Bringing Nonlinear <inline-formula><tex-math notation="LaTeX">$\mathcal {H}_\infty$</tex-math> </inline-formula> Optimality to Robot Controllers

Abstract

This paper proposes a framework called nonlinear robust internal-loop compensator that enables us to bring nonlinear H ∞ optimality to robot controllers in a unified and simple way. Using the framework, a controller designed for the nominal plant can achieve additional robustness by simply adding PID-type auxiliary input to the original control law. Robust performance is guaranteed by the nonlinear H ∞ optimality and robust stability is guaranteed by proving the extended disturbance input-to-state stability. Moreover, the framework preserves the passivity property of the original controller. Finally, the performance bound can be predicted and leads to the gain tuning rules. By virtue of the tuning rules, the performance can be tuned using only a single variable. The proposed method was validated through the simulations and experiments.1 Strictly speaking, L 2 -gain is less than γ. However, γ will be expressed as L 2 -gain throughout the paper for simplicity of writing. 1552-3098

Robust design and task‐priority control for rescue robot HURCULES

“…For the joint space control, we leverage an inverse optimal PID control scheme to guarantee robust performance in the face of a wide range of payload variation from 0 to 120 kg. The control law and the state and control input weighting matrices are inversely obtained from $${{\rm{ {\mathcal H} }}}_{\infty }$$ optimality and Lyapunov function (Choi et al, 2001; Kim et al, 2015). Figures 6 and 7 show weight lifting motions and the corresponding control errors respectively when the payload of 120 kg is acting on the system.…”

Safety and Performance of Industrial Collaborative Robots: Bounded Compensation in Precision Motion Control

“…The nonlinear robust internal-loop compensator (NRIC) framework [21] can be explained as the nonlinear DOB structure as shown in Fig. 1 (b), which can be seamlessly applied to multidimensional nonlinear systems.…”

“…Mn ṡrn + Ĉn s rn = −τ a + w rn (21) where s rn ≜ ėrn + K p e rn + K I e rn and the extended disturbance is represented with tedious calculation as…”

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Compensation Modulation for Tracking Accuracy in Free Motion and Compliance During Interaction

“…Thus, hrn must be bounded regardless of xrn 6. It is to be noted that (36) is the Ricatti equations related to the H optimal control problem[21].© 2024 IEEE. Personal use of this material is permitted.…”