Alvin Combrink

I began my PhD in discrete optimisation for healthcare — assigning shifts and similar resource-scheduling problems using off-the-shelf SMT and MILP solvers. That project was discontinued after major organisational changes at the partner hospital. In April 2024, I took over a project on autonomous mobile robot scheduling from a colleague going on sabbatical — which turned out to be multi-agent path finding (MAPF), a topic that, amusingly, echoes my bachelor's thesis on robotic formation control which I had since left. Having to pivot halfway through my PhD studies, and having worked across healthcare scheduling, motion planning, and now MAPF, has given me a broader toolkit than if I'd specialised in one area from the start.

What drew me to continuous time specifically is that discretising time is a modelling choice made for convenience, not a constraint inherent to real systems — relaxing it opens the door to better solutions and far more realistic environments. That freedom comes at a cost, though: once agents can occupy any point in continuous time, you have to account for their physical volume and their actual position in space rather than on an abstract graph. From there, the natural extensions are multi-agent motion planning — letting agents follow kinodynamically feasible trajectories instead of straight lines at constant speed — and multi-goal tasks, since most real work involves picking something up and carrying it somewhere, not a single point-to-point trip.

My most significant contribution so far has been theoretical: Conflict-Based Search for continuous time (CCBS), a foundational method in the field, was recently found not to satisfy its own claimed optimality and termination guarantees. Correcting this took considerable groundwork, but with it in place I now have a solid foundation to build on. My current work is an anytime-optimal algorithm — one that returns a fast, suboptimal solution immediately and converges to the optimum given more time — aimed at larger systems with agents of many kinds and conflict types beyond simple geometric collision.

My division works across a broad mix of topics in automation and control; MAPF continues a lineage of work here on AMR scheduling and low-level robot control that predates my own involvement. I'll soon be applying for funding for an international postdoc, and welcome opportunities to collaborate on continuous-time planning, multi-robot coordination, and related problems.