Tuning and Analysis of Geometric Tracking Controllers on SO(3)

This paper concerns the robustness of attitude controllers for dynamics configured on the SO(3) manifold and poses a set of bilinear matrix inequalities to find an optimal controller tuning with respect to (i) the ultimate bound of the error-state trajectories when perturbed by naturally arising disturbances, and (ii) the worst-case decay rate of the tracking errors. The presented optimization problem can be solved both to generate a robust tuning for experimental applications, and also to facilitate qualitative comparisons of different attitude controllers present in the literature. To solve the tuning problem, we propose an algorithm based on alternating semidefinite programming, with local linearizations of an upper bound of the associated cost function. The soundness of this approach is illustrated by comparison to an interior-point method. The algorithm is subsequently used to provide insights for the tuning of the considered controllers, and finally demonstrated by a closed-loop simulation example.