T. K. Satish Kumar

Formation change for robot groups in occluded environments

We study formation change for robot groups in known environments. We are given a team of robots partitioned into groups, where robots in the same group are interchangeable with each other. A formation specifies the locations occupied by each group. The objective is to find collision-free paths that move all robots from a given start formation to a given goal formation. Our algorithm TAPF* has the following features: (a) it incorporates kinematic constraints of robots in form of velocity limits; (b) it maintains a user-specified safety distance between robots; (c) it attempts to minimize the makespan; and (d) it runs efficiently for hundreds of robots and dozens of groups even in dense 3D environments with narrow corridors and other occlusions. We demonstrate the efficiency and effectiveness of TAPF* in simulation and on robots.

A New Solver for the Minimum Weighted Vertex Cover Problem

Given a vertex-weighted graph (G = langle V, E rangle ), the minimum weighted vertex cover (MWVC) problem is to choose a subset of vertices with minimum total weight such that every edge in the graph has at least one of its endpoints chosen. While there are good solvers for the unweighted version of this NP-hard problem, the weighted version—i.e., the MWVC problem—remains understudied despite its common occurrence in many areas of AI—like combinatorial auctions, weighted constraint satisfaction, and probabilistic reasoning. In this paper, we present a new solver for the MWVC problem based on a novel reformulation to a series of SAT instances using a primal-dual approximation algorithm as a starting point. We show that our SAT-based MWVC solver (SBMS) significantly outperforms other methods.

The Nemhauser-Trotter Reduction and Lifted Message Passing for the Weighted CSP

We study two important implications of the constraint composite graph (CCG) associated with the weighted constraint satisfaction problem (WCSP). First, we show that the Nemhauser-Trotter (NT) reduction popularly used for kernelization of the minimum weighted vertex cover (MWVC) problem can also be applied to the CCG of the WCSP. This leads to a polynomial-time preprocessing algorithm that fixes the optimal values of a large subset of the variables in the WCSP. Second, belief propagation (BP) is a well-known technique used for solving many combinatorial problems in probabilistic reasoning, artificial intelligence and information theory. The min-sum message passing (MSMP) algorithm is a simple variant of BP that has also been successfully employed in several research communities. Unfortunately, the MSMP algorithm has met with little success on the WCSP. We revive the MSMP algorithm for solving the WCSP by applying it on the CCG of a given WCSP instance instead of its original form. We refer to this new MSMP algorithm as the lifted MSMP algorithm for the WCSP. We demonstrate the effectiveness of our algorithms through experimental evaluations.

A Constraint Composite Graph-Based ILP Encoding of the Boolean Weighted CSP

The weighted constraint satisfaction problem (WCSP) occurs in the crux of many real-world applications of operations research, artificial intelligence, bioinformatics, etc. Despite its importance as a combinatorial substrate, many attempts for building an efficient WCSP solver have been largely unsatisfactory. In this paper, we introduce a new method for encoding a (Boolean) WCSP instance as an integer linear program (ILP). This encoding is based on the idea of the constraint composite graph (CCG) associated with a WCSP instance. We show that our CCG-based ILP encoding of the Boolean WCSP is significantly more efficient than previously known ILP encodings. Theoretically, we show that the CCG-based ILP encoding has a number of interesting properties. Empirically, we show that it allows us to solve many hard Boolean WCSP instances that cannot be solved by ILP solvers with previously known ILP encodings.

The FastMap Algorithm for Shortest Path Computations

We present a new preprocessing algorithm for embedding the nodes of a given edge-weighted undirected graph into a Euclidean space. The Euclidean distance between any two nodes in this space approximates the length of the shortest path between them in the given graph. Later, at runtime, a shortest path between any two nodes can be computed with A* search using the Euclidean distances as heuristic. Our preprocessing algorithm, called FastMap, is inspired by the data mining algorithm of the same name and runs in near-linear time. Hence, FastMap is orders of magnitude faster than competing approaches that produce a Euclidean embedding using Semidefinite Programming. FastMap also produces admissible and consistent heuristics and therefore guarantees the generation of shortest paths. Moreover, FastMap applies to general undirected graphs for which many traditional heuristics, such as the Manhattan Distance heuristic, are not well defined. Empirically, we demonstrate that A* search using the FastMap heuristic is competitive with A* search using other state-of-the-art heuristics, such as the Differential heuristic.

