Safe Control of a Reaction Wheel Pendulum Using Control Barrier Function

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.

Time‐optimal trajectory generation and observer‐based hierarchical sliding mode control for ballbots with system constraints

“…Because the ballbot system is a high‐relative degree system, the CBF constraint should be selected as the exponential CBF. If using CBF for output constraint, the selected barrier certificate $$$ h $$$ must depend on the first derivative of the state variable 40 . However, the control designs generate abrupt changes in control signals.…”

“…If using CBF for output constraint, the selected barrier certificate h must depend on the first derivative of the state variable. 40 However, the control designs generate abrupt changes in control signals.…”

Design, Implementation, and Control of a Wheel-Based Inverted Pendulum

“…A mathematical model of inverted pendulum systems was derived in [11]. Special attention has also been paid to the system modelling problem [12]. Finally, since not all state variables are available, the importance of an accurate state estimation is discussed in [13].…”