Title: Gaussian Process Barrier States for Safe Trajectory Optimization and Control Show Chinese title

Title: 高斯过程障碍状态用于安全轨迹优化与控制

Abstract: This paper proposes embedded Gaussian Process Barrier States (GP-BaS), a methodology to safely control unmodeled dynamics of nonlinear system using Bayesian learning. Gaussian Processes (GPs) are used to model the dynamics of the safety-critical system, which is subsequently used in the GP-BaS model. We derive the barrier state dynamics utilizing the GP posterior, which is used to construct a safety embedded Gaussian process dynamical model (GPDM). We show that the safety-critical system can be controlled to remain inside the safe region as long as we can design a controller that renders the BaS-GPDM's trajectories bounded (or asymptotically stable). The proposed approach overcomes various limitations in early attempts at combining GPs with barrier functions due to the abstention of restrictive assumptions such as linearity of the system with respect to control, relative degree of the constraints and number or nature of constraints. This work is implemented on various examples for trajectory optimization and control including optimal stabilization of unstable linear system and safe trajectory optimization of a Dubins vehicle navigating through an obstacle course and on a quadrotor in an obstacle avoidance task using GP differentiable dynamic programming (GP-DDP). The proposed framework is capable of maintaining safe optimization and control of unmodeled dynamics and is purely data driven. Show Chinese abstract

Abstract: 本文提出了一种嵌入式高斯过程屏障状态（GP-BaS）方法，用于通过贝叶斯学习安全控制非线性系统的未建模动态。 高斯过程（GPs）被用来建模安全关键系统，随后用于GP-BaS模型中。 我们利用GPs后验推导出屏障状态动力学，用以构建一个嵌入安全性的高斯过程动态模型（GPDM）。 我们证明，只要能够设计出一种控制器，使BaS-GPDM的轨迹有界（或渐近稳定），就可以控制安全关键系统保持在安全区域内。 由于摒弃了诸如系统相对于控制的线性假设、约束相对次数以及约束数量或性质等限制性假设，所提出的方法克服了早期尝试结合GPs与屏障函数时的各种局限性。 这项工作在多个轨迹优化和控制示例上实现，包括不稳定线性系统的最优稳定化、穿越障碍物的Dubins车辆的安全轨迹优化，以及在避障任务中使用GP可微动态规划（GP-DDP）的四旋翼飞行器。 所提出的框架能够维持对未建模动态的安全优化和控制，并且完全是数据驱动的。