Multi-Agent Path Finding with Deadlines

We formalize Multi-Agent Path Finding with Deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within the deadline, without colliding with each other. We first show that MAPF-DL is NP-hard to solve optimally. We then present two classes of optimal algorithms, one based on a reduction of MAPF-DL to a flow problem and a subsequent compact integer linear programming formulation of the resulting reduced abstracted multi-commodity flow network and the other one based on novel combinatorial search algorithms. Our empirical results demonstrate that these MAPF-DL solvers scale well and each one dominates the other ones in different scenarios.

Anytime Focal Search with Applications

Focal search (FS) is a bounded-suboptimal search (BSS) variant of A*. Like A*, it uses an open list whose states are sorted in increasing order of their f -values. Unlike A*, it also uses a focal list containing all states from the open list whose f -values are no larger than a suboptimality factor times the smallest f -value in the open list. In this paper, we develop an anytime version of FS, called anytime FS (AFS), that is useful when deliberation time is limited. AFS finds a “good” solution quickly and refines it to better and better solutions if time allows. It does this refinement efficiently by reusing previous search efforts. On the theoretical side, we show that AFS is bounded suboptimal and that anytime potential search (ATPS/ANA*), a state-of-theart anytime bounded-cost search (BCS) variant of A*, is a special case of AFS. In doing so, we bridge the gap between anytime search algorithms based on BSS and BCS. We also identify different properties of priority functions, used to sort the focal list, that may allow for efficient reuse of previous search efforts. On the experimental side, we demonstrate the usefulness of AFS for solving hard combinatorial problems, such as the generalized covering traveling salesman problem and the multiagent pathfinding problem.

A Warning Propagation-Based Linear-Time-and-Space Algorithm for the Minimum Vertex Cover Problem on Giant Graphs

A vertex cover (VC) of a graph (G) is a subset of vertices in (G) such that at least one endpoint vertex of each edge in (G) is in this subset. The minimum VC (MVC) problem is to identify a VC of minimum size (cardinality) and is known to be NP-hard. Although many local search algorithms have been developed to solve the MVC problem close-to-optimally, their applicability on giant graphs (with no less than 100,000 vertices) is limited. For such graphs, there are two reasons why it would be beneficial to have linear-time-and-space algorithms that produce small VCs. Such algorithms can: (a) serve as preprocessing steps to produce good starting states for local search algorithms and (b) also be useful for many applications that require finding small VCs quickly. In this paper, we develop a new linear-time-and-space algorithm, called MVC-WP, for solving the MVC problem on giant graphs based on the idea of warning propagation, which has so far only been used as a theoretical tool for studying properties of MVCs on infinite random graphs. We empirically show that it outperforms other known linear-time-and-space algorithms in terms of sizes of produced VCs.

Solving Multiagent Constraint Optimization Problems on the Constraint Composite Graph

We introduce the Constraint Composite Graph (CCG) for Distributed Constraint Optimization Problems (DCOPs), a popular paradigm used for the description and resolution of cooperative multi-agent problems. The CCG is a novel graphical representation of DCOPs on which agents can coordinate their assignments to solve the distributed problem suboptimally. By leveraging this representation, agents are able to reduce the size of the problem. We propose a novel variant of Max-Sum—a popular DCOP incomplete algorithm—called CCG-Max-Sum, which is applied to CCGs, and demonstrate its efficiency and effectiveness on DCOP benchmarks based on several network topologies.

Summary: Multi-Agent Path Finding with Kinematic Constraints

Multi-Agent Path Finding (MAPF) is well studied in both AI and robotics. Given a discretized environment and agents with assigned start and goal locations, MAPF solvers from AI find collision-free paths for hundreds of agents with user-provided sub-optimality guarantees. However, they ignore that actual robots are subject to kinematic constraints (such as velocity limits) and suffer from imperfect plan-execution capabilities. We therefore introduce MAPF-POST to postprocess the output of a MAPF solver in polynomial time to create a plan-execution schedule that can be executed on robots. This schedule works on non-holonomic robots, considers kinematic constraints, provides a guaranteed safety distance between robots, and exploits slack to avoid time-intensive replanning in many cases. We evaluate MAPF-POST in simulation and on differential-drive robots, showcasing the practicality of our approach.