Online Automatic Gain Tuning for Geometric Attitude Control

Bee Vang, Roberto Tron

Abstract: We present a framework to automatically tune the gains of a geometric attitude controller based on operating conditions (distance from equilibrium). We propose a two-thread architecture: on the one hand, a computationally simple geometric control law provides real-time control inputs to globally stabilize the system; on the other hand, an optimization procedure continuously varies the gains of the control law to improve the convergence rate guarantees when possible. In particular, we use Control Barrier and Lyapunov functions to find rates of change for the gains that improve bounds on the convergence rate while guaranteeing exponential stability for all subsequent times. The advantage of our architecture is that the gain updates can be computed at a rate possibly much slower than the control law; thanks to the constraints used, even if the gain updates were to stop, exponential stability would still be guaranteed for all future times.The resulting controller is compared via simulations against a static feedback controller and a version based on traditional discontinuous gain scheduling. While we focus on attitude control, our framework could be generalized to any static feedback controller equipped with explicit convergence conditions.