Safety is one of the fundamental problems in robotics. Recently, one-step or multi-step optimal control problems for discrete-time nonlinear dynamical system were formulated to offer tracking stability using control Lyapunov functions (CLFs) while subject to input constraints as well as safety-critical constraints using control barrier functions (CBFs). The limitations of these existing approaches are mainly about feasibility and safety. In the existing approaches, the feasibility of the optimization and the system safety cannot be enhanced at the same time theoretically. In this paper, we propose two formulations that unifies CLFs and CBFs under the framework of nonlinear model predictive control (NMPC). In the proposed formulations, safety criteria is commonly formulated as CBF constraints and stability performance is ensured with either a terminal cost function or CLF constraints. Slack variables with relaxing technique are introduced on the CBF constraints to resolve the tradeoff between feasibility and safety so that they can be enhanced at the same. The advantages about feasibility and safety of proposed formulations compared with existing methods are analyzed theoretically and validated with numerical results.
翻译:安全是机器人的根本问题之一。最近,为使用控制 Lyapunov 功能(CLFs)来跟踪稳定性,制定了离散非线性动态系统的一步或多步最佳控制问题,以利用控制 Lyapunov 功能(CLFs)来跟踪稳定性,同时受到投入限制以及使用控制屏障功能(CBFs)来进行安全临界限制。这些现有方法的局限性主要在于可行性和安全。在现有方法中,优化和系统安全的可行性无法同时在理论上得到加强。在本文件中,我们提出了在非线性模型预测控制(NMPC)的框架内统一CLFs和CBFs的两个公式。在拟议的配方中,安全标准通常是作为CBFF的制约和稳定性性能得到保证,要么是终端成本功能,要么是CLFs的限制。在CFF的制约上引入了放松技术的变数变量,以解决可行性和安全之间的权衡,以便提高它们之间的平衡。在理论上分析与现有方法相比,拟议配方的可行性和安全的优点,并以数字结果加以验证。