In this paper we discuss the problem of planning safe paths amidst unpredictably moving obstacles in the plane. Given the initial positions and the maximal velocities of the moving obstacles, the regions that are possibly not collision-free are modeled by discs that grow over time. We present an approach to compute the shortest path between two points in the plane that avoids these growing disc...

This paper presents a novel randomized motion planner for robots that must achieve a specified goal under kinematic and/or dynamic motion constraints while avoiding collision with moving obstacles with known trajectories. The planner encodes the motion constraints on the robot with a control system and samples the robot’s state×time space by picking control inputs at random and integrating its ...

This work presents new methods and algorithms for tracking the shape and trajectory of moving reflecting obstacles with broken rays, or rays reflecting at an obstacle. While in tomography the focus of the reconstruction method is to recover the velocity structure of the domain, the shape and trajectory reconstruction procedure directly finds the shape and trajectory of the obstacle. The physica...

We study the uniqueness and accuracy of the numerical solution of the problem of reconstruction of the shape and trajectory of a reflecting obstacle moving in an inhomogeneous medium from travel times, start and end points, and initial angles of ultrasonic rays reflecting at the obstacle. The speed of sound in the domain when there is no obstacle present is known and provided as an input parame...

We present a novel approach to perform probabilistic collision detection between a high-DOF robot and high-DOF obstacles in dynamic, uncertain environments. In dynamic environments with a highDOF robot and moving obstacles, our approach efficiently computes accurate collision probability between the robot and obstacles with upper error bounds. Furthermore, we describe a prediction algorithm for...

An important problem that a navigating robot is facing in a crowded environment is that it can easily get blocked by moving humans and obstacles. In such cases, the robot becomes immobilized and not able to continue its movement towards its goal position until the moving obstacles and humans free its way. To avoid ever getting in such a situation, many researchers have tried to predict the moti...