Safe Control of a Reaction Wheel Pendulum Using Control Barrier Function

This paper presents a safe control applied to a reaction wheel pendulum, assuring that the system satisfies stability objectives and safety constraints. Safety constraints are specified in terms of a set invariance and verified through control barrier functions (CBFs). The existence of a CBF satisfying specific conditions implies set invariance. The control framework considered unifies stability objectives, expressed as a nominal control law, and safety constraints, expressed as a CBF, through quadratic programming (QP). The work focuses on safety; thus, the nominal control law applied was a simple linear quadratic regulator (LQR). The safety constraint is considered to guarantee that the pendulum angular position never exceeds a predetermined value. The control framework was applied and analyzed considering continuous-time and discrete-time situations. The results from numerical simulations and experimental tests indicate that the pendulum is well stabilized while satisfying a safety constraint when forced to leave the safe set.