Learning Safety-Guaranteed, Non-Greedy Control Barrier Functions Using Reinforcement Learning
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Australian Centre for Robotics, The University of Sydney（悉尼大学澳大利亚机器人中心）；University of Auckland（奥克兰大学）
Minduli Wijayatunga, Nathan Wallace, Salah Sukkarieh, Roberto Armellin
Spacecraft rendezvous and proximity operations (RPO) pose safety risks to high-value assets, so formal safety guarantees are critical. Yet conservative safety controllers can reduce mission efficiency. We propose a unified two-stage reinforcement learning (RL) framework that addresses two complementary limitations of Input-Constrained Control Barrier Functions (ICCBFs) for safety-critical, fuel-limited spacecraft control. Given a certified safe set S, ICCBFs guarantee forward invariance of an inner set C* under input bounds, but the resulting per-step quadratic programme (QP) is greedy and fuel-inefficient within C*, and recoverable states outside C* are conservatively discarded. Stage 1 learns state-dependent class-K-infinity parameters that adapt ICCBF/CLF decay rates, embedding long-horizon cost awareness while preserving invariance in C*. Stage 2 learns a residual barrier h_RL(x) that certifies recoverability for a subset of S minus C*. At run time, the controller selects the appropriate barrier formulation (Stage 1 or Stage 2) and solves a lightweight ZOH QP. Both stages are trained with PPO using rewards that penalise constraint violations, control effort, and task metrics. We evaluate three benchmarks: cruise control, spacecraft rendezvous with a rotating target, and inspection that maximises observability subject to keep-in and keep-out zone constraints. Across test cases, the method reduces median fuel relative to ICCBF baselines by 12 to 25 percent and increases the fraction of trajectories that remain in S by 7 to 8 percent, while retaining real-time QP complexity.
In this paper, we will develop a systematic approach to deriving guaranteed bounds for approximate dynamic programming (ADP) schemes in optimal control problems. Our approach is inspired by our recent results on bounding the performance of greedy strategies in optimization of string-submodular functions over a finite horizon. The approach is to derive a string-submodular optimization problem, for which the optimal strategy is the optimal control solution and the greedy strategy is the ADP solution. Using this approach, we show that any ADP solution achieves a performance that is at least a fac…
This paper presents a strategy for control of a spacecraft docking with a non-maneuvering target in the presence of safety constraints and bounded disturbances. The presence of disturbances prevents convergence to a unique docking state, so in our formulation, docking is defined as occurring within a set constructed using prescribed tolerances. Safety is ensured via application of Robust Control Barrier Functions to render a designated safe set forward invariant for any allowable disturbance. However, this safety strategy necessarily presumes a worst-case disturbance, and thus restricts trajec…
This paper studies the general problem of operating energy storage under uncertainty. Two fundamental sources of uncertainty are considered, namely the uncertainty in the unexpected fluctuation of the net demand process and the uncertainty in the locational marginal prices. We propose a very simple algorithm termed Online Modified Greedy (OMG) algorithm for this problem. A stylized analysis for the algorithm is performed, which shows that comparing to the optimal cost of the corresponding stochastic control problem, the sub-optimality of OMG is bounded and approaches zero in various scenarios.…
This paper aims at the safety-critical control synthesis of network systems such that the satisfaction of the safety constraints can be guaranteed. To handle the large state dimension of such systems, an assume-guarantee contract is used to break the large synthesis problem into smaller subproblems. Parameterized signal temporal logic (pSTL) is used to formally describe the behaviors of the subsystems, which we use as the template for the contract. We show that robust control invariant sets (RCIs) for the subsystems can be composed to form a robust control invariant set for the whole network s…
Min-max optimization of an objective function $f: \mathbb{R}^d \times \mathbb{R}^d \rightarrow \mathbb{R}$ is an important model for robustness in an adversarial setting, with applications to many areas including optimization, economics, and deep learning. In many applications $f$ may be nonconvex-nonconcave, and finding a global min-max point may be computationally intractable. There is a long line of work that seeks computationally tractable algorithms for alternatives to the min-max optimization model. However, many of the alternative models have solution points which are only guaranteed to…
This paper proposes an optimization with penalty-based feedback design framework for safe stabilization of control affine systems. Our starting point is the availability of a control Lyapunov function (CLF) and a control barrier function (CBF) defining affine-in-the-input inequalities that certify, respectively, the stability and safety objectives for the dynamics. Leveraging ideas from penalty methods for constrained optimization, the proposed design framework imposes one of the inequalities as a hard constraint and the other one as a soft constraint. We study the properties of the closed-loo…
Multi-agent partially observable Markov decision processes (MPOMDPs) provide a framework to represent heterogeneous autonomous agents subject to uncertainty and partial observation. In this paper, given a nominal policy provided by a human operator or a conventional planning method, we propose a technique based on barrier functions to design a minimally interfering safety-shield ensuring satisfaction of high-level specifications in terms of linear distribution temporal logic (LDTL). To this end, we use sufficient and necessary conditions for the invariance of a given set based on discrete-time…
It has been shown that satisfying state and control constraints while optimizing quadratic costs subject to desired (sets of) state convergence for affine control systems can be reduced to a sequence of quadratic programs (QPs) by using Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). One of the main challenges in this approach is ensuring the feasibility of these QPs, especially under tight control bounds and safety constraints of high relative degree. In this paper, we provide sufficient conditions for guranteed feasibility. The sufficient conditions are captured by a …
Polytope Volume Monitoring Problem: Formulation and Solution via Parametric Linear Program Based Control Barrier Function
Institute of Robotics and Automatic Information System, College of Artificial Intelligence, Nankai University（机器人与自动化信息系统研究所，人工智能学院，南开大学）；Institute of Intelligence Technology and Robotic Systems, Shenzhen Research Institute of Nankai University（智能技术与机器人系统研究所，南开大学深圳研究院）；Key Laboratory of Intelligent Control and Optimization for Industrial Equipment of Ministry of Education, Dalian University of Technology（教育部智能控制与工业设备优化重点实验室，大连理工大学）
