Energy based Control Barrier Functions for Robotic Systems
Energy based Control Barrier Functions for Robotic Systems
复制标题
机器人系统基于能量的控制屏障功能
DOI：
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发表时间：
2020
期刊：
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通讯作者：
Shishir N Y Kolathaya
中科院分区：
文献类型：
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作者：
Shishir N Y Kolathaya
基于控制屏障函数（CBF）的二次规划（qp）于2014年初引入，作为保证仿射控制系统安全与稳定性/跟踪的一种手段。然而，由于基于模型的项的存在，它们不能在模型扰动下提供保证。因此，在本文中，我们提出了一类新的cbf用于机器人系统，以传统形式增加动能。我们表明，在扭矩限制允许的情况下，在运动学模型准确已知的情况下，可以保证由运动学约束（位置和速度）生成的安全集的正向不变性。所提出的方法是由使用动能函数的基于控制李雅普诺夫函数（CLF）的qp驱动的。利用CBF-QPs的性质，我们证明了所得到的点最小范数控制律是可行的，并且是Lipschitz连续的，并且可以通过KKT条件解析导出。为了将稳定性和安全性结合起来，我们还在cbf - qp中增加了基于CLF的约束，以实现一个统一的控制律，该律允许在不考虑机器人惯性参数的情况下进行安全跟踪。我们将展示这类cbf - qp在两个机器人平台中的鲁棒性：1-DOF和2-DOF机械手，通过将质量缩放到100，然后模拟产生的动力学。
Control barrier function (CBF) based Quadratic Programs (QPs) were introduced in early 2014 as a means to guarantee safety in affine control systems in conjunction with stability/tracking. However, due to the presence of model-based terms, they fail to provide guarantees under model perturbations. Therefore, in this paper, we propose a new class of CBFs for robotic systems that augment kinetic energy with the traditional forms. We show that with torque limits permitting, and with the kinematic models accurately known, forward invariance of safe sets generated by kinematic constraints (position and velocity) can be guaranteed. The proposed methodology is motivated by the control Lyapunov function (CLF) based QPs that use the kinetic energy function. By the property of CBF-QPs, we show that the pointwise min-norm control laws obtained are feasible and Lipschitz continuous, and can be derived analytically via the KKT conditions. In order to include stability with safety, we also augment CLF based constraints in the CBF-QPs to realize a unified control law that allows tracking with safety irrespective of the inertial parameters of the robot. We will demonstrate the robustness of this class of CBF-QPs in two robotic platforms: a 1-DOF and a 2-DOF manipulator, by scaling the masses by up to 100, and then simulating the resulting dynamics.