Direct collocation

Summary

Direct collocation is a method of trajectory optimization that turns an optimal control problem into a finite nonlinear program. It represents the state and the control by their values on a time grid. It imposes the differential equation only at chosen collocation points, through a polynomial model of the state on each interval. The cost integral becomes a quadrature sum, and the resulting sparse nonlinear program is solved by a general optimiser. It is "direct" because it discretises first and does not use the maximum principle.