Related papers: Towards a Model of Puzznic
We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…
We propose a novel Linear Program (LP) based formula- tion for solving jigsaw puzzles. We formulate jigsaw solving as a set of successive global convex relaxations of the stan- dard NP-hard formulation, that can describe both jigsaws with…
We study a family of sorting match puzzles on grids, which we call permutation match puzzles. In this puzzle, each row and column of a $n \times n$ grid is labeled with an ordering constraint -- ascending (A) or descending (D) -- and the…
Understanding the properties of games played under computational constraints remains challenging. For example, how do we expect rational (but computationally bounded) players to play games with a prohibitively large number of states, such…
Solving Sudoku puzzles is one of the most popular pastimes in the world. Puzzles range in difficulty from easy to very challenging; the hardest puzzles tend to have the most empty cells. The current paper explains and compares three…
Robot motion planning involves computing a sequence of valid robot configurations that take the robot from its initial state to a goal state. Solving a motion planning problem optimally using analytical methods is proven to be PSPACE-Hard.…
We propose an integrated behavior and motion planning framework for the lane-merging problem. The behavior planner combines search-based planning with game theory to model vehicle interactions and plan multi-vehicle trajectories. Inspired…
This paper focuses on "tracing player knowledge" in educational games. Specifically, given a set of concepts or skills required to master a game, the goal is to estimate the likelihood with which the current player has mastery of each of…
We introduce an alternative approach for constrained mathematical programming problems. It rests on two main aspects: an efficient way to compute optimal solutions for unconstrained problems, and multipliers regarded as variables for a…
An unconstrained crossword puzzle is a generalization of the constrained crossword problem. In this problem, only the word vocabulary, and optionally the grid dimensions are known. Hence, it not only requires the algorithm to determine the…
Recognition of goals and plans using incomplete evidence from action execution can be done efficiently by using planning techniques. In many applications it is important to recognize goals and plans not only accurately, but also quickly. In…
Planning is central to agents and agentic AI. The ability to plan, e.g., creating travel itineraries within a budget, holds immense potential in both scientific and commercial contexts. Moreover, optimal plans tend to require fewer…
In this paper, we present SeGMan, a hybrid motion planning framework that integrates sampling-based and optimization-based techniques with a guided forward search to address complex, constrained sequential manipulation challenges, such as…
We propose an algorithm for solving bound-constrained mathematical programs with complementarity constraints on the variables. Each iteration of the algorithm involves solving a linear program with complementarity constraints in order to…
Model Predictive Control (MPC) is a successful control methodology, which is applied to increasingly complex systems. However, real-time feasibility of MPC can be challenging for complex systems, certainly when an (extremely) large number…
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…
Multimodal planning capabilities refer to the ability to predict, reason, and design steps for task execution with multimodal context, which is essential for complex reasoning and decision-making across multiple steps. However, current…
Fuzzy constraints are a popular approach to handle preferences and over-constrained problems in scenarios where one needs to be cautious, such as in medical or space applications. We consider here fuzzy constraint problems where some of the…
Given a series of photographs taken during a Go game, we describe the techniques we successfully employ for pinpointing the grid lines of the Go board and for tracking their small movements between consecutive photographs; then we discuss…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…