  Accurately predicting the dynamics of robotic systems is crucial for
model-based control and reinforcement learning. The most common way to estimate
dynamics is by fitting a one-step ahead prediction model and using it to
recursively propagate the predicted state distribution over long horizons.
Unfortunately, this approach is known to compound even small prediction errors,
making long-term predictions inaccurate. In this paper, we propose a new
parametrization to supervised learning on state-action data to stably predict
at longer horizons -- that we call a trajectory-based model. This
trajectory-based model takes an initial state, a future time index, and control
parameters as inputs, and predicts the state at the future time. Our results in
simulated and experimental robotic tasks show that our trajectory-based models
yield significantly more accurate long term predictions, improved sample
efficiency, and ability to predict task reward.
