Trajectory Tracking for Aerial Robots: an Optimization-Based Planning and Control Approach

In this work, we present an optimization-based trajectory tracking solution for multirotor aerial robots given a geometrically feasible path.
A trajectory planner generates a minimum-time kinematically and dynamically feasible trajectory that includes not only standard restrictions such as continuity and limits on the trajectory, constraints in the waypoints, and maximum distance between the planned trajectory and the given path, but also restrictions in the actuators of the aerial robot based on its dynamic model, guaranteeing that the planned trajectory is achievable.
Our novel compact multi-phase trajectory definition, as a set of two different kinds of polynomials, provides a higher semantic encoding of the trajectory, which allows calculating an optimal solution but following a predefined simple profile.

A Model Predictive Controller ensures that the planned trajectory is tracked by the aerial robot with the smallest deviation.
Its novel formulation takes as inputs all the magnitudes of the planned trajectory (i.e. position and heading, velocity, and acceleration) to generate the control commands, demonstrating through in-lab real flights an improvement of the tracking performance when compared with a controller that only uses the planned position and heading.

To support our optimization-based solution, we discuss the most commonly used representations of orientations, as well as both the difference as well as the scalar error between two rotations, in both tridimensional and bidimensional spaces $SO(3)$ and $SO(2)$.
We demonstrate that quaternions and error-quaternions have some advantages when compared to other formulations.