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DirectTrajOpt.jl

Documentation
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MIT License

DirectTrajOpt.jl is a framework for direct trajectory optimization via nonlinear programming. It converts continuous optimal control problems into finite-dimensional NLPs using direct transcription, then solves them with Ipopt.

Problem Formulation

DirectTrajOpt solves problems of the form:

\[\begin{align*} \underset{x_{1:N}, u_{1:N}}{\text{minimize}} \quad & J(x_{1:N}, u_{1:N}) \\ \text{subject to} \quad & f(x_{k+1}, x_k, u_k, \Delta t, t_k) = 0, \quad k = 1, \ldots, N-1\\ & c_k(x_k, u_k) \geq 0, \quad k = 1, \ldots, N \\ & x_1 = x_{\text{init}}, \quad x_N = x_{\text{goal}} \\ \end{align*}\]

where:

  • J(x, u) is the objective function to minimize
  • f(.) represents system dynamics encoded via integrators
  • c(.) represents additional nonlinear constraints
  • x is the state trajectory
  • u is the control trajectory

Installation

using Pkg
Pkg.add("DirectTrajOpt")

Quick Example

using DirectTrajOpt
using NamedTrajectories

# Define trajectory
traj = NamedTrajectory(
    (x = randn(2, 50), u = randn(1, 50), Δt = fill(0.1, 50));
    timestep=:Δt,
    controls=:u,
    initial=(x = [0.0, 0.0],),
    final=(x = [1.0, 0.0],)
)

# Define dynamics: dx/dt = (A + u * B) * x
G_drift = [-0.1 1.0; -1.0 -0.1]
G_drives = [[0.0 1.0; 1.0 0.0]]
G = u -> G_drift + sum(u .* G_drives)
integrator = BilinearIntegrator(G, :x, :u, traj)

# Define objective
obj = QuadraticRegularizer(:u, traj, 1.0)

# Create and solve problem
prob = DirectTrajOptProblem(traj, obj, integrator)
solve!(prob; max_iter=100)

Key Features

  • Flexible dynamics: Define system evolution via bilinear, time-dependent, or derivative integrators
  • Modular objectives: Combine cost terms with + and * (regularization, minimum time, terminal cost, etc.)
  • Constraint support: Bounds, equality, nonlinear, symmetry, and L1 slack constraints
  • Automatic differentiation: Sparse Jacobians and Hessians via ForwardDiff
  • Solver callbacks: Monitor and control the optimization process

Contributing

Building Documentation

This package uses a shared Documenter config. First-time setup:

./docs/get_docs_utils.sh

Build docs:

julia --project=docs docs/make.jl

Live editing:

julia --project=docs -e '
  using LiveServer, DirectTrajOpt, Revise
  servedocs(
    literate_dir="docs/literate",
    skip_dirs=["docs/src/generated", "docs/src/assets/"],
    skip_files=["docs/src/index.md"]
  )'

Note:servedocs will loop if it watches generated files. Ensure all generated files are in the skip dirs/files args.