Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Saturated RISE control for considering rotor thrust saturation of fully actuated multirotor

Dongjae Lee, H. Jin Kim

TL;DR

This paper addresses rotor-thrust saturation and disturbance rejection for fully actuated multirotors by introducing a saturated RISE controller tailored to systems with a non-diagonal, state-dependent input matrix. A reformulation yields a symmetric mass matrix and symmetric input bounds, enabling a robust control law that fully exploits the actuator limits without conservative bound shrinking. A Lyapunov-based stability analysis demonstrates local asymptotic stability under time-varying disturbances, and simulations show improved tracking and saturation compliance over baseline methods and with/without the sign term. The work lays a foundation for hardware experiments to validate rotor-saturation-aware robust control in realistic flight scenarios.

Abstract

This work proposes a saturated robust controller for a fully actuated multirotor that takes disturbance rejection and rotor thrust saturation into account. A disturbance rejection controller is required to prevent performance degradation in the presence of parametric uncertainty and external disturbance. Furthermore, rotor saturation should be properly addressed in a controller to avoid performance degradation or even instability due to a gap between the commanded input and the actual input during saturation. To address these issues, we present a modified saturated RISE (Robust Integral of the Sign of the Error) control method. The proposed modified saturated RISE controller is developed for expansion to a system with a non-diagonal, state-dependent input matrix. Next, we present reformulation of the system dynamics of a fully actuated multirotor, and apply the control law to the system. The proposed method is validated in simulation where the proposed controller outperforms the existing one thanks to the capability of handling the input matrix.

Saturated RISE control for considering rotor thrust saturation of fully actuated multirotor

TL;DR

This paper addresses rotor-thrust saturation and disturbance rejection for fully actuated multirotors by introducing a saturated RISE controller tailored to systems with a non-diagonal, state-dependent input matrix. A reformulation yields a symmetric mass matrix and symmetric input bounds, enabling a robust control law that fully exploits the actuator limits without conservative bound shrinking. A Lyapunov-based stability analysis demonstrates local asymptotic stability under time-varying disturbances, and simulations show improved tracking and saturation compliance over baseline methods and with/without the sign term. The work lays a foundation for hardware experiments to validate rotor-saturation-aware robust control in realistic flight scenarios.

Abstract

This work proposes a saturated robust controller for a fully actuated multirotor that takes disturbance rejection and rotor thrust saturation into account. A disturbance rejection controller is required to prevent performance degradation in the presence of parametric uncertainty and external disturbance. Furthermore, rotor saturation should be properly addressed in a controller to avoid performance degradation or even instability due to a gap between the commanded input and the actual input during saturation. To address these issues, we present a modified saturated RISE (Robust Integral of the Sign of the Error) control method. The proposed modified saturated RISE controller is developed for expansion to a system with a non-diagonal, state-dependent input matrix. Next, we present reformulation of the system dynamics of a fully actuated multirotor, and apply the control law to the system. The proposed method is validated in simulation where the proposed controller outperforms the existing one thanks to the capability of handling the input matrix.
Paper Structure (11 sections, 2 theorems, 25 equations, 5 figures, 2 tables)

This paper contains 11 sections, 2 theorems, 25 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Notations and preliminaries
  3. Equations of Motion
  4. Controller Design
  5. EoM reformulation
  6. Saturated robust control
  7. Stability Analysis
  8. Results
  9. Simulation setup
  10. Analysis
  11. Conclusion

Key Result

Lemma 1

By taking a sufficient large $\Theta$ satisfying $\theta_i > \zeta_{N_{d1},i} + \lambda_{3,i}^{-1} \zeta_{N_{d2},i}$, then $P(t) \geq 0$$\forall t \geq t_0$.

Figures (5)

  • Figure 1: A fully actuated multirotor considered in this work. $u = [u_1, \cdots, u_6]^\top$ indicates the rotor thrust, and $L$ is the distance from the geometric center of the multirotor to a rotor.
  • Figure 2: Simulation 1 -- results of modified-fischer2012saturatedfischer2014saturated.
  • Figure 3: Simulation 2 -- results without the $\text{sgn}$ term.
  • Figure 4: Simulation 3 -- results with the proposed method.
  • Figure 5: Comparison between the results of simulation 2 and 3. To compare the results during the steady-state phase, we only plot the results after the transient phase (i.e. $t \geq 5$ s).

Theorems & Definitions (4)

  • Lemma 1
  • proof
  • Theorem 1
  • proof