Related papers: PACE Solver Description: Exact Solution of the One…
Trajectory optimization offers mature tools for motion planning in high-dimensional spaces under dynamic constraints. However, when facing complex configuration spaces, cluttered with obstacles, roboticists typically fall back to…
In the Minimum Clique Routing Problem on Cycles \textsc{MCRPC} we are given a cycle together with a set of demands (weighted origin-destination pairs) and the goal is to route all the pairs minimizing the maximum weighted clique of the…
Partially Observable Markov Decision Processes (POMDPs) are systems in which one agent interacts with a stochastic environment, and receives only partial information about the current state. In a multi-environment POMDP (MEPOMDP), the…
We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize…
A metro-line crossing minimization problem is to draw multiple lines on an underlying graph that models stations and rail tracks so that the number of crossings of lines becomes minimum. It has several variations by adding restrictions on…
The Shortest-Path Problem in Graph of Convex Sets (SPP in GCS) is a recently developed optimization framework that blends discrete and continuous decision making. Many relevant problems in robotics, such as collision-free motion planning,…
Reference tracking and obstacle avoidance rank among the foremost challenging aspects of autonomous driving. This paper proposes control designs for solving reference tracking problems in autonomous driving tasks while considering static…
The Minimum Dominating Set (MDS) problem is a well-established combinatorial optimization problem with numerous real-world applications. Its NP-hard nature makes it increasingly difficult to obtain exact solutions as the graph size grows.…
We describe the algorithm behind our PACE 2017 submission to the heuristic tree decomposition computation track. It was the only competitor to solve all instances and won a tight second place. The algorithm was originally developed in the…
Given a set of points in the plane, we are interested in matching them with straight line segments. We focus on perfect (all points are matched) non-crossing (no two edges intersect) matchings. Apart from the well known MinMax variation,…
This note introduces Bute-Plus, an exact solver for the treedepth problem. The core of the solver is a positive-instance driven dynamic program that constructs an elimination tree of minimum depth in a bottom-up fashion. Three features…
Consider a general path planning problem of a robot on a graph with edge costs, and where each node has a Boolean value of success or failure (with respect to some task) with a given probability. The objective is to plan a path for the…
We address the following problem: Given a simple polygon $P$ with $n$ vertices and two points $s$ and $t$ inside it, find a minimum link path between them such that a given target point $q$ is visible from at least one point on the path.…
In this report, we describe three encodings of the multiple constant multiplication (MCM) problem to pseudo-boolean satisfiability (PBS), and introduce an algorithm to solve the MCM problem optimally. To the best of our knowledge, the…
Matrix completion (MC) is a promising technique which is able to recover an intact matrix with low-rank property from sub-sampled/incomplete data. Its application varies from computer vision, signal processing to wireless network, and…
We consider the problem of bridging the gap between geometric tracking control theory and implementation of model predictive control (MPC) for robotic systems operating on manifolds. We propose a generic on-manifold MPC formulation based on…
Coupled partial differential equations underpin a wide range of multiphysics systems, yet existing neural PDE solvers still struggle to resolve localized high-risk regions and often fail to preserve structural admissibility across coupled…
In this work we address a game theoretic variant of the shortest path problem, in which two decision makers (players) move together along the edges of a graph from a given starting vertex to a given destination. The two players take turns…
Model predictive control (MPC) has shown great success for controlling complex systems such as legged robots. However, when closing the loop, the performance and feasibility of the finite horizon optimal control problem (OCP) solved at each…
An algorithm is presented which produces the minimum cost bipartite matching between two sets of M points each, where the cost of matching two points is proportional to the minimum distance by which a particle could reach one point from the…