Safety Embedded Differential Dynamic Programming Using Discrete Barrier States

TL;DR

This paper introduces a novel safety-embedded trajectory optimization method using discrete barrier states integrated into differential dynamic programming, enabling safe control in robotics applications like navigation and quadrotor tasks.

Contribution

It extends the barrier state concept to discrete systems and embeds safety directly into the system dynamics for improved safe trajectory planning.

Findings

DBaS-DDP outperforms penalty methods in safety-critical tasks.

The approach ensures safety without sacrificing performance.

Validated on robotic navigation and quadrotor control scenarios.

Abstract

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.