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Reachability analysis is at the core of many applications, from neural network verification, to safe trajectory planning of uncertain systems. However, this problem is notoriously challenging, and current approaches tend to be either too…
In this paper, we address the problem of scheduling a set of robots to complete tasks in a laboratory environment, modelled as a graph, while avoiding collisions. We analyze the dynamic programming algorithm (PA) introduced in…
Neural Networks (NNs) can provide major empirical performance improvements for closed-loop systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating…
We present a new and more efficient technique for computing the route that maximizes the probability of on-time arrival in stochastic networks, also known as the path-based stochastic on-time arrival (SOTA) problem. Our primary contribution…
Intelligent interaction with the real world requires robotic agents to jointly reason over high-level plans and low-level controls. Task and motion planning (TAMP) addresses this by combining symbolic planning and continuous trajectory…
Reachability analysis of hybrid systems has been used as a safety verification tool to assess offline whether the state of a system is capable of remaining within a designated safe region for a given time horizon. Although it has been…
This paper investigates Path planning Among Movable Obstacles (PAMO), which seeks a minimum cost collision-free path among static obstacles from start to goal while allowing the robot to push away movable obstacles (i.e., objects) along its…
This article introduces a numerical algorithm that serves as a preliminary step toward solving continuous-time model predictive control (MPC) problems directly without explicit time-discretization. The chief ingredients of the underlying…
Path-following algorithms are frequently used in composite optimization problems where a series of subproblems, with varying regularization hyperparameters, are solved sequentially. By reusing the previous solutions as initialization,…
Range-only (RO) pose estimation involves determining a robot's pose over time by measuring the distance between multiple devices on the robot, known as tags, and devices installed in the environment, known as anchors. The nonconvex nature…
In this paper, we consider the Constant-cost Orienteering Problem (COP) where a robot, constrained by a limited travel budget, aims at selecting a path with the largest reward in an aisle-graph. The aisle-graph consists of a set of loosely…
The shortest path problem in graphs is fundamental to AI. Nearly all variants of the problem and relevant algorithms that solve them ignore edge-weight computation time and its common relation to weight uncertainty. This implies that taking…
This paper presents an optimisation-based approach for an obstacle avoidance problem within an autonomous vehicle racing context. Our control regime leverages online reachability analysis and sensor data to compute the maximal safe…
Reachability questions are one of the most fundamental algorithmic primitives in temporal graphs -- graphs whose edge set changes over discrete time steps. A core problem here is the NP-hard Short Restless Temporal Path: given a temporal…
Robots often need to solve path planning problems where essential and discrete aspects of the environment are partially observable. This introduces a multi-modality, where the robot must be able to observe and infer the state of its…
Task and motion planning (TAMP) for multi-robot systems, which integrates discrete task planning with continuous motion planning, remains a challenging problem in robotics. Existing TAMP approaches often struggle to scale effectively for…
Gradient-based trajectory optimization (GTO) has gained wide popularity for quadrotor trajectory replanning. However, it suffers from local minima, which is not only fatal to safety but also unfavorable for smooth navigation. In this paper,…
Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the…
Task And Motion Planning (TAMP) is the problem of finding a solution to an automated planning problem that includes discrete actions executable by low-level continuous motions. This field is gaining increasing interest within the robotics…
This paper presents a unified optimization-based path planning approach to efficiently compute locally optimal solutions to advanced path planning problems. The approach is motivated by first showing that a lattice-based path planner can be…