Global Attitude Stabilization using Pseudo-Targets
For control engineers and roboticists, this work provides a practical solution to the long-standing problem of global attitude stabilization using continuous feedback, though it is incremental as it builds on existing concepts.
This paper presents novel control algorithms using pseudo-targets to achieve global asymptotic stabilization of rigid body attitude with only continuous memory-less state-feedback, overcoming topological obstructions. The methods are validated through simulations and experiments, demonstrating effectiveness.
The topological obstructions on the attitude space of a rigid body make global asymptotic stabilization impossible using continuous state-feedback. This paper presents novel algorithms to overcome such topological limitations and achieve arbitrary attitude maneuvers with only continuous, memory-less state-feedback. We first present nonlinear control laws using both rotation matrices and quaternions that give rise to one almost globally asymptotically stabilizable equilibrium along with a nowhere dense set of unstable equilibria. The unstable equilibria are uniquely identified in the attitude error space. Pseudo-targets are then designed to make the controller believe that the attitude error is within the region of attraction of the stable equilibrium. Further, the pseudo-target ensures that maximum control action is provided to push the closed-loop system toward the stable equilibrium. The proposed algorithms are validated using both numerical simulations and experiments to show their simplicity and effectiveness.