Multi-agent Collective Construction using 3D Decomposition

This paper addresses a Multi-Agent Collective Construction (MACC) problem that aims to build a three-dimensional structure comprised of cubic blocks. We use cube-shaped robots that can carry one cubic block at a time, and move forward, reverse, left, and right to an adjacent cell of the same height or climb up and down one cube height. To construct structures taller than one cube, the robots must build supporting stairs made of blocks and remove the stairs once the structure is built. Conventional techniques solve for the entire structure at once and quickly become intractable for larger workspaces and complex structures, especially in a multi-agent setting. To this end, we present a decomposition algorithm that computes valid substructures based on intrinsic structural dependencies. We use Mixed Integer Linear Programming (MILP) to solve for each of these substructures and then aggregate the solutions to construct the entire structure. Extensive testing on 200 randomly generated structures shows an order of magnitude improvement in the solution computation time compared to an MILP approach without decomposition. Additionally, compared to Reinforcement Learning (RL) based and heuristics-based approaches drawn from the literature, our solution indicates orders of magnitude improvement in the number of pick-up and drop-off actions required to construct a structure. Furthermore, we leverage the independence between substructures to detect which sub-structures can be built in parallel. With this parallelization technique, we illustrate a further improvement in the number of time steps required to complete building the structure. This work is a step towards applying multi-agent collective construction for real-world structures by significantly reducing solution computation time with a bounded increase in the number of time steps required to build the structure.Comment: Presented at the Multi-agent Path Finding Workshop at AAAI 202

Motion Primitive Path Planning for Parametrically Uncertain Systems via the Koopman Operator

Kinodynamic motion planning addresses the problem of finding the control inputs to a dynamical system such that that system's trajectory satisfies constraints such as obstacle avoidance or entering a goal set. Motion primitives are a popular tool for kinodynamic motion planning as they allow constructing trajectories that are guaranteed to satisfy the system dynamics without requiring on-demand simulation. This work provides a generalization of motion primitives to systems subject to parametric uncertainty. Quantities of interest in optimal motion planning, including integrated cost terms and constraint indicator functions, are cast as expectations of functions of the terminal state of a motion primitive. Explicit uncertainty quantification via the Koopman operator is used to obtain sample-efficient schemes for evaluating these expectations. The sampling scheme permits casting the planning problem as a Chance-Constrained Markov Decision Process with a finite set of actions, for which a policy can be obtained by forward search on an And/Or graph. Techniques for efficient solution of this search problem are presented. The key bottleneck is identified as the expected value calculation, which is a high dimensional integral. One way to accelerate such calculations is through the use of a "sparse" numerical integration scheme. A method is described for obtaining maximally sparse numerical integration schemes for use with hypergraph search algorithms. The approach formulates a mixed-integer linear program that is tailored to the specific structure of the hypergraph on which chance-constrained motion primitive planning problems are solved. Finally, the effectiveness of Monte Carlo Tree Search and Lazy constraint enforcement is investigated.Ph.D