This work investigates the use of flow-based connectivity maintenance constraints in mixed-integer linear programming (MILP) trajectory planning and decision-making models for networked multi-agent systems (MAS). We integrate flow-based encodings for standard and k-hop connectivity into MILP multi-vehicle maneuvering models that are widely used alongside receding horizon planning strategies. Their necessity and sufficiency is demonstrated, guaranteeing full coverage of potential network topologies. The flow formulation for standard connectivity decreases the growth of the required inequality constraints from exponential to polynomial w.r.t. the size of the MAS when compared to the state-of-the-art subtour elimination (SEC) method. The flow-based k-hop connectivity constraints decrease the number of required binary variables and decouple its growth from the number of hops. However, the impact of these formulations in performance is not straightforward due to the introduction of a substantial number of continuous flow optimization variables and, in the case of k-hop connectivity, additional inequality constraints. We investigate this trade-off through a statistical evaluation of costs and optimization times using a conventional branch-and-bound commercial solver and trials performed with randomized environments for increasingly larger MAS. The results show that the flow formulation outperforms SEC in standard connectivity problems, enabling the solutions to be computed for larger MAS considering the imposed optimization time limit. The reduction in number of binary variables enabled by the k-hop flow formulations decreases the theoretical worst-case number of iterations required by the branch-and-bound algorithm to compute the global optimal solution. Our results show that this advantage did not translate into improvements in the average performance when compared to the baseline.
Multi-agent motion planning (MAMP) is an important problem for autonomous systems with multiple agents. In this work we propose a two-step method for finding optimized and kinematically feasible solutions to MAMP problems. The first step finds an initial feasible solution using state-of-the-art methods such as conflict-based search (CBS) or priority-based search (PBS), and the second step is an improvement step which improves the solution by solving a multi-phase optimal control problem (OCP) where the initial solution is used to warm-start the solver. We also propose a method for generating motion primitives in an optimized way under the constraint that the primitive durations are all multiples of the same sample time. We evaluate our proposed framework on a MAMP problem for tractor-trailer systems. We extend the safe interval path planning with interval projections (SIPP-IP) algorithm so it can handle more general cost functions and larger agents, but our results show that for the tractor-trailer system a simple lattice-based planner performs better due to less conservative collision checks. Our experiments also indicate that CBS performs better than PBS for this system as it achieves a higher success rate in environments with obstacles and had a lower average runtime, although both planners achieve solutions of similar quality after the improvement step.
Anja Hellander, Kristoffer Bergman, Daniel Axehill
Multi-agent systems (MAS) were expected to overcome the limitation of single-agent systems (SAS) through collaboration. However, under typicality conditions on the task's constraint graph and bounded inter-agent communication, we prove that the success probability of a MAS is closely tied to the connectivity of task constraints, where each agent has limited information-processing capacity. Specifically, the success probability decays exponentially with an information bottleneck that emerges from partitioning the task's constraint graph among agents. We define this quantity as the \emph{minimum cut cost} Cmin of the potential constraint graph of each task. This information-theoretic bound applies to both open systems with external feedback and closed systems without. We validate our theory on both synthetic experiments and real-world empirical data from SWE-bench submissions. From our framework, effective MAS design should incorporate task-inherent constraints alongside engineering optimization, and when \Cmin is high, practitioners should restructure tasks rather than simply scaling agents or communication.
Many research fields share a common structure: a set of agents, each pursuing its own goal, whose actions must be coordinated so that no two of them conflict. Multi-Agent Path Finding (MAPF) is a concrete instance of this structure, with applications from warehouses to road traffic and airports. Much of MAPF research assumes discrete time, circular agents sharing one spatial graph, a single goal per agent, and that an agent must remain at its goal once reached, precluding heterogeneous fleets, non-geometric conflicts, task sequences, and agents that move on after completing them. We generalise the MAPF formulation to lift these assumptions, and present Anytime-Optimal Continuous-time Conflict-Based Search (AOC-CBS), an exact and solution-complete solver for it. AOC-CBS guarantees the eventual return of an optimal solution, while reporting an incumbent with a known optimality gap upper bound throughout its runtime; it is configurable with a portfolio of repair functions, one of which we introduce (Tier-Prioritized Safe Interval Path Planning), and can exploit multiple processor cores. We demonstrate AOC-CBS on a mixed fleet of non-convex agents moving along smooth, kinodynamically feasible trajectories. Preliminary experiments against the exact solver OC-CBS, on well-known benchmarks and roadmaps we sample from them, show AOC-CBS is comparable at finding optimal solutions while extending scalability from the tens to the hundreds of agents when a bounded optimality gap is accepted.
Alvin Combrink, Sabino Francesco Roselli, Martin Fabian