[论文解读] Safe and Compliant Control of Redundant Robots Using Superimposition of Passive Task-Space Controllers

Carlo Tiseo, Wolfgang Merkt+3 more|Edinburgh Research Explorer (University of Edinburgh)|Feb 27, 2020

Piezoelectric Actuators and Control被引用 5

一句话总结

该论文提出了一种新颖的、固有稳定的冗余机器人控制框架，通过叠加被动任务空间控制器，确保在无需动力学模型知识的情况下具备柔顺性和安全性。通过结合多个被动控制器与平滑、自适应的刚度分布，该方法在快速、动态任务中实现了亚厘米级的跟踪精度，同时对奇异性及未知环境交互保持鲁棒性。

ABSTRACT

Safe and compliant control of dynamic systems in interaction with the environment, e.g., in shared workspaces, continues to represent a major challenge. Mismatches in the dynamic model of the robots, numerical singularities, and the intrinsic environmental unpredictability are all contributing factors. Online optimization of impedance controllers has recently shown great promise in addressing this challenge, however, their performance is not sufficiently robust to be deployed in challenging environments. This work proposes a compliant control method for redundant manipulators based on a superimposition of multiple passive task-space controllers in a hierarchy. Our control framework of passive controllers is inherently stable, numerically well-conditioned (as no matrix inversions are required), and computationally inexpensive (as no optimization is used). We leverage and introduce a novel stiffness profile for a recently proposed passive controller with smooth transitions between the divergence and convergence phases making it particularly suitable when multiple passive controllers are combined through superimposition. Our experimental results demonstrate that the proposed method achieves sub-centimeter tracking performance during demanding dynamic tasks with fast-changing references, while remaining safe to interact with and robust to singularities. he proposed framework achieves such results without knowledge of the robot dynamics and thanks to its passivity is intrinsically stable. The data further show that the robot can fully take advantage of the redundancy to maintain the primary task accuracy while compensating for unknown environmental interactions, which is not possible from current frameworks that require accurate contact information.

研究动机与目标

• 解决在动力学特性不确定且可能发生奇异性的情况下，动态、不可预测环境中安全且柔顺控制的挑战。
• 克服现有基于优化的阻抗控制方法在鲁棒性方面的局限性，并避免对精确接触或动力学模型的依赖。
• 使冗余机器人能够在被动、分层控制下维持末端执行器的任务精度，同时补偿未知的环境交互作用。
• 开发一种计算高效、数值条件良好（well-conditioned）的控制方法，避免矩阵求逆与在线优化。
• 通过无源性实现内在稳定性，确保在突发扰动或构型变化下仍能实现安全交互。

提出的方法

• 以分层结构叠加多个被动任务空间控制器，每个控制器作用于机器人的不同部分（例如末端执行器和中间关节）。
• 采用一种新颖的分形阻抗控制器，实现发散与收敛阶段之间的平滑过渡，确保能量流的连续性并避免不连续性。
• 利用无源运动范式（PMP）与分段光滑的能量流形，无需反向动力学或矩阵求逆即可保证李雅普诺夫稳定性。
• 基于期望位置、力限制和刚度分布定义任务空间控制器，辅以次级控制器引导关节构型以利用冗余度。
• 在切换点（例如从发散到收敛）应用能量守恒原理，确保李雅普诺夫函数的连续性与稳定性。
• 采用基于发散阶段最大位移自适应调整的刚度分布，实现扰动下的渐进退化。

Figure 1 : Stack of Passive Controllers executing a reference motion to follow a line trajectory while an unknown external disturbance is introduced to the elbow joint. The controller adapts safely and compliantly to the disturbance and degrades tracking performance gracefully.

实验结果

研究问题

• RQ1 通过叠加被动任务空间控制器，是否可在不依赖动力学模型知识的情况下，实现冗余机器人稳定且柔顺的控制？
• RQ2 如何组合被动控制器，以在补偿未知环境交互作用的同时保持末端执行器的精度？
• RQ3 平滑、自适应的刚度分布是否能提升被动控制器在控制阶段切换过程中的鲁棒性？
• RQ4 在奇异性或快速变化参考信号存在的情况下，该方法在多大程度上仍保持稳定与数值条件良好？
• RQ5 该框架是否能在无需实时优化或精确接触传感的情况下，实现冗余度的利用以提升柔顺性与安全性？

主要发现

• 所提方法在具有快速变化参考信号的动态任务中实现了亚厘米级的跟踪性能，即使在未知外部扰动下也表现良好。
• 由于无源性，该控制框架具有内在稳定性，无需了解机器人动力学参数（如惯性、摩擦或重力）。
• 系统对数值奇异性具有鲁棒性，并因控制器的无源特性而保持与环境的安全交互。
• 机器人成功利用冗余度在补偿未知环境交互作用的同时维持了末端执行器的精度，这是现有框架所不具备的能力。
• 李雅普诺夫稳定性证明表明，控制器在切换点处维持了有限的能量流与连续的能量流形，确保了非光滑区域的稳定性。
• 该方法计算效率高，避免了矩阵求逆与在线优化，适用于复杂动态环境中实时部署。

Figure 2 : Conceptual overview of the stack of passive task-space controllers framework: (a) The primary task is defined in terms of desired position, accuracy, and maximum exerted force produces a non-linear impedance profile to constrain the robot’s end-effector ( $3^{\text{rd}}$ -link). Impedance