Robust Dynamic Tube MPC

This repo contains uncertain discrete time linear models and examples of applying time-varying tube-based model predictive control (MPC). Global RRT/RRT* planner included for tube-to-tube steering with obstacles.

Dependenices:

• MATLAB controls toolbox
• YALMIP
• MOSEK
• MPT3

Setup

startup
test(true)

Example Use Cases

Elastic Tube Optimal Control

1. Edit initial state and elasticity weighting in example file
2. Set useDataFile to false to recompute tube approximation parameters if you want to see all the action

run_planar_double_integrator

Tube-to-Tube Sampling-Based Motion Planning

1. Edit maximum iterations, initial/final nominal states, and ETOC solver tube length(s) in example file
2. Create additional obstacles using polytopes in build_map.m

run_rrt_example

Data Structures

Tube

Fields	Description	Size	Type
z	Nominal state trajectory	(nx,N)	float
v	Nominal control input sequence	(nu,N)	float
a	Cross section elasticitiy parameter sequence	(qs,N)	float
N	Number of time steps	scalar	int
cost	Total cost for tube solution	scalar	float
success	Valid solution success flag	scalar	bool

System

Fields	Description	Size	Type
A	Linear discrete time system state matrix	(nx,nx)	float
B	Linear discrete time system control matrix	(nx,nu)	float
x0	Initial state	(nx,1)	float
x_min	State lower bound	(nx,1)	float
x_max	State upper bound	(nx,1)	float
u_min	Control lower bound	(nu,1)	float
u_max	Control upper bound	(nu,1)	float
w_min	Disturbance lower bound	(nw,1)	float
w_max	Disturbance upper bound	(nw,1)	float
name	System name (for plotting)	1	str
nx	Number of states	1	float
nu	Number of controls	1	float
nw	Number of disturbances	1	float

TODO

March 2022

• Speed up preprocessing
• Add support for homothetic and fixed size tubes
• Add different boundary condition options
  • Set-based initial and final conditions
  • Support mixed set and state boundary conditions
• Verify objective function for non-zero goal state
• Update stale models
  • double_integrator_model.m
  • spring_mass_damper_model.m
• Add full state vs. time plotting to all postprocessing scripts
• Decide on node and edge data for tube-to-tube RRT* tree
• Add RRT planner

April 2022

• Add tube-to-tube ETOC steering to RRT planner
  • Add tube obstacle collision check
  • Decide on constant or decreasing prediction horizon
• Decide on rewiring strategy for RRT* planner
• Full example using basic map and planar_double_integrator_model.m
• RRT* planner (DOING)
• Add vehicle model
• Add additional map options to build_map.m
  • Map saving
  • Non-convex obstacles
• Additional example with more complex obstacle environment

References

ETMPC

@INPROCEEDINGS{7525471,
author={Raković, Sas̆a V. and Levine, William S. and Açikmese, Behçet}, 
booktitle={2016 American Control Conference (ACC)},   
title={Elastic tube model predictive control},   
year={2016},  
volume={},  
number={},  
pages={3594-3599},  
doi={10.1109/ACC.2016.7525471}}

HTMPC

@INPROCEEDINGS{6561023,
author={Raković, Saša V. and Cheng, Qifeng},
booktitle={2013 25th Chinese Control and Decision Conference (CCDC)},
title={Homothetic tube MPC for constrained linear difference inclusions},
year={2013},
volume={},
number={},
pages={754-761},
doi={10.1109/CCDC.2013.6561023}}