Configuring and solving optimal control (trajectory optimisation) problems using collocation

Collocation 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 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. Our collocation solver is integral to both our simulations platform and our self-driving solution.


Elite motorsport teams from across the globe use our simulations platform to leapfrog the competition. Canopy gives our customers best-in-class simulation capability at a fraction of the cost of developing in-house.

Canopy’s collocation solver allows us to quickly find the 60,000 unknowns required to drive an F1 car around a track in the minimum time possible, while respecting regulatory constraints, such as fuel and energy limits.


INEOS Team UK used Canopy’s collocation solver to develop their America’s Cup boat model, resulting in the world’s first, probably only, optimal control simulation of a fully dynamic model of a foiling sailing boat. This has proved extremely useful to the team not only for designing a type of boat that no-one has built before, but for teaching the sailors how to sail it. As ITUK chief designer Nick Holroyd said,

“The partnership with Canopy Simulations has given us big gains in the design process . . . we’ve quickly learnt how to sail the boat in the most efficient way – all whilst staying on dry land.”

The mathematical details are fiendish, but the applications of the Canopy collocation solver are many and varied, and all deliver performance, cost savings, enhanced safety, or all of the above.