In this paper, we use the derivative of the exponential map to derive the exact evolution of the logarithm of the tracking error for mixed-invariant systems, a class of systems capable of describing rigid body tracking problems in Lie groups. Additionally, we design a log-linear dynamic inversion-based control law to remove the nonlinearities due to spatial curvature and enhance the robustness of the controller. We apply Linear Matrix Inequalities (LMIs) to bound the tracking error given a bounded disturbance amplified by the distortion matrix and leverage the tracking error bound to create flow pipes. To demonstrate the usefulness of our method, we show its application with Urban Air Mobility (UAM) scenarios using a simplified kinematic aircraft model and polynomial-based path planning methods.
Towards provable probabilistic safety for scalable embodied AI systems
Department of Automation, Tsinghua University（清华大学自动化系）；Beijing Academy of Artificial Intelligence（北京人工智能研究院）；School of Intelligence Science and Technology, Peking University（北京大学智能科学与技术学院）；School of Computer, Liaocheng University（聊城大学计算机学院）；Department of Automation, Southeast University（东南大学自动化学院）；Department of Mechanical and Aerospace Engineering, George Washington University（乔治华盛顿大学机械与航空航天工程系）；University of Michigan Transportation Research Institute（密歇根大学交通研究所）；Department of Civil and Environmental Engineering, University of Michigan（密歇根大学土木与环境工程系）
Contact-Aware Safety in Soft Robots Using High-Order Control Barrier and Lyapunov Functions
Laboratory for Information and Decision Systems, Massachusetts Institute of Technology（信息与决策系统实验室，麻省理工学院）；Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology（计算机科学与人工智能实验室，麻省理工学院）；Cognitive Robotics, Delft University of Technology（认知机器人学，代尔夫特理工大学）；Robotics Engineering Department, Worcester Polytechnic Institute（机器人工程系，沃斯特理工学院）
Fixed time convergence guarantees for Higher Order Control Barrier Functions
Department of Engineering Design, Indian Institute of Technology, Madras（工程设计系，印度理工学院，马德拉斯）；Center for Cyber-Physical Systems, Indian Institute of Science (IISc), Bengaluru（网络物理系统中心，印度科学研究院（IISc），班加罗尔）
