Safety Embedded Differential Dynamic Programming using Discrete Barrier States

Certified safe control is a growing challenge in robotics, especially when performance and safety objectives must be concurrently achieved. In this work, we extend the barrier state (BaS) concept, recently proposed for safe stabilization of continuous time systems, to safety-embedded trajectory optimization for discrete time systems using discrete barrier states (DBaS). The constructed DBaS is embedded into the discrete model of the safety-critical system integrating safety objectives into systems dynamics and performance objectives. Thereby, the control policy is now a function of the barrier state which directly supplies the controller with local information not available otherwise. This allows us to employ the DBaS with differential dynamic programming (DDP) to plan and execute safe optimal trajectories. The proposed algorithm is leveraged on various safety-critical control and planning problems including a differential wheeled robot safe navigation in complex environments and on a quadrotor to safely perform reaching and tracking tasks. The DBaS-based DDP (DBaS-DDP) is shown to consistently outperform penalty methods commonly used in constrained DDP problems.