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This paper investigates the scheduling problem related to engaging a swarm of attacking drones with a single defensive turret. The defending turret must turn, with a limited slew rate, and remain facing a drone for a dwell time to eliminate it. The turret must eliminate all the drones in the swarm before any drone reaches the turret. In 2D, this is an example of a Traveling Salesman Problem with Time Windows (TSPTW) where the turret must visit each target during the window. In 2D, the targets and turret are restricted to a plane and the turret rotates with one degree of freedom. In 3D, the turret can pan and tilt, while the drones attempt to reach a safe zone anywhere along the vertical axis above the turret. This 3D movement makes the problem more challenging, since the azimuth angles of the turret to the drones vary as a function of time. This paper investigates the theoretical optimal solution for simple swarm configurations. It compares heuristic approaches for the path scheduling problem in 2D and 3D using a simulation of the swarm behavior. It provides results for an improved heuristic approach, the Threat-Aware Nearest Neighbor. 

This paper investigates the pursuit-evasion problem of a defensive gun turret and one or more attacking drones. The turret must "visit" each attacking drone once, as quickly as possible, to defeat the threat. This constitutes a Shortest Hamiltonian Path (SHP) through the drones. The investigation considers situations with increasing fidelity, starting with a 2D kinematic model and progressing to a 3D dynamic model. In 2D we determine the region from which one or more drones can always reach a turret, or the region close enough to it where they can evade the turret. This provides optimal starting angles for n drones around a turret and the maximum starting radius for one and two drones.We show that safety regions also exist in 3D and provide a controller so that a drone in this region can evade the pan-tilt turret. Through simulations we explore the maximum range n drones can start and still have at least one reach the turret, and analyze the effect of turret behavior and the drones’ number, starting configuration, and behaviors. 

This paper examines a family of designs for magnetic cubes and counts how many configurations are possible for each design as a function of the number of modules. Magnetic modular cubes are cubes with magnets arranged on their faces. The magnets are positioned so that each face has either magnetic south or north pole outward. Moreover, we require that the net magnetic moment of the cube passes through the center of opposing faces. These magnetic arrangements enable coupling when cube faces with opposite polarity are brought in close proximity and enable moving the cubes by controlling the orientation of a global magnetic field. This paper investigates the 2D and 3D shapes that can be constructed by magnetic modular cubes, and describes all possible magnet arrangements that obey these rules. We select ten magnetic arrangements and assign a "color" to each of them for ease of visualization and reference. We provide a method to enumerate the number of unique polyominoes and polycubes that can be constructed from a given set of colored cubes. We use this method to enumerate all arrangements for up to 20 modules in 2D and 16 modules in 3D. We provide a motion planner for 2D assembly and through simulations compare which arrangements require fewer movements to generate and which arrangements are more common. Hardware demonstrations explore the self-assembly and disassembly of these modules in 2D and 3D. 

Quadcopters are increasingly popular for robotics applications. Being able to efficiently calculate the set of positions reachable by a quadcopter within a time budget enables collision avoidance and pursuit-evasion strategies.This paper examines the set of positions reachable by a quadcopter within a specified time limit using a simplified 2D model for quadcopter dynamics. This popular model is used to determine the set of candidate optimal control sequences to build the full 3D reachable set. We calculate the analytic equations that exactly bound the set of positions reachable in a given time horizon for all initial conditions. To further increase calculation speed, we use these equations to derive tight upper and lower spherical bounds on the reachable set. 

It is now possible to deploy swarms of drones with populations in the thousands. There is growing interest in using such swarms for defense, and it has been natural to program them with bio-mimetic motion models such as flocking or swarming. However, these motion models evolved to survive against predators, not enemies with modern firearms. This paper presents experimental data that compares the survivability of several motion models for large numbers of drones. This project tests drone swarms in Virtual Reality (VR), because it is prohibitively expensive, technically complex, and potentially dangerous to fly a large swarm of drones in a testing environment. We model the behavior of drone swarms flying along parametric paths in both tight and scattered formations. We add random motion to the general motion plan to confound path prediction and targeting. We describe an implementation of these flight paths as game levels in a VR environment. We then allow players to shoot at the drones and evaluate the difference between flocking and swarming behavior on drone survivability. 

We consider recognition and reconfiguration of lattice-based cellular structures by very simple robots with only basic functionality. The underlying motivation is the construction and modification of space facilities of enormous dimensions, where the combination of new materials with extremely simple robots promises structures of previously unthinkable size and flexibility; this is also closely related to the newly emerging field of programmable matter. Aiming for large-scale scalability, both in terms of the number of the cellular components of a structure, as well as the number of robots that are being deployed for construction requires simple yet robust robots and mechanisms, while also dealing with various basic constraints, such as connectivity of a structure during reconfiguration. To this end, we propose an approach that combines ultra-light, cellular building materials with extremely simple robots. We develop basic algorithmic methods that are able to detect and reconfigure arbitrary cellular structures, based on robots that have only constant-sized memory. As a proof of concept, we demonstrate the feasibility of this approach for specific cellular materials and robots that have been developed at NASA. 

In this video, we consider recognition and reconfiguration of lattice-based cellular structures by very simple robots with only basic functionality. The underlying motivation is the construction and modification of space facilities of enormous dimensions, where the combination of new materials with extremely simple robots promises structures of previously unthinkable size and flexibility. We present algorithmic methods that are able to detect and reconfigure arbitrary polyominoes, based on finite-state robots, while also preserving connectivity of a structure during reconfiguration. Specific results include methods for determining a bounding box, scaling a given arrangement, and adapting more general algorithms for transforming polyominoes. 

Image-guided and robot-assisted surgical procedures are rapidly evolving due to their potential to improve patient management and cost effectiveness. Magnetic Resonance Imaging (MRI) is used for pre-operative planning and is also investigated for real-time intra-operative guidance. A new type of technology is emerging that uses the magnetic field gradients of the MR scanner to maneuver ferromagnetic agents for local delivery of therapeutics. With this approach, MRI is both a sensor and forms a closed-loop controlled entity that behaves as a robot (we refer to them as MRbots). The objective of this paper is to introduce a computational framework for preoperative planning using MRI and modeling of MRbot maneuvering inside tortuous blood vessels. This platform generates a virtual corridor that represents a safety zone inside the vessel that is then used to access the safety of the MRbot maneuvering. In addition, to improve safety we introduce a control that sets speed based on the local curvature of the vessel. The functionality of the framework was then tested on a realistic operational scenario of accessing a neurological lesion, a meningioma. This virtual case study demonstrated the functionality and potential of MRbots as well as revealed two primary challenges: real-time MRI (during propulsion) and the need of very strong gradients for maneuvering small MRbots inside narrow cerebral vessels. Our ongoing research focuses on further developing the computational core, MR tracking methods, and on-line interfacing to the MR scanner.