Viability Envelopes
Maciej Kalisiak
Michiel van de Panne
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
Envelope example: rocket
• Xout = Xf Xfi
• Xin = Xop Xur
• want to operate in Xop…
• ... or at least Xin
Containment: 1-step
• idea: override user input if it breaches envelope in 1 time step
• limited usefulness: sharp corrections
Containment: multi-step
• idea: look further ahead• advantages:
– milder corrections
– useful info for haptics, allows guidance
– more robust with approximate envelopes
Practical Trade-offs• approximate envelope
using Nearest Neighbor• discretize control space
Results
[show movies externally]
• rocket (2D)• car on straight road (2D)• bicycle balance (2D)• car in arbitrary terrain (3D)
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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