Add collocation method for optimal control problems #799
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This PR changes the default way that optimal control problems are solved from using a shooting method to using collocation. This results in more robust (and faster) solutions, especially for trajectory generation for unstable or marginally stable systems (where shooting is very sensitive to small parameter variations).
The following new functionality is included:
solve_ocp()
function andOptimalControlProblem
class have new parameterstrajectory_method
that be set to eithershooting
(default for discrete time systems) orcollocation
(default for continuous time systems).initial_guess
parameter can either be an input trajectory (as before) or a tuple consisting of a state trajectory and an input trajectory.LinearConstraint(A, lb, ub)
orNonlinearConstraint(fun, lb, ub)
instead of the previous forms(LinearConstraint, A, lb, ub)
and(NonlinearConstraint, fun, lb, ub)
. The legacy format is still supported.This PR also addresses issue #782 (see also discussion in #781) which were showing some of the weakness of the shooting methodology.