  Trajectory optimization methods have achieved an exceptional level of
performance on real-world robots in recent years. These methods heavily rely on
accurate analytical models of the dynamics, yet some aspects of the physical
world can only be captured to a limited extent. An alternative approach is to
leverage machine learning techniques to learn a differentiable dynamics model
of the system from data. In this work, we use trajectory optimization and model
learning for performing highly dynamic and complex tasks with robotic systems
in absence of accurate analytical models of the dynamics. We show that a neural
network can model highly nonlinear behaviors accurately for large time
horizons, from data collected in only 25 minutes of interactions on two
distinct robots: (i) the Boston Dynamics Spot and an (ii) RC car. Furthermore,
we use the gradients of the neural network to perform gradient-based trajectory
optimization. In our hardware experiments, we demonstrate that our learned
model can represent complex dynamics for both the Spot and Radio-controlled
(RC) car, and gives good performance in combination with trajectory
optimization methods.
