Improved Exploration for Safety-Embedded Differential Dynamic Programming Using Tolerant Barrier States

In this paper, we introduce Tolerant Discrete Barrier States (T-DBaS), a novel safety-embedding technique for trajectory optimization with enhanced exploratory capabilities. The proposed approach generalizes the standard discrete barrier state (DBaS) method by accommodating temporary constraint violation during the optimization process while still approximating its safety guarantees. Consequently, the proposed approach eliminates the DBaS's safe nominal trajectories assumption, while enhancing its exploration effectiveness for escaping local minima. Towards applying T-DBaS to safety-critical autonomous robotics, we combine it with Differential Dynamic Programming (DDP), leading to the proposed safe trajectory optimization method T-DBaS-DDP, which inherits the convergence and scalability properties of the solver. The effectiveness of the T-DBaS algorithm is verified on differential drive robot and quadrotor simulations. In addition, we compare against the classical DBaS-DDP as well as Augmented-Lagrangian DDP (AL-DDP) in extensive numerical comparisons that demonstrate the proposed method's competitive advantages. Finally, the applicability of the proposed approach is verified through hardware experiments on the Georgia Tech Robotarium platform.