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<p>Model-based motion control is essential for accurate trajectory tracking in parallel kinematic machines (PKMs), especially during high-speed dynamic tasks. This requires formulating constrained dynamics in appropriate minimal coordinates. For non-redundant PKMs, actuated joint positions naturally serve as minimal coordinates since parameterization singularities coincide with input singularities. In contrast, redundantly actuated PKMs (RA-PKMs) exhibit larger singularity-free workspaces. Using fixed minimal coordinates imposes the same parameterization singularity limitations as in non-redundant systems, failing to leverage the benefits of additional actuation. To fully exploit the advantages of RA-PKMs, this work proposes a novel model-based control scheme using an orthogonally moving frame constructed along the reference trajectory. For acceleration-bounded reference trajectories, the scheme guarantees local exponential stability. Unlike minimal-coordinate switching methods, it generates smooth feedback forces without reformulating dynamics. Compared to computed-torque control in redundant coordinates, it guarantees stability regardless of reference velocity magnitude. With an added robust term, the proposed controller further achieves local asymptotic stability for velocity-bounded reference trajectories. Rigorous theoretical proofs and simulations on two planar RA-PKMs and one spatial RA-PKM validate the approach.</p>

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Robust Trajectory Tracking of Redundantly Actuated Parallel Manipulators Based on Orthogonal Moving Frames

  • 期刊论文

  • 发表日期：

    2026年2月11日

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  • Hongchen Li,
  • Ye Ding

摘要

Model-based motion control is essential for accurate trajectory tracking in parallel kinematic machines (PKMs), especially during high-speed dynamic tasks. This requires formulating constrained dynamics in appropriate minimal coordinates. For non-redundant PKMs, actuated joint positions naturally serve as minimal coordinates since parameterization singularities coincide with input singularities. In contrast, redundantly actuated PKMs (RA-PKMs) exhibit larger singularity-free workspaces. Using fixed minimal coordinates imposes the same parameterization singularity limitations as in non-redundant systems, failing to leverage the benefits of additional actuation. To fully exploit the advantages of RA-PKMs, this work proposes a novel model-based control scheme using an orthogonally moving frame constructed along the reference trajectory. For acceleration-bounded reference trajectories, the scheme guarantees local exponential stability. Unlike minimal-coordinate switching methods, it generates smooth feedback forces without reformulating dynamics. Compared to computed-torque control in redundant coordinates, it guarantees stability regardless of reference velocity magnitude. With an added robust term, the proposed controller further achieves local asymptotic stability for velocity-bounded reference trajectories. Rigorous theoretical proofs and simulations on two planar RA-PKMs and one spatial RA-PKM validate the approach.