This repository implements Model Predictive Path Integral (MPPI) with approximate dynamics in pytorch. MPPI typically requires actual trajectory samples, but this paper showed that it could be done with approximate dynamics (such as with a neural network) using importance sampling.

Thus it can be used in place of other trajectory optimization methods such as the Cross Entropy Method (CEM), or random shooting.

Clone repository somewhere, then pip3 install -e . to install in editable mode. See tests/pendulum_approximate.py for usage with a neural network approximating the pendulum dynamics. See the not_batch branch for an easier to read algorithm. Basic use case is shown below

from pytorch_mppi import mppi
# create controller with chosen parameters
ctrl = mppi.MPPI(dynamics, running_cost, nx, noise_sigma, num_samples=N_SAMPLES, horizon=TIMESTEPS,
                         lambda_=lambda_, device=d, 
                         u_min=torch.tensor(ACTION_LOW, dtype=torch.double, device=d),
                         u_max=torch.tensor(ACTION_HIGH, dtype=torch.double, device=d))

# assuming you have a gym-like env
obs = env.reset()
for i in range(100):
    action = ctrl.command(obs)
    obs, reward, done, _ = env.step(action.cpu().numpy())

lambda_ - higher values increases the cost of control noise, so you end up with more samples around the mean; generally lower values work better (try 1e-2)

num_samples - number of trajectories to sample; generally the more the better. Runtime performance scales much better with num_samples than horizon, especially if you're using a GPU device (remember to pass that in!)

noise_mu - the default is 0 for all control dimensions, which may work out really poorly if you have control bounds and the allowed range is not 0-centered. Remember to change this to an appropriate value for non-symmetric control dimensions.

• pytorch (>= 1.0)
• next state <- dynamics(state, action) function (doesn't have to be true dynamics)
  • state is K x nx, action is K x nu
• cost <- running_cost(state, action) function
  • cost is K x 1, state is K x nx, action is K x nu

• Approximate dynamics MPPI with importance sampling
• Parallel/batch pytorch implementation for accelerated sampling
• Control bounds via sampling control noise from rectified gaussian
• Handle stochastic dynamic models (assuming each call is a sample) by sampling multiple state trajectories for the same action trajectory with rollout_samples

You'll need to install gym<=0.20 to run the tests (for the Pendulum-v0 environment). The easy way to install this and other testing dependencies is running python setup.py test. Note that gym past 0.20 deprecated Pendulum-v0 for Pendulum-v1 with incompatible dynamics.

Under tests you can find the MPPI method applied to known pendulum dynamics and approximate pendulum dynamics (with a 2 layer feedforward net estimating the state residual). Using a continuous angle representation (feeding cos(\theta), sin(\theta) instead of \theta directly) makes a huge difference. Although both works, the continuous representation is much more robust to controller parameters and random seed. In addition, the problem of continuing to spin after over-swinging does not appear.

Sample result on approximate dynamics with 100 steps of random policy data to initialize the dynamics:

• pytorch CEM - an alternative MPC shooting method with similar API as this project