Formation Tracking Control and Obstacle Avoidance of Unicycle-Type Robots Guaranteeing Continuous Velocities

Martínez, José; Becerra, Héctor M.; Gómez‐Gutiérrez, David

doi:10.3390/s21134374

Cited by 12 publications

(5 citation statements)

References 46 publications

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“…Considering the feedback-linearization technique used in [54], we introduce the common unicycle model, represented FIGURE 8: Guided partitioning converges to the "best possible" approximation error in 2 s, whereas uniform partitioning still has not converged using 12 × 12 partitioning with 5 s of calculation time.…”

Section: B Linearized Ground Robotmentioning

confidence: 99%

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

Rober

Katz

Sidrane

et al. 2023

IEEE Open J. Control. Syst.

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As neural networks (NNs) become more prevalent in safety-critical applications such as control of vehicles, there is a growing need to certify that systems with NN components are safe. This paper presents a set of backward reachability approaches for safety certification of neural feedback loops (NFLs), i.e., closed-loop systems with NN control policies. While backward reachability strategies have been developed for systems without NN components, the nonlinearities in NN activation functions and general noninvertibility of NN weight matrices make backward reachability for NFLs a challenging problem. To avoid the difficulties associated with propagating sets backward through NNs, we introduce a framework that leverages standard forward NN analysis tools to efficiently find over-approximations to backprojection (BP) sets, i.e., sets of states for which an NN policy will lead a system to a given target set. We present frameworks for calculating BP over-approximations for both linear and nonlinear systems with control policies represented by feedforward NNs and propose computationally efficient strategies. We use numerical results from a variety of models to showcase the proposed algorithms, including a demonstration of safety certification for a 6D system.

show abstract

Section: B Linearized Ground Robotmentioning

confidence: 99%

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

Rober

Katz

Sidrane

et al. 2023

IEEE Open J. Control. Syst.

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show abstract

“…Using the feedback linearization technique proposed in [35], we represent the common unicycle model as a pair of integrators…”

Section: B Linearized Ground Robotmentioning

confidence: 99%

Backward Reachability Analysis for Neural Feedback Loops

Rober¹,

Everett²,

How³

2022

Preprint

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The increasing prevalence of neural networks (NNs) in safety-critical applications calls for methods to certify their behavior and guarantee safety. This paper presents a backward reachability approach for safety verification of neural feedback loops (NFLs), i.e., closed-loop systems with NN control policies. While recent works have focused on forward reachability as a strategy for safety certification of NFLs, backward reachability offers advantages over the forward strategy, particularly in obstacle avoidance scenarios. Prior works have developed techniques for backward reachability analysis for systems without NNs, but the presence of NNs in the feedback loop presents a unique set of problems due to the nonlinearities in their activation functions and because NN models are generally not invertible. To overcome these challenges, we use existing forward NN analysis tools to find affine bounds on the control inputs and solve a series of linear programs (LPs) to efficiently find an approximation of the backprojection (BP) set, i.e., the set of states for which the NN control policy will drive the system to a given target set. We present an algorithm to iteratively find BP set estimates over a given time horizon and demonstrate the ability to reduce conservativeness in the BP set estimates by up to 88% with low additional computational cost. We use numerical results from a double integrator model to verify the efficacy of these algorithms and demonstrate the ability to certify safety for a linearized ground robot model in a collision avoidance scenario where forward reachability fails.

show abstract

“…Using a feedback linearization technique [51], we represent the common unicycle model as a pair of integrators…”

Section: B Linearized Ground Robotmentioning

confidence: 99%

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

Rober¹,

Katz²,

Sidrane³

et al. 2022

Preprint

View full text Add to dashboard Cite

The increasing prevalence of neural networks (NNs) in safety-critical applications calls for methods to certify safe behavior. This paper presents a backward reachability approach for safety verification of neural feedback loops (NFLs), i.e., closed-loop systems with NN control policies. While recent works have focused on forward reachability as a strategy for safety certification of NFLs, backward reachability offers advantages over the forward strategy, particularly in obstacle avoidance scenarios. Prior works have developed techniques for backward reachability analysis for systems without NNs, but the presence of NNs in the feedback loop presents a unique set of problems due to the nonlinearities in their activation functions and because NN models are generally not invertible. To overcome these challenges, we use existing forward NN analysis tools to efficiently find an over-approximation of the backprojection (BP) set, i.e., the set of states for which the NN control policy will drive the system to a given target set. We present frameworks for calculating BP over-approximations for both linear and nonlinear systems with control policies represented by feedforward NNs and propose computationally efficient strategies. We use numerical results from a variety of models to showcase the proposed algorithms, including a demonstration of safety certification for a 6D system.

show abstract

Formation Tracking Control and Obstacle Avoidance of Unicycle-Type Robots Guaranteeing Continuous Velocities

Cited by 12 publications

References 46 publications

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

Backward Reachability Analysis for Neural Feedback Loops

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

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