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We present a motion planner for planning through space-time with dynamic obstacles, velocity constraints, and unknown arrival time. Our algorithm, Space-Time RRT* (ST-RRT*), is a probabilistically complete, bidirectional motion planning…
The decomposition of complex structures into simpler substructures is a powerful technique with a wide range of applications. We study the computation of decompositions in the context of programmable matter. The amoebot model is a…
We present progress on the problem of reconfiguring a 2D arrangement of building material by a cooperative group of robots. These robots must avoid collisions, deadlocks, and are subjected to the constraint of maintaining connectivity of…
Shape formation is one of the most thoroughly studied problems in programmable matter and swarm robotics. However, in many models, the class of shapes that can be formed is highly restricted due to the particles' limited memory. In the…
To solve the Kohn-Sham equation within the framework of density functional theory, we develop a scheme to construct numerical atomic orbital (NAO) basis sets by contracting truncated spherical waves (TSWs). The contraction minimizes the…
Optimizing a connection through a quantum repeater network requires careful attention to the photon propagation direction of the individual links, the arrangement of those links into a path, the error management mechanism chosen, and the…
This paper focuses on showing time-message trade-offs in distributed algorithms for fundamental problems such as leader election, broadcast, spanning tree (ST), minimum spanning tree (MST), minimum cut, and many graph verification problems.…
The paper introduces an asymptotically optimal lifelong sampling-based path planning algorithm that combines the merits of lifelong planning algorithms and lazy search algorithms for rapid replanning in dynamic environments where edge…
In this paper, we present an online method for converting an arbitrary geometric path represented by a sequence of states, generated by any planner (e.g., sampling-based planners like RRT or PRM, search-based planners like ARA*, etc.), into…
We describe a simple quantum error correcting code built out of a time-dependent transverse field Ising model. The code is similar to a repetition code, but has two advantages: an $N$-qubit code can be implemented with a finite-depth…
Trajectory planning for quadrotors in cluttered environments has been challenging in recent years. While many trajectory planning frameworks have been successful, there still exists potential for improvements, particularly in enhancing the…
In the modular robot reconfiguration problem, we are given $n$ cube-shaped modules (or robots) as well as two configurations, i.e., placements of the $n$ modules so that their union is face-connected. The goal is to find a sequence of moves…
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of a transport equation with additional growth and non-local…
We describe and implement a randomized algorithm that inputs a polyhedron, thought of as the space of states of some automated guided vehicle $\mathcal{R}$, and outputs an explicit system of piecewise linear motion planners for…
Algorithmic self-assembly, a generalization of crystal growth processes, has been proposed as a mechanism for autonomous DNA computation and for bottom-up fabrication of complex nanostructures. A `program' for growing a desired structure…
In this paper, we study spline trajectory generation via the solution of two optimisation problems: (i) a quadratic program (QP) with linear equality constraints and (ii) a nonlinear and nonconvex optimisation program. We propose an…
For enabling efficient, large-scale coordination of unmanned aerial vehicles (UAVs) under the labeled setting, in this work, we develop the first polynomial time algorithm for the reconfiguration of many moving bodies in three-dimensional…
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce…
In the presence of dynamic insertions and deletions into a partially reconfigurable FPGA, fragmentation is unavoidable. This poses the challenge of developing efficient approaches to dynamic defragmentation and reallocation. One key aspect…
This study presents a system integration approach for planning schedules, sequences, tasks, and motions for reconfigurable robots to automatically disassemble constrained structures in a non-destructive manner. Such systems must adapt their…