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随着协作机器人在工业制造、医疗健康、日常辅助等领域逐渐广泛应用，协作机器人所需应对的工作环境以及任务要求也日趋复杂。例如当协作机器人协助人类日常生活完成拉锯任务时，不仅需要能够在受到外界干扰的情况下准确有效地完成任务，同时也需要能够对不同的操作环境（如不同刚度的拉锯对象）具有一定的适应能力。这些要求推动协作机器人规划控制技术的不断发展。在规划方面，传统的运动控制算法需要根据不同的任务需求规划机器人运动轨迹，缺乏泛化能力。基于示教学习的方法利用人类的运动示教数据编码轨迹生成模型，能够根据任务需求的变化（如目标位置的变化）生成新的轨迹，因而具有较强的泛化能力。然而此类方法对“人类具有根据不同任务调整自身刚度的能力”学习不足，应用场景受到了限制。在控制方面，由于协作机器人的应用场景存在大量的人机交互，能够保证柔顺性的阻抗控制已经成为主流方法。然而，如何根据人类协作者的意图优化阻抗，从而减少对人类运动阻碍方面的研究还有所不足。此外，如何保障变阻抗控制下受交互力影响时的人机协作安全性还需要进一步的分析。为解决上述问题，本文结合了示教学习和变阻抗控制的优点，在构建能编码刚度信息的示教学习、设计顺应人类协作者意图的刚度优化方法、分析受扰时变阻抗控制下的人机协作安全三个方面展开研究，以满足协作机器人在协作任务场景下的工作需求。本文的主要工作与创新点归纳如下。

本文提出了一种编码变刚度协作行为的示教学习方法。传统的示教学习方法忽略了刚度、交互力、运动时间之间的关系，从而阻碍了机器人准确复现协作任务。同时，此类方法对不同的协作场景下的刚度泛化尚未进行很好的考虑，限制了机器人的适应能力。本文设计了一种基于动态运动原语和高斯混合模型的协作行为建模方法，采用弹簧阻尼模型来构建运动原语，而将模型中的期望任务轨迹和交互刚度建模为与时间和交互力相关的条件概率模型。对于给定的任务时刻和交互力参数，利用高斯混合回归算法来生成应该采用的任务轨迹和刚度参数。所设计的算法具有对时间、目标位置、操作对象的泛化能力，能够有效增强机器人对复杂人机协作场景的适应能力。
本文提出了一种根据协作者意图迭代优化控制器刚度参数的控制策略。使用示教学习生成的刚度参数能够驱使机器人有效柔顺地完成协作任务。然而，当前已有的阻抗控制方法未考虑按照人类需求优化调整机器人刚度，无法达到令人满意的协作性能。为此，本文设计了一种迭代优化按需辅助控制算法。首先设计了表征协作者运动意图强弱的量化方法，再构建了一种新型迭代刚度参数更新律来根据意图调整刚度大小。最终，本文将所提出的按需辅助变阻抗控制方法和之前设计的示教学习相结合，使机器人能够在模仿人类协作行为的同时根据协作者运动意图对控制参数进行优化。当协作者运动意图弱时，机器人将采用更大的刚度带领协作者完成协作任务。
本文提出了一种变刚度参数下保障人机协作安全的无源模型预测阻抗控制器。当机器人应用于日常协作场景时，在受扰情况下保障人机协作的安全性是控制器设计的重要目标。然而传统变阻抗控制器不能确保闭环机器人系统状态满足无源性条件，进而导致协作过程中机器人的存储能量快速增加，威胁到协作者的安全。为处理该问题，本文设计了一种无源模型预测阻抗控制器来保障机器人系统的安全性。在控制器中，底层的阻抗控制负责控制机器人按照期望的弹簧阻尼模型运动。顶层的模型预测控制负责计算出一个尽可能小的补偿输入，使系统状态能够满足安全无源性约束。最终所设计的算法能够驱使机器人与协作者完成任务，并保证协作过程的安全。
 

