Traditionally, models for control and motion planning were derived from physical properties of the system. While such a classical approach provides mathematical performance guarantees, modeling complex systems is not always feasible. On the other hand, recent advances in machine learning allow for the acquisition of models automatically from data. However, naive empirical methods do not provide performance guarantees, may be slow to train, and often generalize poorly to new situations.

In this dissertation, we present a combination of both approaches -- infusing prior knowledge by incorporating structure into learning methods. We show the benefits of this combined approach in three robotics settings. First, we show that incorporating prior knowledge -- in combination with a manifold learning technique -- applied to learning the latent space dynamics for a tactile servoing testbed, can help simplify the control problem representation such that the solution can be derived analytically from the learned model. Second, we show that infusing physical properties into learning inverse dynamics with a differentiable Newton-Euler algorithm speeds-up the learning process and improves the generalization capability of the model. Finally, we show that structure can be incorporated into the learning framework for feedback models of reactive behaviors, facilitating guarantees on desirable system properties like goal-convergence.