Adriaan ter Mors

Coordinating Self-interested Planning Agents

We consider planning problems where a number of non-cooperative agents have to work on a joint problem. Such problems consist in completing a set of interdependent, hierarchically ordered tasks. Each agent is assigned a subset of tasks to perform for which it has to construct a plan. Since the agents are non-cooperative, they insist on planning independently and do not want to revise their individual plans when the joint plan has to be assembled from the individual plans. We present a general formal framework to study some computational aspects of this non-cooperative coordination problem and we establish some complexity results to identify some of the factors that contribute to the complexity of this problem. Finally, we illustrate our approach with an application to coordination in multi-modal logistic planning.

Context-aware route planning

In context-aware route planning, there is a set of transportation agents each with a start and destination location on a shared infrastructure. Each agent wants to find a shortest-time route plan without colliding with any of the other agents, or ending up in a deadlock situation. We present a single-agent route planning algorithm that is both optimal and conflict-free. We also present a set of experiments that compare our algorithm to finding a conflict-free schedule along a fixed path. In particular, we will compare our algorithm to the approach where the shortest conflict-free schedule is chosen along one of k shortest paths. Although neither approach can guarantee optimality with regard to the total set of agent route plans -- and indeed examples can be constructed to show that either approach can outperform the other -- our experiments show that our approach consistently outperforms fixed-path scheduling.

Framework and complexity results for coordinating non-cooperative planning agents

In multi-agent planning problems agents are requested to jointly solve a complex task consisting of a set of interrelated tasks. Since none of the agents is capable to solve the whole task on its own, usually each of them is assigned to a subset of tasks. If agents are dependent upon each other via interrelated tasks they are assigned to, moderately coupled teams of agents are called for. Such teams solve the task by coordinating during or after planning and revising their plans if necessary. In this paper we show that such complex tasks also can be solved by loosely coupled teams of agents that are able to plan independently, although the computational complexity of the coordination problems involved is high. We also investigate some of the factors influencing this complexity.

Push and rotate: a complete multi-agent pathfinding algorithm

Multi-agent Pathfinding is a relevant problem in a wide range of domains, for example in robotics and video games research. Formally, the problem considers a graph consisting of vertices and edges, and a set of agents occupying vertices. An agent can only move to an unoccupied, neighbouring vertex, and the problem of finding the minimal sequence of moves to transfer each agent from its start location to its destination is an NP-hard problem. We present Push and Rotate, a new algorithm that is complete for Multi-agent Pathfinding problems in which there are at least two empty vertices. Push and Rotate first divides the graph into subgraphs within which it is possible for agents to reach any position of the subgraph, and then uses the simple push, swap, and rotate operations to find a solution; a post-processing algorithm is also presented that eliminates redundant moves. Push and Rotate can be seen as extending Luna and Bekriss Push and Swap algorithm, which we showed to be incomplete in a previous publication. In our experiments we compare our approach with the Push and Swap, MAPP, and Bibox algorithms. The latter algorithm is restricted to a smaller class of instances as it requires biconnected graphs, but can nevertheless be considered state of the art due to its strong performance. Our experiments show that Push and Swap suffers from incompleteness, MAPP is generally not competitive with Push and Rotate, and Bibox is better than Push and Rotate on randomly generated biconnected instances, while Push and Rotate performs better on grids.

Coordination by design and the price of autonomy

We consider a multi-agent planning problem as a set of activities that has to be planned by several autonomous agents. In general, due to the possible dependencies between the agents’ activities or interactions during execution of those activities, allowing agents to plan individually may lead to a very inefficient or even infeasible solution to the multi-agent planning problem. This is exactly where plan coordination methods come into play. In this paper, we aim at the development of coordination by design techniques that (i) let each agent construct its plan completely independent of the others while (ii) guaranteeing that the joint combination of their plans always is coordinated. The contribution of this paper is twofold. Firstly, instead of focusing only on the feasibility of the resulting plans, we will investigate the additional costs incurred by the coordination by design method, that means, we propose to take into account the price of autonomy: the ratio of the costs of a solution obtained by coordinating selfish agents versus the costs of an optimal solution. Secondly, we will point out that in general there exist at least two ways to achieve coordination by design: one called concurrent decomposition and the other sequential decomposition. We will briefly discuss the applicability of these two methods, and then illustrate them with two specific coordination problems: coordinating tasks and coordinating resource usage. We also investigate some aspects of the price of autonomy of these two coordination methods.

Coordinating Competitive Agents in Dynamic Airport Resource Scheduling

In real-life multi-agent planning problems, long-term plans will often be invalidated by changes in the environment during or after the planning process. When this happens, short-term operational planning and scheduling methods have to be applied in order to deal with these changed situations. In addition to the dynamic environment, in such planning systems we also have to be aware of sometimes conflicting interests of different parties, which render a centralized approach undesirable. In this paper we investigate two agent-based scheduling architectures where stakeholders are modelled as autonomous agents. We discuss this approach in the context of an interesting airport planning problem: the planning and scheduling of deicing and anti-icing activities. To coordinate the competition between agents over scarce resources, we have developed two mechanisms: one mechanism based on decommitment penalties, and one based on a more traditional (Vickrey) auction. Experiments show that the auction-based mechanism best respects the preferences of the individual agents, whereas the decommitment mechanism ensures a fairer distribution of delay over the agents.

Conflict-free route planning in dynamic environments

Motion planning for multiple robots is tractable in case we can assume a roadmap on which all the robots travel, which is often the case in many automated guided vehicle domains, such as factory floors or container terminals. We present an O(nv log(nv) + n2v) (n the number of nodes, v the number of vehicles) route planning algorithm for a single robot, which can find the minimum-time route given a set of existing route plans that it may not interfere with. In addition, we present an algorithm that can propagate delay through the plans of the robots in case one or more robots are delayed. This delay-propagation algorithm allows us to implement a Pareto-optimal plan repair scheme, in which one robot can improve its route plan without adversely affecting the other robots. We compare this approach to several plan repair schemes from the literature, which are based on the idea of giving a higher priority to non-delayed agents.

Complexity of coordinating autonomous planning agents

We assume that a number of agents have to work together on some joint task T consisting of a number of elementary tasks tj, partially ordered by a set of precedence constraints. The elementary tasks are allocated to the agents using some given task allocation protocol (cf. [2]). We assume that (i) to perform its set of tasks, an agent needs to make a plan, and that (ii) each agent wishes to retain full planning autonomy, i.e., to retain the freedom to decide how to best perform its tasks.

Plan Repair in Conflict-Free Routing

In conflict-free routing a set of agents have to traverse a common infrastructure without interfering with each other. Maza and Castagna [1] showed how the route plans of such agents can be repaired by maintaining the priority of agents on infrastructure resources. They also developed an algorithm that allows agents to change priorities to avoid long waits. We extend the work of Maza and Castagna by (i ) specifying an algorithm that allows more priority changes, and by (ii ) defining a graph structure that can predict exactly which priority changes will lead to a deadlock, and which will not.

Complexity of task coordination for non cooperative planning agents

We discuss task planning problems where a number of agents have to work on a joint planning problem that consists of a set of interdependent, hierarchically ordered tasks. Each agent is assigned a subset of tasks to perform for which it has to construct a plan. The agents are non-cooperative in that they insist on planning autonomously and do not want to revise their individual plans when a joint plan has to be assembled. The aim of this paper is twofold: first of all to present a general formal framework to study some computational aspects of this non-cooperative coordination problem, and secondly to establish some complexity results and to identify some of the factors that contribute to the complexity of this problem.