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We show under weak hypotheses that the pushforward $\{Z_no\}$ of a random-walk to a CAT(0) cube complex converges to a point on the boundary. We introduce the notion of squeezing points, which allows us to consider the convergence in either…
Timed pushdown automata are pushdown automata extended with a finite set of real-valued clocks. Additionaly, each symbol in the stack is equipped with a value representing its age. The enabledness of a transition may depend on the values of…
We introduce and investigate the computational complexity of a novel physical problem known as the Pinball Wizard problem. It involves an idealized pinball moving through a maze composed of one-way gates (outswing doors), plane walls,…
The reachability analysis of weighted pushdown systems is a very powerful technique in verification and analysis of recursive programs. Each transition rule of a weighted pushdown system is associated with an element of a bounded semiring…
We study the first-order model checking problem on two generalisations of pushdown graphs. The first class is the class of nested pushdown trees. The other is the class of collapsible pushdown graphs. Our main results are the following.…
Probabilistic Virtual Fixtures (VFs) enable the adaptive selection of the most suitable haptic feedback for each phase of a task, based on learned or perceived uncertainty. While keeping the human in the loop remains essential, for…
Several planners have been developed to compute dynamically feasible, collision-free robot paths from an initial to a goal configuration. A key assumption in these works is that the goal region is reachable; an assumption that often fails…
Robotic systems operating in unstructured environments require the ability to switch between compliant and rigid states to perform diverse tasks such as adaptive grasping, high-force manipulation, shape holding, and navigation in…
The design process and complexity of existing safety controls are heavily determined by the geometrical properties of the environment, which affects the proof of convergence, design scalability, performance robustness, and numerical…
Consider the problem of planning collision-free motion of $n$ objects in the plane movable through contact with a robot that can autonomously translate in the plane and that can move a maximum of $m \leq n$ objects simultaneously. This…
The ability to solve motion-planning queries within a fixed time budget is critical for deploying robotic systems in time-sensitive applications. Semi-static environments, where most of the workspace remains fixed while a subset of…
We study the verification of distributed systems where processes are finite automata with access to a shared pool of locks. We consider objectives that are boolean combinations of local regular constraints. We show that the problem,…
Task-space Passivity-Based Control (PBC) for manipulation has numerous appealing properties, including robustness to modeling error and safety for human-robot interaction. Existing methods perform poorly in singular configurations, however,…
We address the verification problem of ordered multi-pushdown automata: A multi-stack extension of pushdown automata that comes with a constraint on stack transitions such that a pop can only be performed on the first non-empty stack.…
For mobile robots, navigating cluttered or dynamic environments often necessitates non-prehensile manipulation, particularly when faced with objects that are too large, irregular, or fragile to grasp. The unpredictable behavior and varying…
We consider the model of parametrized asynchronous shared-memory pushdown systems, as introduced in [Hague'11]. In a series of recent papers it has been shown that reachability in this model is PSPACE-complete [Esparza, Ganty, Majumdar'13]…
Graph algorithms applied in many applications, including social networks, communication networks, VLSI design, graphics, and several others, require dynamic modifications -- addition and removal of vertices and/or edges -- in the graph.…
Despite decades of work in fast reactive planning and control, challenges remain in developing reactive motion policies on non-Euclidean manifolds and enforcing constraints while avoiding undesirable potential function local minima. This…
Here we introduce a new game on graphs, called cup stacking, following a line of what can be considered as $0$-, $1$-, or $2$-person games such as chip firing, percolation, graph burning, zero forcing, cops and robbers, graph pebbling, and…
Model Predictive Control (MPC) has proven to be a powerful tool for the control of systems with constraints. Nonetheless, in many applications, a major challenge arises, that is finding the optimal solution within a single sampling instant…