  In recent times, an increasing number of researchers have been devoted to
utilizing deep neural networks for end-to-end flight navigation. This approach
has gained traction due to its ability to bridge the gap between perception and
planning that exists in traditional methods, thereby eliminating delays between
modules. However, the practice of replacing original modules with neural
networks in a black-box manner diminishes the overall system's robustness and
stability. It lacks principled explanations and often fails to consistently
generate high-quality motion trajectories. Furthermore, such methods often
struggle to rigorously account for the robot's kinematic constraints, resulting
in the generation of trajectories that cannot be executed satisfactorily. In
this work, we combine the advantages of traditional methods and neural networks
by proposing an optimization-embedded neural network. This network can learn
high-quality trajectories directly from visual inputs without the need of
mapping, while ensuring dynamic feasibility. Here, the deep neural network is
employed to directly extract environment safety regions from depth images.
Subsequently, we employ a model-based approach to represent these regions as
safety constraints in trajectory optimization. Leveraging the availability of
highly efficient optimization algorithms, our method robustly converges to
feasible and optimal solutions that satisfy various user-defined constraints.
Moreover, we differentiate the optimization process, allowing it to be trained
as a layer within the neural network. This approach facilitates the direct
interaction between perception and planning, enabling the network to focus more
on the spatial regions where optimal solutions exist. As a result, it further
enhances the quality and stability of the generated trajectories.
