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tube-mpc
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# 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](https://www.mathworks.com/products/control.html) - [YALMIP](https://yalmip.github.io/tutorial/installation/) - [MOSEK](https://www.mosek.com/products/academic-licenses/) - [MPT3](https://www.mpt3.org/)   ## 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 - [x] Speed up preprocessing - [x] Add support for homothetic and fixed size tubes - [x] Add different boundary condition options - [x] Set-based initial and final conditions - [x] Support mixed set and state boundary conditions - [x] Verify objective function for non-zero goal state - [x] Update stale models - [x] `double_integrator_model.m` - [x] `spring_mass_damper_model.m` - [x] Add full state vs. time plotting to all postprocessing scripts - [x] Decide on node and edge data for tube-to-tube RRT* tree - [x] Add RRT planner ### April 2022 - [x] Add tube-to-tube ETOC steering to RRT planner - [x] Add tube obstacle collision check - [x] Decide on constant or decreasing prediction horizon - [x] Decide on rewiring strategy for RRT* planner - [x] 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}} ```
