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<p>Underactuated mechanical systems often need to achieve trajectory tracking and obstacle avoidance simultaneously under coupled equality and inequality constraints. This paper presents an adaptive robust control framework that integrates generalized Udwadia–Kalaba (GUK) theory, diffeomorphic state transformation, and neural activation mechanisms for underactuated mechanical systems subject to mixed constraints. Within a unified constraint-following formulation, trajectory-tracking and obstacle-avoidance objectives are embedded into the GUK dynamics. Neural activation functions enable smooth arbitration between competing task objectives, while a diffeomorphic transformation maps inequality constraints into unconstrained variables that are regulated through null-space control inputs without disturbing the equality-constrained motion. Lyapunov-based analysis establishes closed-loop stability in the presence of bounded uncertainties and disturbances. The proposed framework is validated through simulations and real-world experiments on a differential-drive mobile robot, and benchmarked against the linear quadratic regulator (LQR) and sliding-mode control (SMC) under identical operating conditions. In simulation, the proposed controller reduces IAE, ISE, and ITAE by 34%, 39%, and 51%, respectively, relative to LQR, and by 22%, 16%, and 47%, respectively, relative to SMC. In physical experiments, the cumulative tracking error is reduced to approximately 49% and 62% of that obtained with LQR and SMC, respectively, while maintaining obstacle avoidance and strict satisfaction of the prescribed inequality constraints. While validated on a representative single-robot platform, the framework generalizes naturally to a broad class of underactuated systems and higher-dimensional settings.</p>

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Adaptive robust control of underactuated mechanical systems with inequality constraints via generalized Udwadia–Kalaba theory and neural activation

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Peng Zhang,
  • Jiale Zhang,
  • Wenlu Fan,
  • Che Wang,
  • Dongsheng Zhang,
  • Shengjie Jiao

摘要

Underactuated mechanical systems often need to achieve trajectory tracking and obstacle avoidance simultaneously under coupled equality and inequality constraints. This paper presents an adaptive robust control framework that integrates generalized Udwadia–Kalaba (GUK) theory, diffeomorphic state transformation, and neural activation mechanisms for underactuated mechanical systems subject to mixed constraints. Within a unified constraint-following formulation, trajectory-tracking and obstacle-avoidance objectives are embedded into the GUK dynamics. Neural activation functions enable smooth arbitration between competing task objectives, while a diffeomorphic transformation maps inequality constraints into unconstrained variables that are regulated through null-space control inputs without disturbing the equality-constrained motion. Lyapunov-based analysis establishes closed-loop stability in the presence of bounded uncertainties and disturbances. The proposed framework is validated through simulations and real-world experiments on a differential-drive mobile robot, and benchmarked against the linear quadratic regulator (LQR) and sliding-mode control (SMC) under identical operating conditions. In simulation, the proposed controller reduces IAE, ISE, and ITAE by 34%, 39%, and 51%, respectively, relative to LQR, and by 22%, 16%, and 47%, respectively, relative to SMC. In physical experiments, the cumulative tracking error is reduced to approximately 49% and 62% of that obtained with LQR and SMC, respectively, while maintaining obstacle avoidance and strict satisfaction of the prescribed inequality constraints. While validated on a representative single-robot platform, the framework generalizes naturally to a broad class of underactuated systems and higher-dimensional settings.