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A Scalable Safety Critical Control Framework for Nonlinear Systems

Gurriet, Thomas and Mote, Mark and Singletary, Andrew and Nilsson, Petter and Feron, Eric and Ames, Aaron D. (2020) A Scalable Safety Critical Control Framework for Nonlinear Systems. IEEE Access, 8 . pp. 187249-187275. ISSN 2169-3536. https://resolver.caltech.edu/CaltechAUTHORS:20200925-104734853

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Abstract

There are two main approaches to safety-critical control. The first one relies on computation of control invariant sets and is presented in the first part of this work. The second approach draws from the topic of optimal control and relies on the ability to realize Model-Predictive-Controllers online to guarantee the safety of a system. In the second approach, safety is ensured at a planning stage by solving the control problem subject for some explicitly defined constraints on the state and control input. Both approaches have distinct advantages but also major drawbacks that hinder their practical effectiveness, namely scalability for the first one and computational complexity for the second. We therefore present an approach that draws from the advantages of both approaches to deliver efficient and scalable methods of ensuring safety for nonlinear dynamical systems. In particular, we show that identifying a backup control law that stabilizes the system is in fact sufficient to exploit some of the set-invariance conditions presented in the first part of this work. Indeed, one only needs to be able to numerically integrate the closed-loop dynamics of the system over a finite horizon under this backup law to compute all the information necessary for evaluating the regulation map and enforcing safety. The effect of relaxing the stabilization requirements of the backup law is also studied, and weaker but more practical safety guarantees are brought forward. We then explore the relationship between the optimality of the backup law and how conservative the resulting safety filter is. Finally, methods of selecting a safe input with varying levels of trade-off between conservatism and computational complexity are proposed and illustrated on multiple robotic systems, namely: a two-wheeled inverted pendulum (Segway), an industrial manipulator, a quadrotor, and a lower body exoskeleton.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/access.2020.3025248DOIArticle
ORCID:
AuthorORCID
Gurriet, Thomas0000-0002-5240-3720
Singletary, Andrew0000-0001-6635-4256
Nilsson, Petter0000-0001-8748-6936
Feron, Eric0000-0001-7717-2159
Ames, Aaron D.0000-0003-0848-3177
Additional Information:© 2020 The Author(s). This work is licensed under a Creative Commons Attribution 4.0 License. The associate editor coordinating the review of this manuscript and approving it for publication was Wonhee Kim. This work has been supported by Wandercraft, the Caltech Big Ideas and ZEITLIN Funds, the NASA JPL President’s and Director’s Fund, the NSF Graduate Research Fellowship No. DGE-1745301, and NSF Awards No. 1724464, 1544332, 1724457, 1446758. The authors would like to thank Laurent Ciarletta for his pivotal role in making this work possible. The authors would also like to thank Maegan Tucker for her valuable help with the Variable Assistance part of this work, and Terry Suh for seeding the Industrial Manipulator part of this work.
Funders:
Funding AgencyGrant Number
WandercraftUNSPECIFIED
Caltech Big Ideas FundUNSPECIFIED
JPL President and Director's FundUNSPECIFIED
Zac and Amanda Zeitlin Family FundUNSPECIFIED
NSF Graduate Research FellowshipDGE-1745301
NSFIIS-1724464
NSFCNS-1544332
NSFCNS-1724457
NSFCNS-1446758
Subject Keywords:Safety-critical Control, Nonlinear Control, Real-time Optimization, Optimal Control, Viability Theory, Barrier Functions
Record Number:CaltechAUTHORS:20200925-104734853
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200925-104734853
Official Citation:T. Gurriet, M. Mote, A. Singletary, P. Nilsson, E. Feron and A. D. Ames, "A Scalable Safety Critical Control Framework for Nonlinear Systems," in IEEE Access, vol. 8, pp. 187249-187275, 2020, doi: 10.1109/ACCESS.2020.3025248.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105555
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:25 Sep 2020 19:38
Last Modified:20 Nov 2020 23:30

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