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We present a novel framework for solving optimal transport (OT) problems based on the Hamilton--Jacobi (HJ) equation, whose viscosity solution uniquely characterizes the OT map. By leveraging the method of characteristics, we derive…
Autonomous highway driving involves high-speed safety risks due to limited reaction time, where rare but dangerous events may lead to severe consequences. This places stringent requirements on trajectory planning in terms of both…
When learning to act in a stochastic, partially observable environment, an intelligent agent should be prepared to anticipate a change in its belief of the environment state, and be capable of adapting its actions on-the-fly to changing…
This paper introduces a novel methodology that leverages the Hamilton-Jacobi solution to enhance non-linear model predictive control (MPC) in scenarios affected by navigational uncertainty. Using Hamilton-Jacobi-Theoretic approach, a…
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…
Provably safe and scalable multi-vehicle path planning is an important and urgent problem due to the expected increase of automation in civilian airspace in the near future. Hamilton-Jacobi (HJ) reachability is an ideal tool for analyzing…
Hamilton-Jacobi reachability (HJR) provides a value function that encodes the set of states from which a system with bounded control inputs can reach or avoid a target despite any bounded disturbance, and the corresponding robust, optimal…
Neural network (NN) dynamics models and control policies achieve strong performance in robotics, but providing sound guarantees under uncertainty remains difficult, especially for closed-loop NN systems. Existing reachability tools provide…
Autonomous systems operating in close proximity with each other to cover a specified area has many potential applications, but to achieve effective coordination, two key challenges need to be addressed: coordination and safety. For…
Control Barrier Functions (CBFs) are a powerful tool for ensuring robotic safety, but designing or learning valid CBFs for complex systems is a significant challenge. While Hamilton-Jacobi Reachability provides a formal method for…
Autonomous navigation in partially observable environments requires agents to reason beyond immediate sensor input, exploit occlusion, and ensure safety while progressing toward a goal. These challenges arise in many robotics domains, from…
Recent advances in machine learning technologies and sensing have paved the way for the belief that safe, accessible, and convenient autonomous vehicles may be realized in the near future. Despite tremendous advances within this context,…
Continuum robots are well suited for navigating confined and fragile environments, such as vascular or endoluminal anatomy, where contact with surrounding structures is often unavoidable. While controlled contact can assist motion,…
We describe a task and motion planning architecture for highly dynamic systems that combines a domain-independent sampling-based deliberative planning algorithm with a global reactive planner. We leverage the recent development of a…
We investigate methods to provide safety assurances for autonomous agents that incorporate predictions of other, uncontrolled agents' behavior into their own trajectory planning. Given a learning-based forecasting model that predicts…
The framework of deep operator network (DeepONet) has been widely exploited thanks to its capability of solving high dimensional partial differential equations. In this paper, we incorporate DeepONet with a recently developed policy…
Ensuring safe driving while maintaining travel efficiency for autonomous vehicles in dynamic and occluded environments is a critical challenge. This paper proposes an occlusion-aware contingency safety-critical planning approach for…
This paper presents a novel contingency planning framework that integrates learning-based multi-modal predictions of traffic participants into Branch Model Predictive Control (MPC). Leveraging reachability analysis, we address the…
Fast and Safe Tracking (FaSTrack) is a modular framework that provides safety guarantees while planning and executing trajectories in real time via value functions of Hamilton-Jacobi (HJ) reachability. These value functions are computed…
Contingency planning is the architectural capability that enables autonomous vehicles (AVs) to anticipate and mitigate discrete, high-impact hazards, such as sensor outages and adversarial interactions. This paper presents a comprehensive…