Every mission starts with motion.
But before motion,
before planning,
before algorithms,
there must be something quieter—
understanding what the problem truly is.
This is Problem Formulation.
Not just a setup,
not just a diagram,
but the moment of definition—
where we decide what matters,
what constraints hold,
and what success looks like.
In robotics, autonomy, and flight systems, problem formulation is not technical decoration.
It is the blueprint.
The contract between the real world and the system that moves through it.
It asks:
– What is the system I’m working with?
– What are the goals?
– What are the constraints?
– What can be controlled?
– What must be observed?
– What defines success—and what defines failure?
A good problem formulation includes:
1. The State Space
What variables define the condition of the system?
Position? Velocity? Orientation? Fuel level? Battery life?
2. The Control Inputs
What can you influence directly?
Throttle? Steering angle? Bank rate? Camera tilt?
3. The Dynamics
How does the system evolve over time?
Are the equations linear or nonlinear? Deterministic or stochastic?
4. The Environment
What surrounds the system?
Obstacles? Winds? No-fly zones? Communication limits?
5. The Objective Function
What are we optimizing?
Time to goal? Energy consumed? Area covered? Risk avoided?
6. The Constraints
What must never be violated?
Minimum altitude? Maximum speed? Line-of-sight visibility? Fuel limits?
7. The Initial and Terminal Conditions
Where does it start—and where must it end?
Each of these is a lever.
Set them carefully, and the system responds in kind.
Miss one, and no algorithm—no matter how clever—can rescue the mission.
Problem formulation is not the place for assumptions to hide.
It is where complexity becomes clarity,
where ambiguity becomes structure,
and where goals become solvable paths.
This step determines:
– What kind of planner you use.
– Whether linear methods are enough.
– How uncertainty will be handled.
– Whether the solution is feasible—or even definable.
It applies across domains:
– For UAVs mapping terrain.
– For robots navigating rooms.
– For swarms dividing labor.
– For systems learning, reacting, and re-planning in real time.
Because even in the most adaptive systems,
the first intelligence is not in how the system moves—
but in how the question is asked.
That is the quiet brilliance of problem formulation:
Before the first move is made,
every important decision has already been shaped.