Attitude determination for multirotor aerial vehicles using a prescribed‐time super‐twisting algorithm

• Published in: International journal of robust and nonlinear control 2025-01, Vol.35 (1), p.62-81
• Main Authors: Silva, João Filipe, Santos, Davi A.
• Format: Article
• Language: English
• Subjects: Algorithms; Angular velocity; attitude determination; Estimates; Kinematic equations; Kinematics; Magnetic properties; multirotor aerial vehicle; prescribed‐time convergence; Robustness; State estimation; super‐twisting algorithm; Twisting
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.7635

This paper is concerned with the prescribed‐time robust attitude determination (AD) of multirotor aerial vehicles (MAVs) using vector measurements from the local magnetic field and local gravity. To address this problem, we first introduce a novel modified super‐twisting algorithm endowed with the prescribed‐time convergence property. The x1$$ {x}_1 $$ state of the proposed algorithm is governed by an unbounded time‐varying gain up to the prescribed settling time (PST) and by a sig$$ \mathrm{sig} $$ function after that. Therefore, after the PST, the new algorithm coincides with the conventional super‐twisting, thus showing robust stability at the origin. This prescribed‐time super‐twisting algorithm (PTSTA) is then applied to the formulation of a three‐stage gyro‐free attitude determination method for MAVs. In the first stage, the classical QUEST algorithm is used to compute a Wahba‐optimal attitude estimate from the vector measurements. In the second stage, the PTSTA is employed in the formulation of a robust state estimator that provides estimates of the attitude Gibbs vector and its rate. Finally, in the third stage, these state estimates as well as the attitude kinematic equation are immediately used to compute the MAV angular velocity. The proposed robust prescribed‐time gyro‐free AD method is evaluated numerically, showing invariance with respect to disturbance and model uncertainty.