  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.
