Safety Embedded Differential Dynamic Programming Using Discrete Barrier States
This work addresses safety-critical control problems in robotics, offering a novel approach for integrating safety into trajectory optimization, though it is incremental as it builds on existing barrier state methods.
The paper tackles the challenge of certified safe control in robotics by extending the barrier state concept to discrete time systems, proposing discrete barrier states (DBaS) embedded into differential dynamic programming (DBaS-DDP) for safe optimal trajectory planning. The method consistently outperforms penalty methods and control barrier function-based safety filters in tasks like robot navigation and quadrotor reaching/tracking.
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 the system's dynamics and performance objectives. Thereby, the control policy is directly supplied by safety-critical information through the barrier state. 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 randomized and 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 to approximate constrained DDP problems as well as CBF-based safety filters.