CLF-CBF-QP新形式下非线性系统的安全攸关控制与优化

利用二次规划(QP)结合控制Lyapunov函数(CLF)和控制障碍函数(CBF)形成非线性系统的一种安全攸关控 制策略, 称为CLF-CBF-QP, 其在实现控制目标和确保安全之间起到协调作用. 然而, 一旦引入附加的约束, 如输入 约束, QP求解可能变得不可行. 另外, 当考虑系统本身的体积或环境中存在快速移动的障碍物时, 动态系统与障碍 物发生碰撞的可能性会极大地提高. 因此, 本文首先从控制输入空间和状态空间的角度分别分析QP求解可行性以 及CLF和CBF中参数对QP求解可行性和系统性能的影响, 并提出一种CLF-CBF-QP新形式来提高优化问题的可解 性; 其次, 在考虑动态系统本身的体积且环境中存在动态障碍物时, 设计一种CBF新形式使其仍能保证系统的安全 性; 最后, 通过线性平面四旋翼在存在动态或静态障碍物的环境中进行轨迹跟踪来验证所提出方法的有效性.

Safety-critical control and optimization of nonlinear systems based on new forms of CLF-CBF-QP

Using quadratic programming (QP) to combine control Lyapunov function (CLF) and control barrier function (CBF) forms a safety-critical control strategy of nonlinear systems, named CLF-CBF-QP, which can mediate between achieving control objective and ensuring safety. However, when additional constraints such as input constraints are introduced, the CLF-CBF-QP may become infeasible. In addition, when considering the volume of the system itself or the presence of fast-moving obstacles in the environment, the possibility of collision between dynamic system and obstacles will be greatly increased. Therefore, this paper firstly analyzes the feasibility of QP solution and the influence of parameters in CLF and CBF on the feasibility of QP solution and system performance from the perspective of control-input-space and state-space, and proposes a new form of CLF-CBF-QP to improve the feasibility of solving optimization problems. Then, when considering the volume of the dynamic system itself and the presence of dynamic obstacles in the environment, a new form of CBF is designed to ensure the safety of the system. Finally, the effectiveness of the proposed algorithms is verified by a simulation case of linear planar quadrotor trajectory tracking in the environment with dynamic or static obstacles.