Collocation Station

A software tool for configuring and solving optimal control (or trajectory optimization) problems via the method of collocation.

What is it?

Our solver, Collocation Station, allows users to solve problems that would once have been deemed impossible. Dynamic optimisation is a fiendishly difficult challenge; when dealing with a dynamic system causality renders traditional optimisation methods almost useless. If, for instance, you change the input to your system at the start of a simulation, that affects the behaviour at all points into the future. This makes it next to impossible to determine the optimal set of inputs over the entire time horizon.

Collocation however, allows a complete solution to such problems. The key step is to transform the simulation problem into an optimisation problem, and simultaneously solve for the controls and the states of the system.

This might sound horribly complicated, and it is! Fortunately, however, our solvers make it easy for users to interface with any dynamical system they choose.

Usage Examples

Find the 60,000 unknowns required to drive an F1 round a track in the minimum time possible, while respecting limits on fuel consumption. 

Use the minimum possible amount of fuel to fly a commercial airliner along a set course through a moving wind field, in a fixed amount of time.

Find the 30,000 unknowns to perform the perfect foiling tack in an America’s Cup yacht.

Determine the optimum set of controls to pilot a container vessel through a varying wind and tide field while using the smallest possible amount of fuel.

Constantly recompute the optimal collision avoidance strategy for a driverless car.


Having been proven to be highly robust and extremely fast, we have licensed out our collocation solver to external customers with great success in addition to using it internally in our industry leading lap time simulation tools.

The mathematical details are fiendish, but the applications of collocation are many and varied, and all deliver either performance or cost savings, or both!