Abstract
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.
Highlights
The reaction wheel pendulum is an inverted pendulum balanced by an actuated rotating reaction wheel
Motivated by several recent works related to the safety of dynamical systems with control barrier function (CBF) [13], [14], in this work we apply a control framework on the reaction wheel pendulum that simultaneously satisfies stability objectives and safety constraints
The system is constituted by an inverted pendulum that is balanced by an actuated reaction wheel. α is the pendulum angle, θ is the wheel angle and τ is the torque acting on the reaction wheel
Summary
The reaction wheel pendulum is an inverted pendulum balanced by an actuated rotating reaction wheel (flywheel). Motivated by several recent works related to the safety of dynamical systems with control barrier function (CBF) [13], [14], in this work we apply a control framework on the reaction wheel pendulum that simultaneously satisfies stability objectives and safety constraints. This methodology, called CBF, ensures safety over the entire set and imposes new conditions on CBF, making the problem minimally restrictive, unlike [20], [21] and [22] It combines performance/stability objectives, expressed as a CLF or a nominal control law and safety constraints, expressed as a CBF.
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