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Sylvia Herbert - IEEE Xplore Author Profile

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Control Lyapunov functions (CLFs) play a vital role in modern control applications, but finding them remains a problem. Recently, the control Lyapunov-value function (CLVF) and robust CLVF have been proposed as solutions for nonlinear time-invariant systems with bounded control and disturbance. However, the CLVF suffers from the “curse of dimensionality”, which hinders its application to practical...Show More
Hamilton-Jacobi Reachability (HJR) is a popular method for analyzing the liveness and safety of a dynamical system with bounded control and disturbance. The corresponding HJ value function offers a robust controller and characterizes the reachable sets, but is traditionally solved with Dynamic Programming (DP) and limited to systems of dimension less than six. Recently, the space-parallelizeable, ...Show More
Safe value functions, such as control barrier functions, characterize a safe set and synthesize a safety filter, overriding unsafe actions, for a dynamic system. While function approximators like neural networks can synthesize approximately safe value functions, they typically lack formal guarantees. In this paper, we propose a local dynamic programming-based approach to “patch” approximately safe...Show More
Inaccurate tool localization is one of the main reasons for failures in automating surgical tasks. Imprecise robot kinematics and noisy observations caused by the poor visual acuity of an endoscopic camera make tool tracking challenging. Previous works in surgical automation adopt environment-specific setups or hard-coded strategies instead of explicitly considering motion and observation uncertai...Show More
The ability to predict future states is crucial to informed decision-making while interacting with dynamic environments. With cameras providing a prevalent and information-rich sensing modality, the problem of predicting future states from image sequences has garnered a lot of attention. Current state-of-the-art methods typically train large parametric models for their predictions. Though often ab...Show More
This paper presents an algorithm to apply nonlinear control design approaches to the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state access and, often, relative degree one. We propose a control design approach that initially generates a control policy for nonlinear deterministic models with full...Show More
Recent literature has proposed approaches that learn control policies with high performance while maintaining safety guarantees. Synthesizing Hamilton-Jacobi (HJ) reachable sets has become an effective tool for verifying safety and supervising the training of reinforcement learning-based control policies for complex, high-dimensional systems. Previously, HJ reachability was restricted to verifying...Show More
Real-time navigation in a priori unknown environment remains a challenging task, especially when an unexpected (unmodeled) disturbance occurs. In this letter, we propose the framework Safe Returning Fast and Safe Tracking (SR-F) that merges concepts from 1) Robust Control Lyapunov-Value Functions (R-CLVF) 1, and 2) the Fast and Safe Tracking (FaSTrack) framework 2. The SR-F computes an R-CLVF offl...Show More
Hamilton-Jacobi reachability analysis is a useful tool for generating reachable sets and corresponding optimal control policies, but its use in high-dimensional systems is hindered by the “curse of dimensionality.” Self-contained subsystem decomposition is a proposed solution, but it can produce conservative or incorrect results due to the “leaking corner issue.” This issue arises from the inexact...Show More
Large offline learning-based models have enabled robots to successfully interact with objects for a wide variety of tasks. However, these models rely on fairly consistent structured environments. For more unstructured environments, an online learning component is necessary to gather and estimate information about objects in the environment in order to successfully interact with them. Unfortunately...Show More
In this letter, we seek to build connections between control Lyapunov functions (CLFs) and Hamilton-Jacobi (HJ) reachability analysis. CLFs have been used extensively in the control community for synthesizing stabilizing feedback controllers. However, there is no systematic way to construct CLFs for general nonlinear systems and the problem can become more complex with input constraints. HJ reacha...Show More
Safety filters based on Control Barrier Functions (CBFs) have emerged as a practical tool for the safety-critical control of autonomous systems. These approaches encode safety through a value function and enforce safety by imposing a constraint on the time derivative of this value function. How-ever, synthesizing a valid CBF that is not overly conservative in the presence of input constraints is a...Show More
