# i2LQR: Iterative LQR for Iterative Tasks in Dynamic Environments

## TL;DR

i2LQR is a new control method that iteratively optimizes trajectories for tasks in dynamic environments, improving performance over existing methods by using historical data and adapting to changing constraints.

## Contribution

The paper introduces i2LQR, a reference-free, iterative control algorithm that enhances closed-loop performance for iterative tasks in dynamic environments using local trajectory optimization.

## Key findings

- i2LQR outperforms LMPC in dynamic environments with obstacles.
- i2LQR achieves better completion time optimization in simulations.
- The method adapts to changing constraints across iterations.

## Abstract

This work introduces a novel control strategy called Iterative Linear Quadratic Regulator for Iterative Tasks (i2LQR), which aims to improve closed-loop performance with local trajectory optimization for iterative tasks in a dynamic environment. The proposed algorithm is reference-free and utilizes historical data from previous iterations to enhance the performance of the autonomous system. Unlike existing algorithms, the i2LQR computes the optimal solution in an iterative manner at each timestamp, rendering it well-suited for iterative tasks with changing constraints at different iterations. To evaluate the performance of the proposed algorithm, we conduct numerical simulations for an iterative task aimed at minimizing completion time. The results show that i2LQR achieves an optimized performance with respect to learning-based MPC (LMPC) as the benchmark in static environments, and outperforms LMPC in dynamic environments with both static and dynamics obstacles.