Risk-Aware Path Planning

My master's research asked a stubborn question: when a drone flies farther than anyone can see it, how should it choose a route that minimizes the damage of being wrong?

Shortest-path is the wrong objective. In controlled airspace, a 3 km route that grazes a hospital helipad is worse than a 5 km route around it — even if the long one is "safe" at the level of meters. Risk is not binary. It has altitude, population, weather, and a time of day.

The core idea: spend resolution where consequence lives

A uniform grid forces one resolution everywhere. Fly over an empty field and you still pay per cell. Fly over a stadium and you still get one coarse "medium risk." Both are wrong.

The framework stores risk in a layered sampling quadtree: dense where the world is dense, sparse where the world is boring, and every level of the tree is queryable at flight time.

L0  ▣ 5 km cells      — corridor-level weather, terrain mask
L1  ▣ 500 m cells     — population, NOTAM regions
L2  ▣ 50 m cells      — no-fly polygons, obstacles, gyms with cranes

Risk at a point is an interval: the coarse layers give a trend, the fine layers give a confidence width. The planner never sees a single optimistic number pretending to be truth.

Risk-aware A*

The planner is A* over a 3D graph with a cost function that reads the quadtree interval — not just the mean. The weighting is where the research lives: how much to pay for variance versus expected exposure.

| Cost term | Plain A* | Risk-aware | | --- | --- | --- | | Distance | ✓ | ✓ | | Expected exposure | — | mean risk × time in cell | | Uncertainty | — | interval width penalty | | Hard constraints | point queries | tree-consistent volumes |

Why a simulator and not just a solver

A planner people can't watch is a planner people won't trust. The second half of the thesis was a Cesium/Unity visualization where routes fly against live terrain and airspace layers — the same interface later doubled as the defense-demo stage.

⌖Calgary — the terrain that taught me why corridor-level weather mattersclick to load

What transferred to industry

• Interval reasoning beats point estimates in production autonomy — the same discipline behind honest confidence in any perception stack.
• Resolution is budget: store truth at the granularity the decision actually consumes, not the granularity available.
• Visual proof sells algorithms. Every reviewer could watch the route fail gracefully around a stadium instead of reading a table.

The full thesis lives at the University of Calgary repository. Happy to walk anyone through the quadtree math — that's what the contact page is for.