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

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

eess.SYApr 5, 2026

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

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

Organizations: The authors are with the Department of Engineering, Nagoya Institute of Technology, Nagoya, 4668555 Aichi, Japan

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.

Figures & tables

Fig. 1: Block diagram of control scheme.

Fig. 2: Evolution of system trajectories (PET-ERG). The body

z

-axis safely navigates around the forbidden conic region to reach the desired orientation.

Fig. 3: Evolution of attitude error

\phi(R,R_{d})

and reference error

\phi(R_{g},R_{d})

under the PET-ERG scheme.

Fig. 4: 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.

Fig. 5: Evolution of the control torque input

\tau

, strictly respecting the saturation limit

\tau_{\max}

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Department of Engineering, Nagoya Institute of Technology, 466-8555 Aichi, Japan · Department of Control Engineering and System Analysis, Universite Libre de Bruxelles, 1050 Brussels, Belgium · Department of Electrical and Computer Engineering, University of Waterloo, ON N2L 3G1, Canada

Control Barrier Functions

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This letter presents a constrained control framework that integrates Explicit Reference Governors (ERG) with Control Barrier Functions (CBF) to ensure recursive feasibility without online optimization. We formulate the reference update as a virtual control input for an augmented system, governed by a smooth barrier function constructed from the softmin aggregation of Dynamic Safety Margins (DSMs). Unlike standard CBF formulations, the proposed method guarantees the feasibility of safety constraints by design, exploiting the forward invariance properties of the underlying Lyapunov level sets. This allows for the derivation of an explicit, closed-form reference update law that strictly enforces safety while minimizing deviation from a nominal reference trajectory. Theoretical results confirm asymptotic convergence, and numerical simulations demonstrate that the proposed method achieves performance comparable to traditional ERG frameworks.

Abstract

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