arXiv subjects

Alvin Combrink

Publications and source records attributed to Alvin Combrink.

6 recordsLinked to original sources

arXiv2026

AOC-CBS: Anytime-Optimal Continuous-time Conflict-Based Search for Generalised Multi-Agent Path Finding

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.

cs.MA↗

arXiv2026

Zero-Shot Generalization from Motion Demonstrations to New Tasks

Learning motion policies from expert demonstrations is an essential paradigm in modern robotics. While end-to-end models aim for broad generalization, they require large datasets and computationally heavy inference. Conversely, learning dynamical systems (DS) provides fast, reactive, and provably stable control from very few demonstrations. However, existing DS learning methods typically model isolated tasks and struggle to reuse demonstrations for novel behaviors. In this work, we formalize the problem of combining isolated demonstrations within a shared workspace to enable generalization to unseen tasks. The Gaussian Graph is introduced, which reinterprets spatial components of learned motion primitives as discrete vertices with connections to one another. This formulation allows us to bridge continuous control with discrete graph search. We propose two frameworks leveraging this graph: Stitching, for constructing time-invariant DSs, and Chaining, giving a sequence-based DS for complex motions while retaining convergence guarantees. Simulations and real-robot experiments show that these methods successfully generalize to new tasks where baseline methods fail.

cs.RO↗

arXiv2026

A General Formulation for the Teaching Assignment Problem: Computational Analysis Over a Real-World Dataset

The Teacher Assignment Problem is a combinatorial optimization problem that involves assigning teachers to courses while guaranteeing that all courses are covered, teachers do not teach too few or too many hours, teachers do not switch assigned courses too often and possibly teach the courses they favor. Typically the problem is solved manually, a task that requires several hours every year. In this work we present a mathematical formulation for the problem and an experimental evaluation of the model implemented using state-of-the-art SMT, CP, and MILP solvers. The implementations are tested over a real-world dataset provided by the Division of Systems and Control at Chalmers University of Technology, and produce teacher assignments with smaller workload deviation, a more even workload distribution among the teachers, and a lower number of switched courses.

eess.SY↗

arXiv2025

Optimal Multi-Agent Path Finding in Continuous Time

Continuous-time Conflict Based Search (CCBS) has been widely used as an exact baseline for Continuous-time Multi-Agent Path Finding (MAPFR), and its correctness guarantees underpin a range of continuation methods built on top of it. Recent work, however, has shown that CCBS's guarantees of exactness and solution completeness do not in fact hold: optimal solutions can be removed from the search, causing the algorithm to return suboptimal solutions. This paper establishes sufficient conditions for exactness and solution completeness in CCBS-style algorithms, and introduces Optimal Continuous-time Conflict-Based Search (OC-CBS) which satisfies these conditions. OC-CBS therefore guarantees an optimal solution on every solvable MAPFR instance. Experiments on benchmark problems show that OC-CBS remains competitive with CCBS in runtime while providing formal correctness guarantees. Because OC-CBS is a drop-in replacement for CCBS, it also restores the theoretical guarantees of existing methods that relied on CCBS's now-invalidated correctness. Finally, the framework and correctness criteria offer a general foundation for analyzing and designing future exact MAPFR solvers.

cs.MA↗

arXiv2025

A Comparative Study of SMT and MILP for the Nurse Rostering Problem

The effects of personnel scheduling on the quality of care and working conditions for healthcare personnel have been thoroughly documented. However, the ever-present demand and large variation of constraints make healthcare scheduling particularly challenging. This problem has been studied for decades, with limited research aimed at applying Satisfiability Modulo Theories (SMT). SMT has gained momentum within the formal verification community in the last decades, leading to the advancement of SMT solvers that have been shown to outperform standard mathematical programming techniques. In this work, we propose generic constraint formulations that can model a wide range of real-world scheduling constraints. Then, the generic constraints are formulated as SMT and MILP problems and used to compare the respective state-of-the-art solvers, Z3 and Gurobi, on academic and real-world inspired rostering problems. Experimental results show how each solver excels for certain types of problems; the MILP solver generally performs better when the problem is highly constrained or infeasible, while the SMT solver performs better otherwise. On real-world inspired problems containing a more varied set of shifts and personnel, the SMT solver excels. Additionally, it was noted during experimentation that the SMT solver was more sensitive to the way the generic constraints were formulated, requiring careful consideration and experimentation to achieve better performance. We conclude that SMT-based methods present a promising avenue for future research within the domain of personnel scheduling.

cs.AI↗

arXiv2025

Prioritized Planning for Continuous-time Lifelong Multi-agent Pathfinding

Multi-agent Path Finding (MAPF) is the problem of planning collision-free movements of agents so that they get from where they are to where they need to be. Commonly, agents are located on a graph and can traverse edges. This problem has many variations and has been studied for decades. Two such variations are the continuous-time and the lifelong MAPF problems. In the former, edges have non-unit lengths and volumetric agents can traverse them at any real-valued time. In the latter, agents must attend to a continuous stream of incoming tasks. Much work has been devoted to designing solution methods within these two areas. To our knowledge, however, the combined problem of continuous-time lifelong MAPF has yet to be addressed. This work addresses continuous-time lifelong MAPF with volumetric agents by presenting the fast and sub-optimal Continuous-time Prioritized Lifelong Planner (CPLP). CPLP continuously assigns agents to tasks and computes plans using a combination of two path planners; one based on CCBS and the other based on SIPP. Experimental results with up to 800 agents on graphs with up to 12 000 vertices demonstrate practical performance, where maximum planning times fall within the available time budget. Additionally, CPLP ensures collision-free movement even when failing to meet this budget. Therefore, the robustness of CPLP highlights its potential for real-world applications.

eess.SY↗