Wasserstein Distributionally Robust Control Barrier Function using Conditional Value-at-Risk with Differentiable Convex Programming

Control Barrier functions (CBFs) have attracted extensive attention for designing safe controllers for their deployment in real-world safety-critical systems. However, the perception of the surrounding environment is often subject to stochasticity and further distributional shift from the nominal one. In this paper, we present distributional robust CBF (DR-CBF) to achieve resilience under distributional shift while keeping the advantages of CBF, such as computational efficacy and forward invariance. To achieve this goal, we first propose a single-level convex reformulation to estimate the conditional value at risk (CVaR) of the safety constraints under distributional shift measured by a Wasserstein metric, which is by nature tri-level programming. Moreover, to construct a control barrier condition to enforce the forward invariance of the CVaR, the technique of differentiable convex programming is applied to enable differentiation through the optimization layer of CVaR estimation. We also provide an approximate variant of DR-CBF for higher-order systems. Simulation results are presented to validate the chance-constrained safety guarantee under the distributional shift in both first and second-order systems

Recent Advances in Path Integral Control for Trajectory Optimization: An Overview in Theoretical and Algorithmic Perspectives

This paper presents a tutorial overview of path integral (PI) control approaches for stochastic optimal control and trajectory optimization. We concisely summarize the theoretical development of path integral control to compute a solution for stochastic optimal control and provide algorithmic descriptions of the cross-entropy (CE) method, an open-loop controller using the receding horizon scheme known as the model predictive path integral (MPPI), and a parameterized state feedback controller based on the path integral control theory. We discuss policy search methods based on path integral control, efficient and stable sampling strategies, extensions to multi-agent decision-making, and MPPI for the trajectory optimization on manifolds. For tutorial demonstrations, some PI-based controllers are implemented in MATLAB and ROS2/Gazebo simulations for trajectory optimization. The simulation frameworks and source codes are publicly available at https://github.com/INHA-Autonomous-Systems-Laboratory-ASL/An-Overview-on-Recent-Advances-in-Path-Integral-Control.Comment: 16 pages, 9 figure

Verification and Synthesis of Robust Control Barrier Functions: Multilevel Polynomial Optimization and Semidefinite Relaxation

We study the problem of verification and synthesis of robust control barrier functions (CBF) for control-affine polynomial systems with bounded additive uncertainty and convex polynomial constraints on the control. We first formulate robust CBF verification and synthesis as multilevel polynomial optimization problems (POP), where verification optimizes -- in three levels -- the uncertainty, control, and state, while synthesis additionally optimizes the parameter of a chosen parametric CBF candidate. We then show that, by invoking the KKT conditions of the inner optimizations over uncertainty and control, the verification problem can be simplified as a single-level POP and the synthesis problem reduces to a min-max POP. This reduction leads to multilevel semidefinite relaxations. For the verification problem, we apply Lasserre's hierarchy of moment relaxations. For the synthesis problem, we draw connections to existing relaxation techniques for robust min-max POP, which first use sum-of-squares programming to find increasingly tight polynomial lower bounds to the unknown value function of the verification POP, and then call Lasserre's hierarchy again to maximize the lower bounds. Both semidefinite relaxations guarantee asymptotic global convergence to optimality. We provide an in-depth study of our framework on the controlled Van der Pol Oscillator, both with and without additive uncertainty.Comment: Accepted to IEEE Conference on Decision and Control (CDC) 202

A Survey on Global LiDAR Localization

Knowledge about the own pose is key for all mobile robot applications. Thus pose estimation is part of the core functionalities of mobile robots. In the last two decades, LiDAR scanners have become a standard sensor for robot localization and mapping. This article surveys recent progress and advances in LiDAR-based global localization. We start with the problem formulation and explore the application scope. We then present the methodology review covering various global localization topics, such as maps, descriptor extraction, and consistency checks. The contents are organized under three themes. The first is the combination of global place retrieval and local pose estimation. Then the second theme is upgrading single-shot measurement to sequential ones for sequential global localization. The third theme is extending single-robot global localization to cross-robot localization on multi-robot systems. We end this survey with a discussion of open challenges and promising directions on global lidar localization

Towards a Theory of Control Architecture: A quantitative framework for layered multi-rate control

This paper focuses on the need for a rigorous theory of layered control architectures (LCAs) for complex engineered and natural systems, such as power systems, communication networks, autonomous robotics, bacteria, and human sensorimotor control. All deliver extraordinary capabilities, but they lack a coherent theory of analysis and design, partly due to the diverse domains across which LCAs can be found. In contrast, there is a core universal set of control concepts and theory that applies very broadly and accommodates necessary domain-specific specializations. However, control methods are typically used only to design algorithms in components within a larger system designed by others, typically with minimal or no theory. This points towards a need for natural but large extensions of robust performance from control to the full decision and control stack. It is encouraging that the successes of extant architectures from bacteria to the Internet are due to strikingly universal mechanisms and design patterns. This is largely due to convergent evolution by natural selection and not intelligent design, particularly when compared with the sophisticated design of components. Our aim here is to describe the universals of architecture and sketch tentative paths towards a useful design theory.Comment: Submitted to IEEE Control Systems Magazin