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Inertial Line-Of-Sight Stabilization Using a 3-DOF Spherical Parallel Manipulator with Coaxial Input Shafts

Alexandre Le, Guillaume Rance, Fabrice Rouillier, Damien Chablat

TL;DR

The paper investigates inertial line-of-sight (LOS) stabilization using a coaxial-input 3-DOF spherical parallel manipulator (CoSPM) with three 3-RRR branches. It delivers a detailed kinematic analysis, deriving the geometric model, first-order kinematics, and a polynomial formulation to study singularities, and proves geometric invariance with respect to the coaxial bearing axis $\chi_3$, ensuring the prescribed workspace avoids both Type-1 and Type-2 singularities. A speed-control law is proposed, yielding decoupled, identical loops that map LOS-frame angular rates to actuator commands via $\mathbf{J}$ and $\mathbf{T}$, with a carefully tuned $K_0(s)$ achieving robust disturbance rejection and satisfactory stability margins ($60^{\circ}$ phase, $14.2$ dB gain). The approach is validated through MATLAB/Simulink simulations and a SimMechanics-based digital model, showing sub-milliradian residuals and modest actuator torques (transient $\leq 4$ Nm, steady $\leq 2.5$ Nm) under sea-state disturbances. The work highlights practical viability of CoSPMs for inertial LOS stabilization while acknowledging limitations in control robustness and suggesting future work on joint-stops management and a full dynamic model for certification under uncertainty.

Abstract

This article dives into the use of a 3-RRR Spherical Parallel Manipulator (SPM) for the purpose of inertial Line Of Sight (LOS) stabilization. Such a parallel robot provides three Degrees of Freedom (DOF) in orientation and is studied from the kinematic point of view. In particular, one guarantees that the singular loci (with the resulting numerical instabilities and inappropriate behavior of the mechanism) are far away from the prescribed workspace. Once the kinematics of the device is certified, a control strategy needs to be implemented in order to stabilize the LOS through the upper platform of the mechanism. Such a work is done with MATLAB Simulink using a SimMechanics model of our robot.

Inertial Line-Of-Sight Stabilization Using a 3-DOF Spherical Parallel Manipulator with Coaxial Input Shafts

TL;DR

The paper investigates inertial line-of-sight (LOS) stabilization using a coaxial-input 3-DOF spherical parallel manipulator (CoSPM) with three 3-RRR branches. It delivers a detailed kinematic analysis, deriving the geometric model, first-order kinematics, and a polynomial formulation to study singularities, and proves geometric invariance with respect to the coaxial bearing axis , ensuring the prescribed workspace avoids both Type-1 and Type-2 singularities. A speed-control law is proposed, yielding decoupled, identical loops that map LOS-frame angular rates to actuator commands via and , with a carefully tuned achieving robust disturbance rejection and satisfactory stability margins ( phase, dB gain). The approach is validated through MATLAB/Simulink simulations and a SimMechanics-based digital model, showing sub-milliradian residuals and modest actuator torques (transient Nm, steady Nm) under sea-state disturbances. The work highlights practical viability of CoSPMs for inertial LOS stabilization while acknowledging limitations in control robustness and suggesting future work on joint-stops management and a full dynamic model for certification under uncertainty.

Abstract

This article dives into the use of a 3-RRR Spherical Parallel Manipulator (SPM) for the purpose of inertial Line Of Sight (LOS) stabilization. Such a parallel robot provides three Degrees of Freedom (DOF) in orientation and is studied from the kinematic point of view. In particular, one guarantees that the singular loci (with the resulting numerical instabilities and inappropriate behavior of the mechanism) are far away from the prescribed workspace. Once the kinematics of the device is certified, a control strategy needs to be implemented in order to stabilize the LOS through the upper platform of the mechanism. Such a work is done with MATLAB Simulink using a SimMechanics model of our robot.
Paper Structure (23 sections, 2 theorems, 25 equations, 16 figures, 1 table)

This paper contains 23 sections, 2 theorems, 25 equations, 16 figures, 1 table.

Table of Contents

  1. Introduction
  2. Context of the study
  3. Presentation of the mechanism
  4. Kinematic analysis
  5. Geometric model
  6. First order kinematic model
  7. Coaxiality of the input shafts
  8. Singularity analysis
  9. Issues & strategies
  10. Type-1 singularities
  11. Type-2 singularities
  12. Control law for the LOS stabilization
  13. Principles & Requirements
  14. Speed control architecture
  15. Description
  16. ...and 8 more sections

Key Result

Proposition 1

For any 3-DOF 3-RRR CoSPM, each actuated joint $\theta_i$ ($i\in\left\llbracket1,3\right\rrbracket$) making the same displacement $-\epsilon$ generates a pure bearing motion $\epsilon$.

Figures (16)

  • Figure 1: Illustration of the SPM with coaxial input shafts of interest
  • Figure 2: Rotation order using the Euler Tait-Bryan ZYX convention
  • Figure 3: Tools for the description of the SPM
  • Figure 4: Details on the design parameters and the vectors of the SPM with coaxial input shafts
  • Figure 5: Prescribed workspace $\calW^\star$ (dashed) and Type-1 Singularity loci (solid) of the mechanism of interest in the $(\chi_1,\chi_2)$-plane
  • ...and 11 more figures

Theorems & Definitions (7)

  • Remark 1
  • Proposition 1
  • proof
  • Lemma 1
  • Remark 2
  • Remark 3
  • Remark 4