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Constrained motion planning is a challenging field of research, aiming for computationally efficient methods that can find a collision-free path on the constraint manifolds between a given start and goal configuration. These planning…
We study synthesis problems with constraints in partially observable Markov decision processes (POMDPs), where the objective is to compute a strategy for an agent that is guaranteed to satisfy certain safety and performance specifications.…
Planning is a fundamental activity, arising frequently in many contexts, from daily tasks to industrial processes. The planning task consists of selecting a sequence of actions to achieve a specified goal from specified initial conditions.…
High-dimensional motion planning problems can often be solved significantly faster by using multilevel abstractions. While there are various ways to formally capture multilevel abstractions, we formulate them in terms of fiber bundles.…
Sampling-based planning methods often become inefficient due to narrow passages. Narrow passages induce a higher runtime, because the chance to sample them becomes vanishingly small. In recent work, we showed that narrow passages can be…
An important problem in geometric reasoning is to find the configuration of a collection of geometric bodies so as to satisfy a set of given constraints. Recently, it has been suggested that this problem can be solved efficiently by…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…
Constraint satisfaction is a critical component in a wide range of engineering applications, including but not limited to safe multi-agent control and economic dispatch in power systems. This study explores violation-free distributed…
This paper deals with the control synthesis problem for a continuous nonlinear dynamical system under a Linear Temporal Logic (LTL) formula. The proposed solution is a top-down hierarchical decomposition of the control problem involving…
Navigating rigid body objects through crowded environments can be challenging, especially when narrow passages are presented. Existing sampling-based planners and optimization-based methods like mixed integer linear programming (MILP)…
It is well established that formulating an effective constraint model of a problem of interest is crucial to the efficiency with which it can subsequently be solved. Following from the observation that it is difficult, if not impossible, to…
Pre-trained large language models (LLMs) show promise for robotic task planning but often struggle to guarantee correctness in long-horizon problems. Task and motion planning (TAMP) addresses this by grounding symbolic plans in low-level…
We review some important ideas in the design and analysis of robust overlapping domain decomposition algorithms for high-contrast multiscale problems and propose a domain decomposition method better performance in terms of the number of…
In real-world applications, the ability to reason about incomplete knowledge, sensing, temporal notions, and numeric constraints is vital. While several AI planners are capable of dealing with some of these requirements, they are mostly…
To date, most work on text simplification has focused on sentence-level inputs. Early attempts at document simplification merely applied these approaches iteratively over the sentences of a document. However, this fails to coherently…
We present a new approach to HPSG processing: compiling HPSG grammars expressed as type constraints into definite clause programs. This provides a clear and computationally useful correspondence between linguistic theories and their…
Long-context large language models remain computationally expensive to run and often fail to reliably process very long inputs, which makes context compression an important component of many systems. Existing compression approaches…
We propose two novel conditional gradient-based methods for solving structured stochastic convex optimization problems with a large number of linear constraints. Instances of this template naturally arise from SDP-relaxations of…
We introduce a constraint-based framework for studying infinite qualitative simulations concerned with contingencies such as time, space, shape, size, abstracted into a finite set of qualitative relations. To define the simulations, we…
While Large Language Models (LLMs) provide semantic flexibility for robotic task planning, their susceptibility to hallucination and logical inconsistency limits their reliability in long-horizon domains. To bridge the gap between…