# This is DDP with multi-shooting method[1].
This code is based on https://kr.mathworks.com/matlabcentral/fileexchange/52069-ilqg-ddp-trajectory-optimization [2].

# How to Use it
(1) open the demo_car.m or demo_linear.m
(2) Set M value 
    (if M = 1 -> DDP with single shooting)
    (if M = 2 -> DDP with multiple shooting(2))
    (if M = 50 -> DDP with multiple shooting(50))
(3) Enjoy this.

# Result
(1) Simple linear system
  - https://youtu.be/3l3JnmAX3to  (for single shooting)
  - https://youtu.be/8XM5ZEnpmEI  (for multiple shooting (50))
  
(2) Car system
  - https://youtu.be/LlpsMyVBrmc  (for single shooting)
  - https://youtu.be/MM8C0l71mHo  (for multiple shooting (50))
  
ps. Maybe this code is not perfect. So, if you find some bugs in this code, plz send to me by mail (ggory15@snu.ac.kr)

[1] A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control
(https://arxiv.org/abs/1711.11006) 
[2] Control-Limited Differential Dynamic Programming
(https://homes.cs.washington.edu/~todorov/papers/TassaICRA14.pdf)