TrajectoryOptimization.jl Documentation
Documentation for TrajectoryOptimization.jl
Overview
This package is a testbed for state-of-the-art trajectory optimization algorithms. Trajectory optimization problems are of the form,
\[\begin{aligned}
\min_{x_{0:N},u_{0:N-1}} \quad & \ell_f(x_N) + \sum_{k=0}^{N-1} \ell_k(x_k, u_k, dt) \\
\textrm{s.t.} \quad & x_{k+1} = f(x_k, u_k), \\
& g_k(x_k,u_k) \leq 0, \\
& h_k(x_k,u_k) = 0.
\end{aligned}\]
This package currently implements the following methods for solving trajectory optimization problems:
- Iterative LQR (iLQR): indirect method based on Differential Dynamic Programming
- AL-iLQR: iLQR within an Augmented Lagrangian framework
- Direct Collocation: direct method that formulates the problem as an NLP and passes the problem off to a commercial NLP solver
- ALTRO (Augmented Lagrangian Trajectory Optimizer): A novel algorithm developed by the Robotic Exploration Lab at Stanford University, which uses iLQR within an augmented Lagrangian framework combined with a "Projected Newton" direct method for solution polishing and enforcement of feasibility.
Key features include:
- Support for general, per-timestep constraints
- ForwardDiff for fast auto-differentiation of dynamics, cost functions, and constraints
Getting Started
To set up and solve a trajectory optimization problem with TrajectoryOptimization.jl, the user will go through the following steps:
- Create a Model
- Create an Objective
- (Optionally) Add constraints
- Instantiate a Problem
- Solve the problem