As collaborative robots are increasingly being used in various fields such as industrial manufacturing, healthcare, and daily assistance, the work environment and task requirements for collaborative robots are becoming increasingly complex. For example, when a collaborative robot assists humans in performing tasks like sawing, it needs to accurately and effectively complete the task even in the presence of external disturbances. Additionally, it also needs to adapt to different operating environments, such as objects with different stiffness levels. These requirements drive the continuous development of planning and control techniques for collaborative robots. In terms of planning, traditional motion control algorithms lack generalization ability as they need to plan robot motion trajectories based on different task requirements. Learning from demonstration methods utilize human motion demonstration data to encode trajectory generation models, allowing the generation of new trajectories based on task requirements changes (e.g., changes in the target position). Therefore, they possess strong generalization capabilities. However, such methods lack the ability to learn ``the capability of humans to adjust their own stiffness based on different tasks,'' which limits their applicability. In terms of control, due to the significant amount of human-robot interaction in collaborative robot applications, impedance control, which ensures compliance, has become a mainstream method. However, there is still a lack of research on optimizing impedance based on human co-worker's intentions to reduce hindrance to human motion. Additionally, further analysis is needed to ensure the safety of human-robot collaboration under interactive force in variable impedance control. To address the aforementioned issues, this thesis combines the advantages of learning from demonstration and variable impedance control. It conducts research in three aspects: building a learning from demonstration framework that can encode stiffness information, designing a stiffness optimization method that aligns with human co-worker's intentions, and analyzing the safety of human-robot collaboration under disturbed conditions in variable impedance control. These efforts aim to meet the work requirements of collaborative robots in collaborative task scenarios. The main contributions and innovations of this thesis are summarized as follows.

This thesis proposes a learning from demonstration method for encoding variable stiffness collaborative behaviors. Traditional learning from demonstration methods overlook the relationship between stiffness, interaction forces, and motion time, which hinders accurate reproduction of collaborative tasks by robots. Moreover, such methods have not adequately considered stiffness generalization in different collaborative scenarios, limiting the adaptability of robots. This thesis designs a collaborative behavior modeling approach based on dynamic motion primitives and Gaussian mixture models. One spring-damping model is employed to construct motion primitives and model the desired task trajectory and interactive stiffness in the model as conditional probability models that are correlated with time and interaction forces. Given a specific task moment and interaction force parameters, the Gaussian mixture regression algorithm is used to generate the appropriate task trajectory and stiffness parameters. The proposed algorithm exhibits generalization capabilities with respect to time, target position, and manipulated objects, thereby effectively enhancing the robot's adaptability to complex human-robot collaborative scenarios.

This thesis proposes a control strategy that iteratively optimizes the controller's stiffness parameters based on the cooperator's intentions. Using stiffness parameters generated through learning from demonstration method enables the robot to effectively and compliantly perform collaborative tasks. However, existing impedance control methods fail to consider optimizing and adjusting the robot's stiffness according to human requirements, leading to unsatisfactory collaborative performance. To address this, this thesis introduces an iterative optimization-based assistive control algorithm. Firstly, a quantification method is designed to represent the strength of the cooperator's motion intentions. Then, a novel iterative stiffness parameter updating rule is developed to adjust the stiffness magnitude based on the intentions. Finally, this thesis combines the proposed assistive variable impedance control method with the previously designed teaching and learning approach, allowing the robot to imitate human collaborative behavior while optimizing the control parameters based on the cooperator's motion intentions. When the cooperator's motion intentions are weak, the robot will adopt a higher stiffness to guide the cooperator in completing the collaborative task.

This thesis proposes a passive model predictive impedance controller for ensuring safe human-robot collaboration under variable stiffness parameters. When robots are employed in everyday collaborative scenarios, ensuring the safety of human-robot collaboration under disturbances is an important objective in controller design. However, traditional variable impedance controllers cannot guarantee that the closed-loop robot system satisfies passivity conditions, leading to rapid energy accumulation in the robot during the collaboration process, which poses a threat to the safety of the cooperator. To address this issue, this thesis designs a passive model predictive impedance controller to ensure the safety of the robot system. In the controller, the lower-level impedance control is responsible for controlling the robot's motion according to the desired spring-damping model. The upper-level model predictive control calculates a compensation input that minimizes the system's violation of passivity constraints. The resulting algorithm drives the robot to collaborate with the cooperator while ensuring the safety of the collaboration process.