5. Solving the Problem

Solving a trajectory optimization is as simple as picking a solver and calling the solve! method. There are several solvers implemented in TrajectoryOptimization.jl, and each has its own limitations and solver options. See Solvers section for a list of the currently implemented solvers, their options, and their associated docstrings. See the Solver Interface section for more information on addition new solvers or leveraging the generic methods implemented by each solver.

Creating a Solver

Every solver is initialized with, at a minimum, a Problem and (optionally) the associated SolverOptions type. For example, let's say we want to solve our cartpole problem created in the previous section with AL-iLQR. Since iLQR is the default unconstrained solver for the Augmented Lagrangian solver, this is as easy as:

solver = AugmentedLagrangianSolver(prob)

Modifying solver options

We have a couple options for changing solver options. First, we can create the SolverOptions type, modify the desired fields, and then pass it into the constructor for the solver. For iLQR this looks like:

opts_ilqr = iLQRSolverOptions()                     # all fields default
opts_ilqr = iLQRSolverOptions(cost_tolerance=1e-4)  # specify options by keyword
opts_ilqr.iterations = 50                           # set fields manually
solver = iLQRSolver(prob, opts_ilqr)                # create the solver with the given options

Second, we can create the solver, and then modify it's options:

solver = iLQRSolver(prob)
solver.opts.iterations = 50

It should be noted that right now, the solver does NOT create a copy of the solver options when it's created. That is, changing opts_ilqr after creating the solver will change the options inside of solver, even after it's created, and vice versa.

Nested Solver Options

Some solvers, such as AugmentedLagrangianSolver and ALTROSolver rely directly on other solvers. As such, their solver option types store the solver options of their dependent solvers explicitly:

opts_al = AugmentedLagrangianSolverOptions()
opts_al.opts_uncon.iterations = 50  # set iLQR iterations
opts_al.iterations = 20             # set outer loop iterations

Solving the Problem

Solving the problem is as simple as calling solve! on the solver:

solver = AugmentedLagrangianSolver(prob)
solve!(solver)

Analyzing the Solution

There a few different ways to analyze the solution after the solve, detailed in the following sections.

Getting the solution

The state and control trajectories can be extracted using the following commands:

states(solver::AbstractSolver)
controls(solver::AbstractSolver)

These can be converted to 2D arrays with simple horizontal concatenation: hcat(X...). Note that these methods work on Problem types as well.