Related papers: Traversability, Reconfiguration, and Reachability …
We initiate a general theory for analyzing the complexity of motion planning of a single robot through a graph of "gadgets", each with their own state, set of locations, and allowed traversals between locations that can depend on and change…
An open-close door gadget has two states and three tunnels that can be traversed by an agent (player, robot, etc.): the "opening" and "closing" tunnels set the gadget's state to open and closed, respectively, while the "traverse" tunnel can…
Games on graphs provide a natural and powerful model for reactive systems. In this paper, we consider generalized reachability objectives, defined as conjunctions of reachability objectives. We first prove that deciding the winner in such…
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a matrix $M \in \mathbb{Q}^{d \times d}$, an initial vector…
We analyze the computational complexity of motion planning through local "input/output" gadgets with separate entrances and exits, and a subset of allowed traversals from entrances to exits, each of which changes the state of the gadget and…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
We consider the mobile robot path planning problem for a class of recurrent reachability objectives. These objectives are parameterized by the expected time needed to visit one position from another, the expected square of this time, and…
We study the problem of deciding reconfigurability of target sets of a graph. Given a graph $G$ with vertex thresholds $\tau$, consider a dynamic process in which vertex $v$ becomes activated once at least $\tau(v)$ of its neighbors are…
Motivated by the increasing appeal of robots in information-gathering missions, we study multi-agent path planning problems in which the agents must remain interconnected. We model an area by a topological graph specifying the movement and…
Reachability problems in infinite-state systems are often subject to extremely high complexity. This motivates the investigation of efficient overapproximations, where we add transitions to obtain a system in which reachability can be…
Rearranging and manipulating deformable objects such as cables, fabrics, and bags is a long-standing challenge in robotic manipulation. The complex dynamics and high-dimensional configuration spaces of deformables, compared to rigid…
We investigate the reachability problem in symmetric vector addition systems with states (VASS), where transitions are invariant under a group of permutations of coordinates. One extremal case, the trivial groups, yields general VASS. In…
We consider the computational complexity of reconfiguration problems, in which one is given two combinatorial configurations satisfying some constraints, and is asked to transform one into the other using elementary transformations, while…
Complex manipulation tasks, such as rearrangement planning of numerous objects, are combinatorially hard problems. Existing algorithms either do not scale well or assume a great deal of prior knowledge about the environment, and few offer…
Many puzzle video games, like Sokoban, involve moving some agent in a maze. The reachable locations are usually apparent for a human player, and the difficulty of the game is mainly related to performing actions on objects, such as pushing…
Graph reachability is the task of understanding whether two distinct points in a graph are interconnected by arcs to which in general a semantic is attached. Reachability has plenty of applications, ranging from motion planning to routing.…
Building agents that can explore their environments intelligently is a challenging open problem. In this paper, we make a step towards understanding how a hierarchical design of the agent's policy can affect its exploration capabilities.…
The dynamics of real-world applications and systems require efficient methods for improving infeasible solutions or restoring corrupted ones by making modifications to the current state of a system in a restricted way. We propose a new…
We extend the motion-planning-through-gadgets framework to several new scenarios involving various numbers of robots/agents, and analyze the complexity of the resulting motion-planning problems. While past work considers just one robot or…
The reachability problem for vector addition systems is a central problem of net theory. This problem is known to be decidable but the complexity is still unknown. Whereas the problem is EXPSPACE-hard, no elementary upper bounds complexity…