This paper works towards unifying two popular approaches in the safety control community: Hamilton-Jacobi (HJ) reachability and Control Barrier Functions (CBFs). HJ Reachability has methods for direct construction of value functions that provide safety guarantees and safe controllers, however the online implementation can be overly conservative and/or rely on chattering bang-bang control. The CBF ...Show More
Autonomous systems like aircraft and assistive robots often operate in scenarios where guaranteeing safety is critical. Methods like Hamilton-Jacobi reachability can provide guaranteed safe sets and controllers for such systems. However, often these same scenarios have unknown or uncertain environments, system dynamics, or predictions of other agents. As the system is operating, it may learn new k...Show More
Real-time, guaranteed safe trajectory planning is vital for navigation in unknown environments. However, real-time navigation algorithms typically sacrifice robustness for computation speed. Alternatively, provably safe trajectory planning tends to be too computationally intensive for real-time replanning. We propose FaSTrack, Fast and Safe Tracking, a framework that achieves both real-time replan...Show More
Learning-based control schemes that can preserve safety without overly constricting the learning process are beneficial to ensure safe operation while a robotic system is learning about its environment and to enable the system to update safety guarantees as it obtains new information. A previously developed safe learning control scheme was successful in utilizing reachability analysis to enable a ...Show More
Hamilton-Jacobi-Isaacs (HJI) reachability analysis is a powerful tool for analyzing the safety of autonomous systems. This analysis is computationally intensive and typically performed offline. Online, however, the autonomous system may experience changes in system dynamics, external disturbances, and/or the surrounding environment, requiring updated safety guarantees. Rather than restarting the s...Show More
Hamilton-Jacobi (HJ) reachability analysis has been developed over the past decades into a widely-applicable tool for determining goal satisfaction and safety verification in nonlinear systems. While HJ reachability can be formulated very generally, computational complexity can be a serious impediment for many systems of practical interest. Much prior work has been devoted to computing approximate...Show More
Robust motion planning is a well-studied problem in the robotics literature, yet current algorithms struggle to operate scalably and safely in the presence of other moving agents, such as humans. This paper introduces a novel framework for robot navigation that accounts for high-order system dynamics and maintains safety in the presence of external disturbances, other robots, and humans. Our appro...Show More
Motion planning is an extremely well-studied problem in the robotics community, yet existing work largely falls into one of two categories: computationally efficient but with few if any safety guarantees, or able to give stronger guarantees but at high computational cost. This work builds on a recent development called FaSTrack in which a slow offline computation provides a modular safety guarante...Show More
Reachability analysis provides formal guarantees for performance and safety properties of nonlinear control systems. Here, one aims to compute the backward reachable set (BRS) or tube (BRT)-the set of states from which the system can be driven into a target set at a particular time or within a time interval, respectively. The computational complexity of current approaches scales poorly, making app...Show More
Hamilton-Jacobi (HJ) reachability analysis is an important formal verification method for guaranteeing performance and safety properties of dynamical systems; it has been applied to many small-scale systems in the past decade. Its advantages include compatibility with general nonlinear system dynamics, formal treatment of bounded disturbances, and the availability of well-developed numerical tools...Show More
Fast and safe navigation of dynamical systems through a priori unknown cluttered environments is vital to many applications of autonomous systems. However, trajectory planning for autonomous systems is computationally intensive, often requiring simplified dynamics that sacrifice safety and dynamic feasibility in order to plan efficiently. Conversely, safe trajectories can be computed using more so...Show More
Hamilton-Jacobi (HJ) reachability is a method that provides rigorous analyses of the safety properties of dynamical systems. These guarantees can be provided by the computation of a backward reachable set (BRS), which represents the set of states from which the system may be driven into violating safety properties despite the system's best effort to remain safe. Unfortunately, the complexity of th...Show More
With the recent surge of interest in using robotics and automation for civil purposes, providing safety and performance guarantees has become extremely important. In the past, differential games have been successfully used for the analysis of safety-critical systems. In particular, the Hamilton-Jacobi (HJ) formulation of differential games provides a flexible way to compute the reachable set, whic...Show More