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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