基于Udwadia-Kalaba方法的柔性关节机器人动力学建模与主动柔顺性控制研究

柔性关节机器人广泛应用于各种受工作环境约束的场合中，因其符合人机共融理念而快速发展。现有柔性关节机器人动力学建模和控制方法不能很好地解决系统中的刚柔耦合矛盾、外界扰动和参数不确定性等问题。项目采用Udwadia-Kalaba方程研究受约束柔性关节机器人动力学建模方法，揭示非完整约束下约束力和主动力之间的关系；在计算出约束力的基础上提出基于模糊动态系统理论（非模糊逻辑）的主动柔顺性控制设计方法，将阻抗控制和自适应鲁棒控制相结合，克服系统中参数不确定性和外界扰动的影响；探索模糊不确定条件下的控制参数优化方法，提出综合考虑系统性能和控制消耗的二次性能指标，利用D-运算将优化问题转化为高阶多元函数极值问题求解。通过项目研究，可获得柔性关节机器人在非完整约束下约束力的解析解模型和主动柔顺性控制及优化方法。项目对完善柔性关节机器人建模和控制理论，促进其在国防和工业中的应用具有重要意义。

Flexible joint robot widely exists in the applications that are constrained by environment. Complying with the concept of Coexisting-Cooperative-Cognitive (Tri-Co) robot, it developed rapidly in past decades. The existing methods are lack of efficacy on dynamical modeling and control for such robot system due to the rigid-flexible coupling contradiction, external disturbances and uncertain parameters. Aiming at these problems, this proposal focuses on establishing the dynamic model of flexible joint robot under environmental constraints based on the Udwadia-Kalaba equation, revealing the relationship between active force and constraint force under nonholonomic constraints. In order to overcome the parameter uncertainties and external disturbances, a fuzzy dynamical system approach based control is proposed by using the obtained constraint force. The control colligates the concepts of impedance control and adaptive robust control. Then, a gain optimization method under the fuzzy description of uncertainty is explored and a quadratic performance index, considering the transient control cost and average control cost, is presented. By using D-operation, the optimal problem associated with control could be equivalent to a minimization problem of a high order multivariate function. Through this study, the closed-form constraint force of flexible joint robot under nonholonomic constraint could be established. Meanwhile, a systematic method for the design and optimization of active compliance control could be established. This study has significant meaning not only in perfecting the modeling method and control theory for flexible joint robot, but also in promoting its application in national defense and industrial production.