Planning With Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz Constants Article Swipe
Craig Knuth
,
Glen Chou
,
Necmiye Özay
,
Dmitry Berenson
·
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1109/lra.2021.3068889
YOU?
·
· 2021
· Open Access
·
· DOI: https://doi.org/10.1109/lra.2021.3068889
We present a method for feedback motion planning of systems with unknown dynamics which provides probabilistic guarantees on safety, reachability, and goal stability. To find a domain in which a learned control-affine approximation of the true dynamics can be trusted, we estimate the Lipschitz constant of the difference between the true and learned dynamics, and ensure the estimate is valid with a given probability. Provided the system has at least as many controls as states, we also derive existence conditions for a one-step feedback law which can keep the real system within a small bound of a nominal trajectory planned with the learned dynamics. Our method imposes the feedback law existence as a constraint in a sampling-based planner, which returns a feedback policy around a nominal plan ensuring that, if the Lipschitz constant estimate is valid, the true system is safe during plan execution, reaches the goal, and is ultimately invariant in a small set about the goal. We demonstrate our approach by planning using learned models of a 6D quadrotor and a 7DOF Kuka arm. We show that a baseline which plans using the same learned dynamics without considering the error bound or the existence of the feedback law can fail to stabilize around the plan and become unsafe.
Related Topics
Concepts
Reachability
Lipschitz continuity
Probabilistic logic
System dynamics
Computer science
Constant (computer programming)
Control theory (sociology)
Motion planning
Trajectory
Invariant (physics)
Constraint (computer-aided design)
Mathematical optimization
Mathematics
Control (management)
Robot
Theoretical computer science
Artificial intelligence
Astronomy
Mathematical physics
Physics
Geometry
Programming language
Mathematical analysis
Metadata
- Type
- preprint
- Language
- en
- Landing Page
- https://doi.org/10.1109/lra.2021.3068889
- OA Status
- green
- Cited By
- 3
- References
- 37
- Related Works
- 20
- OpenAlex ID
- https://openalex.org/W3134132640
All OpenAlex metadata
Raw OpenAlex JSON
- OpenAlex ID
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https://openalex.org/W3134132640Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.1109/lra.2021.3068889Digital Object Identifier
- Title
-
Planning With Learned Dynamics: Probabilistic Guarantees on Safety and Reachability via Lipschitz ConstantsWork title
- Type
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preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2021Year of publication
- Publication date
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2021-03-25Full publication date if available
- Authors
-
Craig Knuth, Glen Chou, Necmiye Özay, Dmitry BerensonList of authors in order
- Landing page
-
https://doi.org/10.1109/lra.2021.3068889Publisher landing page
- Open access
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YesWhether a free full text is available
- OA status
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greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2010.08993Direct OA link when available
- Concepts
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Reachability, Lipschitz continuity, Probabilistic logic, System dynamics, Computer science, Constant (computer programming), Control theory (sociology), Motion planning, Trajectory, Invariant (physics), Constraint (computer-aided design), Mathematical optimization, Mathematics, Control (management), Robot, Theoretical computer science, Artificial intelligence, Astronomy, Mathematical physics, Physics, Geometry, Programming language, Mathematical analysisTop concepts (fields/topics) attached by OpenAlex
- Cited by
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3Total citation count in OpenAlex
- Citations by year (recent)
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2023: 1, 2022: 1, 2021: 1Per-year citation counts (last 5 years)
- References (count)
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37Number of works referenced by this work
- Related works (count)
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20Other works algorithmically related by OpenAlex
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