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.

翻译：本文提出了一种名为容许离散障碍状态（T-DBaS）的新型安全嵌入技术，用于轨迹优化中增强探索能力。该方法通过允许优化过程中暂时违反约束条件，同时近似保持安全保证，推广了标准离散障碍状态（DBaS）方法。因此，该方法消除了DBaS对安全名义轨迹的依赖，同时提升了其逃离局部最优解的探索效率。为将T-DBaS应用于安全关键自主机器人领域，我们将其与差分动态规划（DDP）相结合，提出了安全轨迹优化方法T-DBaS-DDP，该方法继承了求解器的收敛性与可扩展性。通过差分驱动机器人和四旋翼无人机仿真验证了T-DBaS算法的有效性。此外，我们与经典DBaS-DDP及增广拉格朗日DDP（AL-DDP）进行了大量数值对比，证明了所提方法的竞争优势。最后，通过佐治亚理工学院Robotarium平台上的硬件实验验证了该方法的适用性。