iLQR Solver

JAX-based implementation of the iterative Linear Quadratic Regulator (iLQR) with multiple examples. For a full derivation see the tutorial here.

Car Parking	Cart Pole	Rocket Landing

Installation

The repo includes a venv with all dependencies. Just run:

make test

The Makefile uses the venv automatically—no activation needed.

Fresh Installation

# Requires Python 3.10+
python -m venv venv
source venv/bin/activate
pip install -e .

Includes CUDA 12 GPU support by default. For CUDA 11 or CPU-only, edit requirements.txt (see file comments).

Quick Start

from ilqr import iLQR
import jax.numpy as jnp

# Define your dynamics
def dynamics(state, control):
    # Your dynamics here
    return next_state

# Define your cost
def build_cost():
    def stage_cost(x, u):
        # Stage cost
        return cost_value

    def terminal_cost(x_T):
        # Terminal cost
        return cost_value

    def traj_cost(xs, us):
        # Full trajectory cost
        return total_cost

    return {"stage": stage_cost, "terminal": terminal_cost, "traj": traj_cost}

# Setup and solve
cost = build_cost()
dims = {"state": n, "control": m}
ilqr = iLQR(cost, dynamics, horizon, dims)
(states, controls), (success, stats) = ilqr.solve(x0, u_init)

Running Tests

make test-all      # Run all tests and generate animations
make test-parking  # Car parking with animation
make test-cartpole # Cart pole balancing with animation
make test-rocket   # Rocket landing with animation
make test-bicycle  # Bicycle navigation with animation
make test-unit     # Unit test for iLQR in a LQ system

Tests generate plots and animations in figures/.

Available Solvers

• LQR - Linear Quadratic Regulator
• iLQR - Iterative LQR for nonlinear systems
• iLQRAdaptive - iLQR with variable dynamics
• iLQRAdaptiveAugmented - iLQR with constraints (augmented Lagrangian)

Dependencies

Python 3.10+ with:

• JAX 0.6.2 (CUDA 12 GPU support)
• NumPy 2.2.6
• Matplotlib 3.10.6
• SciPy 1.15.3

Fast Iteration

1. Edit src/ilqr/solvers.py
2. Run make test
3. Check figures/ for plots

Changes apply immediately (editable install).