  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 directly predicts the state at the future time index.
Experimental results in simulated and real-world robotic tasks show that
trajectory-based models yield significantly more accurate long term
predictions, improved sample efficiency, and the ability to predict task
reward. With these improved prediction properties, we conclude with a
demonstration of methods for using the trajectory-based model for control.
