1. Viability Envelopes Maciej Kalisiak Michiel van de Panne

2. Idea and Motivation exploring “pushing the envelope” metaphor –i.e., operating at/near (safe) limits have the computer enforce safety –task: contain system state in envelope viability theory: too general, abstract our work: concrete, implementable solution

3. Envelope example: rocket X out = X f  X fi X in = X op  X ur want to operate in X op …... or at least X in

4. Containment: 1-step idea: override user input if it breaches envelope in 1 time step limited usefulness: sharp corrections

5. Containment: multi-step idea: look further ahead advantages: –milder corrections –useful info for haptics, allows guidance –more robust with approximate envelopes

6. Practical Trade-offs approximate envelope using Nearest Neighbor discretize control space

7. Results [show movies externally] rocket (2D) car on straight road (2D) bicycle balance (2D) car in arbitrary terrain (3D)

8. Future work more complex systems local-only knowledge of terrain “building block”, archetype envelopes explore how best to use with haptics

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