Non-linear model predictive control (NMPC) with differential dynamic drogramming (DDP)

https://github.com/isri-aist/NMPC/assets/6636600/02f64c91-88aa-42d8-abfd-f8062d7406e9

Features

C++ header-only library
Treats state and control input dimensions as template parameters
Supports time-varying control input dimensions
Supports constrained control input

Install

See here.

Technical details

See the following for a detailed algorithm.

Y Tassa, T Erez, E Todorov. Synthesis and stabilization of complex behaviors through online trajectory optimization. IROS, 2012.
Y Tassa, N Mansard, E Todorov. Control-limited differential dynamic programming. ICRA, 2014.

The source code implementation is based on the following.

https://www.mathworks.com/matlabcentral/fileexchange/52069-ilqg-ddp-trajectory-optimization

Examples

Make sure that it is built with --catkin-make-args tests option.

Bipedal dynamics

Controlling on CoM-ZMP dynamics with time-variant CoM height. System is linear and time-variant.

$ rosrun nmpc_ddp TestDDPBipedal

$ rosrun nmpc_ddp plotTestDDPBipedal.py

TestDDPBipedal

Controlling vertical motion with time-variant number of contacts (including floating phase). System is linear and time-variant. The dimension of the control input changes (there are even time steps with an empty control input). The upper and lower limits are imposed on the control input.

$ rosrun nmpc_ddp TestDDPVerticalMotion --gtest_filter=*.WithConstraint
$ # rosrun nmpc_ddp TestDDPVerticalMotion --gtest_filter=*.WithoutConstraint # Try the unconstrained case
$ rosrun nmpc_ddp plotTestDDPVerticalMotion.py

TestDDPVerticalMotion

Cart-pole

Controlling cart-pole (also known as inverted pendulum). System is non-linear. This is an example of a realistic setup where the control and simulation have different time periods.

# 10-second simulation
$ rostest nmpc_ddp TestDDPCartPole.test --text
# Endless simulation
$ rostest nmpc_ddp TestDDPCartPole.test no_exit:=true --text

TestDDPCartPole

You can interactively add disturbances and change the target position via the GUI. See the video.

Centroidal motion

$ rosrun nmpc_ddp TestDDPCentroidalMotion