Certified safe control is a growing challenge in robotics, especially when performance and safety objectives are desired to be concurrently achieved. In this work, we extend the barrier state (BaS) concept, recently proposed for stabilization of continuous time systems, to enforce safety for discrete time systems by creating a discrete barrier state (DBaS). The constructed DBaS is embedded into the discrete model of the safety-critical system in order to integrate safety objectives into performance objectives. We subsequently use the proposed technique to implement a safety embedded stabilizing control for nonlinear discrete systems. Furthermore, we employ the DBaS method to develop a safety embedded differential dynamic programming (DDP) technique to plan and execute safe optimal trajectories. The proposed algorithm is leveraged on a differential wheeled robot and on a quadrotor to safely perform several tasks including reaching, tracking and safe multi-quadrotor movement. The DBaS-based DDP (DBaS-DDP) is compared to the penalty method used in constrained DDP problems where it is shown that the DBaS-DDP consistently outperforms the penalty method.
翻译:在这项工作中,我们推广了最近为稳定连续时间系统而提出的屏障状态(BAS)概念,以便通过创建离散屏障状态(DBAS)强制实施离散时间系统的安全性。建造的DBAS已嵌入安全关键系统离散模式,以便将安全目标纳入绩效目标。我们随后使用拟议的技术对非线性离散系统实施安全嵌入稳定控制。此外,我们采用DBAS方法,开发安全嵌入差分动态程序(DDP)技术,以规划和执行安全的最佳轨迹。提议的算法被用在差轮机器人上和孔托上,以安全地执行若干任务,包括达到、跟踪和安全多管轨道移动。基于DBAS的DDP(DBAS-DDP)与在限制DDP问题中使用的惩罚方法相比较,在那里显示DBAS-DDP(DDP)持续超过惩罚方法。