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Periodic Event-Triggered Explicit Reference Governor for Constrained Attitude Control on SO(3)

Satoshi Nakano, Masahiro Suzuki, Misa Ohashi, Noboru Chikami, Shusuke Otabe

Abstract

This letter addresses the constrained attitude control problem for rigid bodies directly on the special orthogonal group SO(3), avoiding singularities associated with parameterizations such as Euler angles. We propose a novel Periodic Event-Triggered Explicit Reference Governor (PET-ERG) that enforces input saturation and geometric pointing constraints without relying on online optimization. A key feature is a periodic event-triggered supervisory update: the auxiliary reference is updated only at sampled instants when a robust safety condition is met, thereby avoiding continuous-time reference updates and enabling a rigorous stability analysis of the cascade system on the manifold. Through this structured approach, we rigorously establish the asymptotic stability and exponential convergence of the closed-loop system for almost all initial configurations. Numerical simulations validate the effectiveness of the proposed control architecture and demonstrate constraint satisfaction and convergence properties.

Periodic Event-Triggered Explicit Reference Governor for Constrained Attitude Control on SO(3)

Abstract

This letter addresses the constrained attitude control problem for rigid bodies directly on the special orthogonal group SO(3), avoiding singularities associated with parameterizations such as Euler angles. We propose a novel Periodic Event-Triggered Explicit Reference Governor (PET-ERG) that enforces input saturation and geometric pointing constraints without relying on online optimization. A key feature is a periodic event-triggered supervisory update: the auxiliary reference is updated only at sampled instants when a robust safety condition is met, thereby avoiding continuous-time reference updates and enabling a rigorous stability analysis of the cascade system on the manifold. Through this structured approach, we rigorously establish the asymptotic stability and exponential convergence of the closed-loop system for almost all initial configurations. Numerical simulations validate the effectiveness of the proposed control architecture and demonstrate constraint satisfaction and convergence properties.

Paper Structure

This paper contains 13 sections, 2 theorems, 19 equations, 5 figures.

Table of Contents

  1. INTRODUCTION
  2. PROBLEM STATEMENT
  3. CONTROL ARCHITECTURE
  4. Attitude Stabilization Controller
  5. Explicit Reference Governor (ERG)
  6. Dynamic Safety Margin (DSM)
  7. Navigation Field (NF)
  8. PERIODIC EVENT-TRIGGERED REFERENCE GOVERNOR ON $SO(3)$
  9. Proposed Update Mechanism
  10. Stability Analysis
  11. Exponential Convergence
  12. NUMERICAL SIMULATION
  13. CONCLUSIONS

Key Result

Theorem 1

Consider the closed-loop system with initial conditions $(\omega_{0},R_{0}) \in \mathbb{R}^{3} \times D$ satisfying $V(R_{0},\omega_{0},R_{0}) \leq \Gamma(R_{0})$. Then the system admits a unique global solution $(R,\omega,R_{g})$ satisfying $R, \omega \in C^{1}([t_0,\infty))$ and $R_{g} \in C([t_0,

Figures (5)

  • Figure C1: Block diagram of control scheme.
  • Figure E1: Evolution of system trajectories (PET-ERG). The body $z$-axis safely navigates around the forbidden conic region to reach the desired orientation.
  • Figure E2: Evolution of attitude error $\phi( \IfStrEqCase{n}{ {n}{R_{}} {d}{\dot{R}_{}} {t}{R_{}^\mathrm{T}} {p}{R_{}^\prime} {pt}{(R_{}^\prime)^\mathrm{T}} {c}{\bar{R}_{}} }[Error] , \IfStrEqCase{n}{ {n}{R_{d}} {d}{\dot{R}_{d}} {t}{R_{d}^\mathrm{T}} {p}{R_{d}^\prime} {pt}{(R_{d}^\prime)^\mathrm{T}} {c}{\bar{R}_{d}} }[Error] )$ and reference error $\phi( \IfStrEqCase{n}{ {n}{R_{g}} {d}{\dot{R}_{g}} {t}{R_{g}^\mathrm{T}} {p}{R_{g}^\prime} {pt}{(R_{g}^\prime)^\mathrm{T}} {c}{\bar{R}_{g}} }[Error] , \IfStrEqCase{n}{ {n}{R_{d}} {d}{\dot{R}_{d}} {t}{R_{d}^\mathrm{T}} {p}{R_{d}^\prime} {pt}{(R_{d}^\prime)^\mathrm{T}} {c}{\bar{R}_{d}} }[Error] )$ under the PET-ERG scheme.
  • Figure E3: Evolution of the Lyapunov function $V$ and the safety thresholds $\Gamma_d$ and $\Gamma_g$. The periodic event-triggered mechanism maintains $V$ strictly below the aggregate margin.
  • Figure E4: Evolution of the control torque input $\tau$, strictly respecting the saturation limit $\tau_{\max}$.

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof