.html

Update: there is also an implementation using PyBullet

pip3 install pybullet
python3 -m pybullet_envs.deep_mimic.testrl --arg_file run_humanoid3d_backflip_args.txt