Adaptive Backstepping Control of a Bicopter in Pure Feedback Form with Dynamic Extension

Abstract

This paper presents a model-based, adaptive, nonlinear controller for the bicopter stabilization and trajectory-tracking problem. The nonlinear controller is designed using the backstepping technique. Due to the non-invertibility of the input map, the bicopter system is first dynamically extended. However, the resulting dynamically extended system is in the pure feedback form with the uncertainty appearing in the input map. The adaptive backstepping technique is then extended and applied to design the controller. The proposed controller is validated in simulation for a smooth and nonsmooth trajectory-tracking problem.

Figures (12)

• Figure 1: Bicopter configuration considered in this paper. The bicopter is constrained to the $\hat{\hat{}} \imath _{\rm A}-\hat{\hat{}} \jmath _{\rm A}$ plane and rotates about the $\hat{k}_{\rm A}$ axis of the inertial frame $\rm F_A.$
• Figure 2: Adaptive backstepping control architecture.
• Figure 3: Elliptical trajectory. Tracking response of the bicopter with the adaptive backstepping controller. Note that the output trajectory is shown in solid blue, and the reference trajectory is in dashed black.
• Figure 4: Elliptical trajectory. Position $(r_1, r_2)$ and roll angle $\theta$ response of the bicopter obtained with adaptive backstepping controller \ref{['eq:u']}.
• Figure 5: Elliptical trajectory. Position errors obtained with the adaptive backstepping controller \ref{['eq:u']} on a logarithmic scale.