Related papers: Optimal online escape path against a certificate
Time-optimal obstacle avoidance is a prevalent problem encountered in various fields, including robotics and autonomous vehicles, where the task involves determining a path for a moving vehicle to reach its goal while navigating around…
Many scientific and engineering applications feature nonsmooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the nonsmooth objective is equipped with…
We present a closed-form expression for the survival probability of a biased random walker to first reach a target site on a 1D lattice. The expression holds for any step number $N$ and is computationally faster than non-closed-form results…
We consider the problem of a particle traveling from an initial configuration to a final configuration (given by a point in the plane along with a prescribed velocity vector) in minimum time with non-homogeneous velocity and with…
The quantum walk dynamics obey the laws of quantum mechanics with an extra locality constraint, which demands that the evolution operator is local in the sense that the walker must visit the neighboring locations before endeavoring to…
In this paper, we address the trajectory planning problem in uncertain nonconvex static and dynamic environments that contain obstacles with probabilistic location, size, and geometry. To address this problem, we provide a risk bounded…
Suppose an unpredictable evader is free to move around in a polygonal environment of arbitrary complexity that is under full camera surveillance. How many pursuers, each with the same maximum speed as the evader, are necessary and…
Environmental contours are tools frequently used in the early design of marine structures. They provide a description of critical design conditions and serve as a means for simplifying expensive long-term response calculations. Here, we…
Uncertain dynamic obstacles, such as pedestrians or vehicles, pose a major challenge for optimal robot navigation with safety guarantees. Previous work on motion planning has followed two main strategies to provide a safe bound on an…
Autonomous exploration is a complex task where the robot moves through an unknown environment with the goal of mapping it. The desired output of such a process is a sequence of paths that efficiently and safely minimise the uncertainty of…
Motion planning in the presence of multiple dynamic obstacles is an important research problem from the perspective of autonomous vehicles as well as space-constrained multi-robot work environment. In this paper, we address the motion…
We present a novel algorithm that fuses the existing convex-programming based approach with heuristic information to find optimality guarantees and near-optimal paths for the Shortest Path Problem in the Graph of Convex Sets (SPP-GCS). Our…
Navigating our physical environment requires changing directions and turning. Despite its ecological importance, we do not have a unified theoretical account of non-straight-line human movement. Here, we present a unified optimality…
Collision avoidance in unknown obstacle-cluttered environments may not always be feasible. This paper focuses on an emerging paradigm shift in which potential collisions with the environment can be harnessed instead of being avoided…
We consider the problem of planning a collision-free path of a robot in the presence of risk zones. The robot is allowed to travel in these zones but is penalized in a super-linear fashion for consecutive accumulative time spent there. We…
A turn constrained vehicle is initially located inside a polygon region and desires to escape in minimum time. First, the method of characteristics is used to describe the time-optimal strategies for reaching a line of infinite length.…
Achieving long-term safety in uncertain/extreme environments while accounting for human preferences remains a fundamental challenge for autonomous systems. Existing methods often trade off long-term guarantees for fast real-time control and…
Motion planning seeks a collision-free path in a configuration space (C-space), representing all possible robot configurations in the environment. As it is challenging to construct a C-space explicitly for a high-dimensional robot, we…
The paper presents a novel sample-based algorithm, called C*, for real-time coverage path planning (CPP) of unknown environments. C* is built upon the concept of a Rapidly Covering Graph (RCG), which is incrementally constructed during…
A barrier certificate often serves as an inductive invariant that isolates an unsafe region from the reachable set of states, and hence is widely used in proving safety of hybrid systems possibly over an infinite time horizon. We present a…