基于李代数的自适应控制，让机器人系统更稳定高效
Lie-algebra Adaptive Tracking Control for Rigid Body Dynamics
- 用李代数将刚体运动约束转化为向量空间，简化控制设计
- 实现参数自适应调节，误差动态线性化且解耦模型参数
- 适合需高精度轨迹跟踪的机器人系统，如机械臂、无人机
自适应轨迹控制在控制与机器人领域至关重要，尤其适用于系统模型参数存在不确定性或变化的情况。然而，多数现有自适应控制方法针对状态位于向量空间的系统设计，常忽略机器人系统固有的流形约束。本文提出一种新型基于李代数的自适应控制方法，利用特殊欧氏群与其伴随李代数之间的内在关系。通过将状态空间从群流形变换到向量空间，推导出解耦模型参数的线性误差动力学模型。该形式支持设计几何一致且计算高效的自适应最优控制方法。大量仿真验证了该方法的有效性与高效性。源代码已公开，以促进后续研究与合作。
原文摘要 · Abstract (English)
Adaptive tracking control for rigid body dynamics is of critical importance in control and robotics, particularly for addressing uncertainties or variations in system model parameters. However, most existing adaptive control methods are designed for systems with states in vector spaces, often neglecting the manifold constraints inherent to robotic systems. In this work, we propose a novel Lie-algebra-based adaptive control method that leverages the intrinsic relationship between the special Euclidean group and its associated Lie algebra. By transforming the state space from the group manifold to a vector space, we derive a linear error dynamics model that decouples model parameters from the system state. This formulation enables the development of an adaptive optimal control method that is both geometrically consistent and computationally efficient. Extensive simulations demonstrate the effectiveness and efficiency of the proposed method. We have made our source code publicly available to the community to support further research and collaboration.
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