Abstract In this paper, a robust adaptive control approach has been proposed for under insufficient excitation Multi-Input Multi-Output (MIMO) systems. The stability and performance of adaptive controllers are highly dependent on initial conditions and speed of convergence of identified parameters. Moreover, the corresponding adaptation rules suffer from system uncertainties, disturbances, and insufficient excitation. In order to overcome such crucial challenges, in this paper a robust adaptive control is proposed. By inspiring from the classic Damped Least Squares (DLS) and Singular Value Decomposition (SVD) methods, a novel algorithm namely, SVD-DLS, is introduced which obtains an optimal solution to the estimation wind-up. Above all, the proposed approach is implemented on a 3 degree-of-freedom spherical parallel robot for stabilization purposes. By avoiding from challenges of model-based approaches, the unknown parameters are obtained without having any prior knowledge which makes the proposed approach more interesting for robotic having complex models. Based on the practical implementation, the oscillations of identified parameters are dampened much smoother than other identification methods in which the ratio of end-effector to base orientation, as a stabilization index, is acquired as 0.134.

中文翻译：

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用于稳定目的的三自由度球形并联机器人在激励不足的情况下鲁棒自适应控制的实验研究

摘要 在本文中，针对激励不足的多输入多输出（MIMO）系统提出了一种鲁棒的自适应控制方法。自适应控制器的稳定性和性能高度依赖于初始条件和识别参数的收敛速度。此外，相应的适应规则受到系统不确定性、干扰和激励不足的影响。为了克服这些关键挑战，本文提出了一种鲁棒自适应控制。受经典阻尼最小二乘法 (DLS) 和奇异值分解 (SVD) 方法的启发，引入了一种新颖的算法，即 SVD-DLS，该算法可以获得估计结束的最优解。首先，出于稳定目的，建议的方法在 3 自由度球形并联机器人上实施。通过避免基于模型的方法的挑战，在没有任何先验知识的情况下获得未知参数，这使得所提出的方法对于具有复杂模型的机器人更有趣。基于实际实施，识别参数的振荡比其他识别方法更平滑，其中末端执行器与基部方向的比率作为稳定指标获得为0.134。