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Computing Reachable Sets via Toolbox of Level Set Methods Mo Chen Slides adapted from Michael Vitus and Jerry Ding.

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Presentation on theme: "Computing Reachable Sets via Toolbox of Level Set Methods Mo Chen Slides adapted from Michael Vitus and Jerry Ding."— Presentation transcript:

1 Computing Reachable Sets via Toolbox of Level Set Methods Mo Chen Slides adapted from Michael Vitus and Jerry Ding

2 Toolbox of Level Set Methods Ian Mitchell –Professor at the University of British Columbia MatLab Toolbox –http://www.cs.ubc.ca/~mitchell/ToolboxLS/ind ex.htmlhttp://www.cs.ubc.ca/~mitchell/ToolboxLS/ind ex.html –Computes the backwards reachable set starting from some final target set –Fixed spacing Cartesian grid –Up to 4 or 5 dimensions

3 Backwards Reachability [Mitchell, 2005]

4 Problem Formulation

5 Backwards Reachable Set

6 Toolbox Formulation

7 Example: Double Integrator

8 Start from Examples\Reachability\air3D.m

9 Example: Grid and Target Set Set-up grid and target set –g.bdry usually –g.bdry for periodic dimensions

10 Example: Double Integrator

11 Hamiltonian and Partial Functions

12 Hamiltonian and Partial Function

13

14 Example: Double Integrator Set up partials function

15 Results

16 Additional Comments Hamiltonian overestimated  reachable set underestimated Partials function (Pages of Toolbox manual) –Underestimation  numerical instability –Overestimation  rounded corners or worst case underestimation of reachable set Computation –The solver grids the state space –Tractable only up to 4-5 continuous states –Advanced: Can also define avoid sets Toolbox –Coding: ~90% is setting up the environment

17 Useful Dynamical Form for Partial Function

18 Other Tools Plotting utilities –Kernel\Helper\Visualization –visualizeLevelSet.m –spinAnimation.m Initial condition helpers –Cylinders, hyperrectangles Advice –Start with a small example –Look over air3D.m along with Section of toolbox manual


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