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<p>In this paper, the dynamic modeling of non-holonomic mobile manipulators is revisited. Accordingly, A direct new formulation is applied to derive an efficient and explicit dynamic model of a high-degree-of-freedom (DOF), nonholonomic, and coupled mobile manipulator. The novelty of this approach lies in its ability to provide the modular form of the equations of motion—in terms of the inertia tensor, centrifugal and Coriolis tensor, gravity vector, and Jacobian tensor—for the unified system directly from the system’s structural parameters (i.e., geometric parameters, center of mass positions, inertia, and mass) and generalized coordinates. This is achieved without the need for intermediate complex computations such as kinetic energy, potential energy, acceleration energy (Gibbs function), or their partial derivatives, relying instead on direct algebraic manipulations using only matrix-vector multiplications. These intermediate steps are often highly complex for high-DOF systems, even when symbolic algebra software is employed. Hence, in addition to symbolic implementation of our method, it can also be fully constructed numerically for online applications, without relying on the complex symbolic expressions typically required by Lagrange’s or Kane’s formulations. Furthermore, the nonholonomic constraints are directly incorporated into the dynamic equations of the entire system, eliminating the need for Lagrange multipliers. A simulation is then conducted for a mobile platform equipped with a 6-DOF manipulator via the proposed algorithm, Kane’s equations, and the Lagrange formulation. Simulation results demonstrate the accuracy and efficiency of the proposed dynamic model. The method also proves to be a strong candidate for algorithmic customization, highlighting its significant potential for real-time control applications. Finally, the approach is implemented in a robust model-based control system that incorporates the analytical expression of uncertainties and external disturbances. As a result, this paper can be considered a detailed, easy and quick guide on how to implement the method on a high-DOF mobile manipulator.</p>

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A clear dynamic formulation of a high-DOF mobile manipulator using a direct formulation including coupling effects and nonholonomic constraints

  • 期刊论文

  • 发表日期：

    2025年9月8日

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  • Otman El Baji,
  • Abdessamad Harrandou,
  • Nabil Ben Said Amrani,
  • Driss Sarsri

摘要

In this paper, the dynamic modeling of non-holonomic mobile manipulators is revisited. Accordingly, A direct new formulation is applied to derive an efficient and explicit dynamic model of a high-degree-of-freedom (DOF), nonholonomic, and coupled mobile manipulator. The novelty of this approach lies in its ability to provide the modular form of the equations of motion—in terms of the inertia tensor, centrifugal and Coriolis tensor, gravity vector, and Jacobian tensor—for the unified system directly from the system’s structural parameters (i.e., geometric parameters, center of mass positions, inertia, and mass) and generalized coordinates. This is achieved without the need for intermediate complex computations such as kinetic energy, potential energy, acceleration energy (Gibbs function), or their partial derivatives, relying instead on direct algebraic manipulations using only matrix-vector multiplications. These intermediate steps are often highly complex for high-DOF systems, even when symbolic algebra software is employed. Hence, in addition to symbolic implementation of our method, it can also be fully constructed numerically for online applications, without relying on the complex symbolic expressions typically required by Lagrange’s or Kane’s formulations. Furthermore, the nonholonomic constraints are directly incorporated into the dynamic equations of the entire system, eliminating the need for Lagrange multipliers. A simulation is then conducted for a mobile platform equipped with a 6-DOF manipulator via the proposed algorithm, Kane’s equations, and the Lagrange formulation. Simulation results demonstrate the accuracy and efficiency of the proposed dynamic model. The method also proves to be a strong candidate for algorithmic customization, highlighting its significant potential for real-time control applications. Finally, the approach is implemented in a robust model-based control system that incorporates the analytical expression of uncertainties and external disturbances. As a result, this paper can be considered a detailed, easy and quick guide on how to implement the method on a high-DOF mobile manipulator.