A fundamental maneuver in autonomous space operations is known as rendezvous, where a spacecraft navigates to and approaches another spacecraft. In this case study, we present linear and nonlinear benchmark models of an active chaser spacecraft performing rendezvous toward a passive, orbiting target. The system is modeled as a hybrid automaton, where the chaser must adhere to different sets of constraints in each discrete mode. A switched LQR controller is designed accordingly to meet this collection of physical and geometric safety constraints, while maintaining liveness in navigating toward the target spacecraft. We extend this benchmark problem to check for passive safety, which is collision avoidance along a passive, propulsion-free trajectory that may be followed in the event of system failures. We show that existing hybrid verification tools like SpaceEx, C2E2, and our own implementation of a simulation-driven verification tool can robustly verify this system with respect to the requirements, and a variety of relevant initial conditions.
Convex MPC and Thrust Allocation with Deadband for Spacecraft Rendezvous
Instituto Superior Técnico（高等技术学院）；University of Lisbon（里斯本大学）；Institute for Systems and Robotics（系统与机器人研究所）；School of Science and Technology from the NOVA University of Lisbon（里斯本新大学科学与技术学院）；Lusófona University（卢索福纳大学）；GMV（GMV公司）
Lightweight Model Predictive Control for Spacecraft Rendezvous Attitude Synchronization
Space Applications Group, e:fs TechHub GmbH（e:fs技术中心空间应用组）；Faculty of Electrical Engineering and Information Technology, Ingolstadt University of Applied Sciences（应用科学大学英戈尔施塔特电气工程与信息技术学院）
Imitation learning-based spacecraft rendezvous and docking method with Expert Demonstration
Department of Control Science and Engineering, Harbin Institute of Technology（控制科学与工程系，哈尔滨工业大学）；Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong（机械与自动化工程系，香港中文大学）
Certifiable Explicit Model Predictive Control for Spacecraft Rendezvous under Bounded Disturbances
NOVA University of Lisbon（诺瓦大学）；Center for Technology and Systems (CTS)（技术与系统中心）；Institute for Systems and Robotics, Instituto Superior Técnico, University of Lisbon（里斯本大学高等技术学院系统与机器人研究所）
Geometric Conditions for Lossless Convexification in Linear Optimal Control with Discrete-Valued Inputs: Real-Time Implementation for Spacecraft Rendezvous
Formally Verifying Deep Reinforcement Learning Controllers with Lyapunov Barrier Certificates
Stanford University（斯坦福大学）；The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；IT University of Copenhagen（哥本哈根信息技术大学）；Google（谷歌公司）；GE Aerospace Research（GE航空航天研究院）
