NMPC for Multicopter's Trajectory Tracking Using Modified Rodrigues Parameters

Unit quaternion has become a favourite singularity-free attitude representation in the attitude control problem of multicopters, enabling them to perform large and complex maneuvers. This paper studies the challenge of implementing Nonlinear Model Predictive Control (NMPC) of a multicopter's pose, using unit quaternion. Alternatively, it proposes representing attitude minimally with Modified Rodrigues Parameters (MRPs) and their shadow set. NMPC is formulated based on the dynamics of a multicopter, with the aim to regulate its position, velocity, error in attitude and error in angular velocity to their desired values. The proposed controller is implemented on-board a hexacopter and verified in simulations and real experiments. The resulting closed loop system is shown to track large set points and perform 360 degree flips without running into a singularity, while demonstrating similar controller performance and computational costs as compared to the one using unit quaternion. Finally, the trajectory tracking capability is demonstrated by implementing 8-shaped trajectory tracking.