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https://github.com/thowell/iterativelqr.jl
A Julia package for constrained iterative LQR (iLQR)
https://github.com/thowell/iterativelqr.jl
control differential-dynamic-programming ilqr motion-planning optimization robotics trajectory-optimization
Last synced: about 5 hours ago
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A Julia package for constrained iterative LQR (iLQR)
- Host: GitHub
- URL: https://github.com/thowell/iterativelqr.jl
- Owner: thowell
- License: mit
- Created: 2021-10-25T03:51:02.000Z (about 3 years ago)
- Default Branch: main
- Last Pushed: 2023-03-17T16:03:07.000Z (over 1 year ago)
- Last Synced: 2024-10-10T05:36:07.708Z (about 1 month ago)
- Topics: control, differential-dynamic-programming, ilqr, motion-planning, optimization, robotics, trajectory-optimization
- Language: Julia
- Homepage:
- Size: 101 KB
- Stars: 41
- Watchers: 2
- Forks: 13
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# IterativeLQR.jl
[](https://github.com/thowell/IterativeLQR.jl/actions/workflows/CI.yml)
[](https://codecov.io/gh/thowell/IterativeLQR.jl)
A Julia package for solving constrained trajectory optimization problems with iterative LQR (iLQR).
$$
\begin{align*}
\underset{x_{1:T}, \phantom{\,} u_{1:T-1}}{\text{minimize }} & \phantom{,} g_T(x_T; \theta_T) + \sum \limits_{t = 1}^{T-1} g_t(x_t, u_t; \theta_t)\\
\text{subject to } & \phantom{,} f_t(x_t, u_t; \theta_t) = x_{t+1}, \phantom{,} \quad t = 1,\dots,T-1,\\
& \phantom{,} c_t(x_t, u_t; \theta_t) \phantom{,}[\leq, =] \phantom{,} 0, \quad t = 1, \dots, T,\\
\end{align*}
$$
with
- $x_{1:T}$: state trajectory
- $u_{1:T-1}$: action trajectory
- $\theta_{1:T}$: problem-data trajectory
- Fast and allocation-free gradients and Jacobians are automatically generated using [Symbolics.jl](https://github.com/JuliaSymbolics/Symbolics.jl) for user-provided costs, constraints, and dynamics.
- Constraints are handled using an [augmented Lagrangian framework](https://en.wikipedia.org/wiki/Augmented_Lagrangian_method).
- Cost, dynamics, and constraints can have varying dimensions at each time step.
- Parameters are exposed (and gradients wrt these values coming soon!)
For more details, see our related paper: [ALTRO: A Fast Solver for Constrained Trajectory Optimization](http://roboticexplorationlab.org/papers/altro-iros.pdf)
## Installation
From the Julia REPL, type `]` to enter the Pkg REPL mode and run:
```julia
pkg> add https://github.com/thowell/IterativeLQR.jl
```
## Quick Start
```julia
using IterativeLQR
using LinearAlgebra
# horizon
T = 11
# particle
num_state = 2
num_action = 1
function particle_discrete(x, u)
A = [1.0 1.0; 0.0 1.0]
B = [0.0; 1.0]
return A * x + B * u[1]
end
# model
particle = Dynamics(particle_discrete, num_state, num_action)
model = [particle for t = 1:T-1]
# initialization
x1 = [0.0; 0.0]
xT = [1.0; 0.0]
ū = [1.0e-1 * randn(num_action) for t = 1:T-1]
x̄ = rollout(model, x1, ū)
# objective
objective = [
[Cost((x, u) -> 0.1 * dot(x, x) + 0.1 * dot(u, u), num_state, num_action) for t = 1:T-1]...,
Cost((x, u) -> 0.1 * dot(x, x), num_state, 0)
]
# constraints
constraints = [
[Constraint() for t = 1:T-1]...,
Constraint((x, u) -> x - xT, num_state, 0)
]
# solver
solver = Solver(model, objective, constraints)
initialize_controls!(solver, ū)
initialize_states!(solver, x̄)
# solve
solve!(solver)
# solution
x_sol, u_sol = get_trajectory(solver)
```
## Examples
Please see the following for examples using this package:
- [Trajectory Optimization with Optimization-Based Dynamics](https://github.com/thowell/optimization_dynamics)
- [Dojo: A Differentiable Simulator for Robotics](https://github.com/dojo-sim/Dojo.jl)