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Inertia Partitioning Modular Control Framework for Reconfigurable Multibody Systems

Mohammad Dastranj, Jouni Mattila

TL;DR

This work addresses the challenge of modular control for reconfigurable multibody systems with closed chains by introducing an inertia-partitioning framework in which each DOF is treated as a module. By formulating the total kinetic energy through a global generalized inertia matrix $\boldsymbol{\Gamma}(\boldsymbol{q})$ assembled from local contributions, the approach yields per-DOF dynamics and a DAE-free model that supports modular controller design and system reconfiguration. The authors derive the modular EOM using minimal coordinates, prove almost-global asymptotic stability of the proposed controller via a Lyapunov function, and validate the method with a Simscape simulation of a 3-DOF series-parallel manipulator, achieving accurate trajectory tracking with low RMSE. The framework offers a scalable, energy-based perspective on modular control for closed-chain multibody systems and lays groundwork for future reconfiguration, uncertainty handling, and experimental validation.

Abstract

A novel modular control framework for reconfigurable rigid multibody systems is proposed, motivated by the challenges of modular control of systems with closed kinematic chains. In the framework, modularity is defined in the sense of degrees of freedom, and the inertial properties of each body are partitioned with respect to how they are reflected in the kinetic energy of the system through the motion induced by each degree of freedom. This approach inherently handles closed chains in the same manner as tree-like structures, eliminating the need for explicit constraint force calculations or formulations based on differential-algebraic equations. The proposed framework is implemented via simulation on a three-degree-of-freedom series-parallel manipulator, with the results being consistent with the expected stability and tracking performance, and indicating the framework's potential for scalability in trajectory-tracking control of multibody systems.

Inertia Partitioning Modular Control Framework for Reconfigurable Multibody Systems

TL;DR

This work addresses the challenge of modular control for reconfigurable multibody systems with closed chains by introducing an inertia-partitioning framework in which each DOF is treated as a module. By formulating the total kinetic energy through a global generalized inertia matrix assembled from local contributions, the approach yields per-DOF dynamics and a DAE-free model that supports modular controller design and system reconfiguration. The authors derive the modular EOM using minimal coordinates, prove almost-global asymptotic stability of the proposed controller via a Lyapunov function, and validate the method with a Simscape simulation of a 3-DOF series-parallel manipulator, achieving accurate trajectory tracking with low RMSE. The framework offers a scalable, energy-based perspective on modular control for closed-chain multibody systems and lays groundwork for future reconfiguration, uncertainty handling, and experimental validation.

Abstract

A novel modular control framework for reconfigurable rigid multibody systems is proposed, motivated by the challenges of modular control of systems with closed kinematic chains. In the framework, modularity is defined in the sense of degrees of freedom, and the inertial properties of each body are partitioned with respect to how they are reflected in the kinetic energy of the system through the motion induced by each degree of freedom. This approach inherently handles closed chains in the same manner as tree-like structures, eliminating the need for explicit constraint force calculations or formulations based on differential-algebraic equations. The proposed framework is implemented via simulation on a three-degree-of-freedom series-parallel manipulator, with the results being consistent with the expected stability and tracking performance, and indicating the framework's potential for scalability in trajectory-tracking control of multibody systems.
Paper Structure (17 sections, 41 equations, 7 figures, 3 tables)

This paper contains 17 sections, 41 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Background
  3. Literature Review
  4. Contributions
  5. Paper Structure
  6. Modular Dynamic Modeling of Multibody Systems
  7. Kinematics of the Multibody System
  8. Generalized Inertia Matrix
  9. Modular Equations of Motion
  10. Multibody System Reconfiguration
  11. Modular Control of Multibody Systems
  12. Controller Design
  13. Stability Analysis
  14. Simulation and Results
  15. Kinematic and Dynamic Modeling
  16. ...and 2 more sections

Figures (7)

  • Figure 1: The schematics for a 3-DoF series-parallel manipulator. The degrees of freedom are made up of two actuated revolute joints for the base and the first link, and an actuated prismatic joint between the first and second links.
  • Figure 2: The required frames of reference and geometric parameters for modeling the 3-DoF series-parallel manipulator. Some frames are shown only in one of the figures for clarity. Top - Side view perpendicular to the links' body-fixed frames $x$-$y$ plane. Bottom - Top view of the base, perpendicular to its frames' $x$-$y$ planes.
  • Figure 3: The geometry of the triangular closed chain. This closed chain consists of one actuated prismatic joint and three passive revolute joints.
  • Figure 4: Desired trajectory for the end effector of the 3-DoF series-parallel manipulator. Top - The desired trajectory in Cartesian space. Bottom - The desired trajectory with respect to time.
  • Figure 5: Desired trajectory for the end effector of the 3-DoF series-parallel manipulator expressed in generalized coordinates.
  • ...and 2 more figures