Multi-Robot Planning on Dynamic Topological Graphs using Mixed-Integer Programming

TL;DR

This paper presents a novel approach for multi-robot planning on topological graphs using mixed-integer programming, and introduces the notion of a dynamic topological graph, where edge weights vary dynamically based on the locations of the robots in the graph.

Abstract

Planning for multi-robot teams in complex environments is a challenging problem, especially when these teams must coordinate to accomplish a common objective. In general, optimal solutions to these planning problems are computationally intractable, since the decision space grows exponentially with the number of robots. In this paper, we present a novel approach for multi-robot planning on topological graphs using mixed-integer programming. Central to our approach is the notion of a dynamic topological graph, where edge weights vary dynamically based on the locations of the robots in the graph. We construct this graph using the critical features of the planning problem and the relationships between robots; we then leverage mixed-integer programming to minimize a shared cost that depends on the paths of all robots through the graph. To improve computational tractability, we formulated our optimization problem with a fully convex relaxation and designed our decision space around eliminating the exponential dependence on the number of robots. We test our approach on a multi-robot reconnaissance scenario, where robots must coordinate to minimize detectability and maximize safety while gathering information. We demonstrate that our approach is able to scale to a series of representative scenarios and is capable of computing optimal coordinated strategic behaviors for autonomous multi-robot teams in seconds.

Figures (6)

• Figure 1: A depiction of our proposed dynamic topological graph applied to a reconnaissance problem. The nodes are in forested regions of cover. Ten robot scouts start at node 1 with the goal of at least one robot reaching node 2, across the meadow. The edges of the graph have cost for transitioning between nodes that is a function of their distance, detectability, and vulnerability. This cost can be reduced by moving in teams and by providing overwatch, where robots at a particular node oversee the movement of robots along a corresponding edge to help mitigate some of the risk of traversing. Overwatch opportunities are indicated with an arrow from the overwatch node pointing toward the edge that can be monitored. The robot team routes through the graph, solved for with our proposed method, represent a solution to this problem.
• Figure 2: Piecewise-Linear Cost Functions
• Figure 3: MIP problem solution to an illustrative multi-robot reconnaissance scenario, sketched in (a). Ten robots start at node 1 with a goal of at least one robot reaching node 5 to observe the adversary units. The light green regions represent areas of cover. The color of the edges indicate the threat level for transitioning between nodes from low to high (LTH): blue, yellow, red. Edge (3,5) has the highest weight due to its visibility by the adversary. In each subplot, the edge labels indicate the edge cost under the current conditions and show in brackets the desired number of robots, $a_e$, due to vulnerability. Overwatch opportunities are shown with a pink arrow from the overwatch node pointing to the edge that can be monitored. At each time step, the position of each robot scout is shown.
• Figure 4: Example solution demonstrating bounding overwatch behavior as all robots move from node 1 to 11. Robot team routes are shown with each time step labeled. The overwatch opportunities, indicated by the pink arrows, are met at time steps 2, 3, 6, and 7. The two teams alternate providing overwatch as they move through the environment.
• Figure 5: Aerial map of a meadow environment showing a sample scenario. Nodes are in regions of cover. Vulnerable edges due to crossing roads are shown in dark blue. The largest cost reductions on these edges come from having four robots. In the solution routes shown, robot teams split up and form new teams as they move through the terrain providing overwatch.