Geometric Reduced-Attitude Tracking under a Time-Varying Conic Constraint via Smooth Reference-Shaping

Abstract

This letter studies reduced-attitude tracking for a rigid body on the 2-sphere under a time-varying conic constraint. Using a kinematic model on S2, we first propose a geometric tracking law that guarantees almost-global asymptotic and regionally exponential convergence in the unconstrained case, where the angular velocity serves as the control input. We then introduce a smooth reference-shaping mechanism that adjusts the desired direction so that the reference provided to the controller satisfies the time-varying conic constraint while preserving the smoothness required by the tracking law. The resulting approach yields smooth continuous feedback and retains the stability guarantees of the unconstrained controller, albeit at the expense of enforcing a soft version of the original constraint. Simulation results illustrate the effectiveness of the method and highlight its suitability for applications where deterministic behavior, smooth control action, and strong stability guarantees are preferred over hard constraint satisfaction.