Supervisory control of differentially flat systems based on abstraction

Colombo, Alessandro; Vecchio, Domitilla Del

doi:10.1109/cdc.2011.6160759

Cited by 24 publications

(22 citation statements)

References 14 publications

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“…While we seek formal guarantees on the behavior of the 12-dimensional closed- loop system, we do not propose to perform formal synthesis on a model this large. Similarly to the work in [8,9], we focus on the regulation of a subset of system states and use advanced nonlinear control methods to transform the complex dynamics to a simpler, more tractable system which is amenable to the correct-by-construction synthesis techniques. In contrast to [8,9], where the authors exploit differential flatness to reduce the nonlinear synthesis problem to a controller design problem for a chain of integrators, our method applies to the aforementioned hybrid system with non-flat outputs.…”

Section: Introductionmentioning

confidence: 99%

First steps toward formal controller synthesis for bipedal robots with experimental implementation

Ames

Tabuada

Jones

et al. 2017

Nonlinear Analysis: Hybrid Systems

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Bipedal robots are prime examples of complex cyber-physical systems (CPS). They exhibit many of the features that make the design and verification of CPS so difficult: hybrid dynamics, large continuous dynamics in each mode (e.g., 10 or more state variables), and nontrivial specifications involving nonlinear constraints on the state variables. In this paper, we propose a two-step approach to formally synthesize controllers for bipedal robots so as to enforce specifications by design and thereby generate physically realizable stable walking. In the first step, we design outputs and classical controllers driving these outputs to zero. The resulting controlled system evolves on a lower dimensional manifold and is described by the hybrid zero dynamics governing the remaining degrees of freedom. In the second step, we construct an abstraction of the hybrid zero dynamics that is used to synthesize a controller enforcing the desired specifications to be satisfied on the full order model. Our two step approach is a systematic way to mitigate the curse of dimensionality that hampers the applicability of formal synthesis techniques to complex CPS. Our results are illustrated with simulations showing how the synthesized controller enforces all the desired specifications and offers improved performance with respect to a classical controller. The practical relevance of the results is illustrated experimentally on the bipedal robot AMBER 3. High-level motion primitives were used on MABEL to allow walking over rough ground without tripping. While tools for automatic low-level control algorithm synthesis are well developed, at the state machine level, all tuning was done by hand for lack of appropriate tools. "Probable correctness" was established through extensive simulation and experiments.

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Section: Introductionmentioning

confidence: 99%

First steps toward formal controller synthesis for bipedal robots with experimental implementation

Ames

Tabuada

Jones

et al. 2017

Nonlinear Analysis: Hybrid Systems

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“…We directly exploit the simple structure of first order vehicle dynamics with model uncertainty to construct a finite deterministic DES abstraction. In contrast to [11], our results deal with model uncertainty and handle the presence of uncontrolled vehicles. In particular, we introduce a deterministic DES that simulates the original continuous system, and such that the continuous system alternatingly simulates the DES (see, e.g., [5] for the definitions of similarity and alternating similarity).…”

Section: Introductionmentioning

confidence: 99%

“…In [10], the problem of robot control is considered by applying an abstraction based on triangularization and designing a low-level (continuous) control to satisfy path specifications expressed in linear temporal logic (LTL). In [11], the dynamic properties of common mechanical systems (including models of vehicle dynamics) were exploited to obtain a safetyenforcing supervisory control based on a deterministic abstraction, irrespective of the stability properties of the dynamics. An alternative solution, based on an equivalence relation between the collision avoidance problem and a scheduling problem, Del Vecchio is with the ME Dept.…”

Section: Introductionmentioning

confidence: 99%

Supervisory control for collision avoidance in vehicular networks using discrete event abstractions

Dallal

Colombo

Vecchio

et al. 2016

Discrete Event Dyn Syst

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Abstract-We consider the problem of collision avoidance at vehicular intersections for a set of controlled and uncontrolled vehicles that are linked by wireless communication. Each vehicle is modeled by a first order system. We use a disturbance to account for bounded model uncertainty. We construct a discrete event system abstraction and formulate the problem in the context of supervisory control for discrete event systems with uncontrollable events. This allows us to mitigate computational limitations related to the presence of continuous dynamics and infinite state spaces. For solving the resulting supervisory control problem at the discrete event level, we develop an algorithm that exploits the structure of the transition map to compute the supremal controllable sublanguage more efficiently than standard algorithms. We present implementation results on an intersection with several vehicles.

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“…The approach presented in this paper cannot be directly extended to the multiple vehicle scenario due to the bad set not being convex. Alternative approaches are being investigated, including discrete abstraction techniques exploiting the fact that the vehicles dynamics are differentially flat and order preserving [4].…”

Section: Application Scenariomentioning

confidence: 99%

Control of Hidden Mode Hybrid Systems: Algorithm termination

Verma

Vecchio

2011

2011 14th International IEEE Conference on Intelligent Transportation Systems (ITSC)

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Abstract-We consider the problem of safety control in Hidden Mode Hybrid Systems (HMHS) that arises in the development of a semi-autonomous cooperative active safety system for collision avoidance at an intersection. We utilize the approach of constructing a new hybrid automaton whose discrete state is an estimate of the HMHS mode. A dynamic feedback map can then be designed that guarantees safety on the basis of the current mode estimate and the concept of the capture set. In this work, we relax the conditions for the termination of the algorithm that computes the capture set by constructing an abstraction of the new hybrid automaton. We present a relation to compute the capture set for the abstraction and show that this capture set is equal to the one for the new hybrid automaton.

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Supervisory control of differentially flat systems based on abstraction

Cited by 24 publications

References 14 publications

First steps toward formal controller synthesis for bipedal robots with experimental implementation

First steps toward formal controller synthesis for bipedal robots with experimental implementation

Supervisory control for collision avoidance in vehicular networks using discrete event abstractions

Control of Hidden Mode Hybrid Systems: Algorithm termination

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