A Data-driven Hierarchical Control Structure for Systems with Uncertainty

Shi, Lu; Teng, Hanzhe; Kan, Xinyue; Karydis, Konstantinos

doi:10.1109/ccta41146.2020.9206349

Cited by 8 publications

(10 citation statements)

References 38 publications

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“…(10) Note that as illustrated in (8), for a dynamical system evolving by K, (11) Using matrix format of (11) and ∆K i = [∆k i ab ] Q×Q from ( 7), we can first compute the dot product of these two matrices and then obtain the prediction error as the sum of each element of the dot product, that is…”

Section: Sensitivity Analysis Of Predicted Outputmentioning

confidence: 99%

“…Yet, there exist many instances in which robots interact physically with their environment and that these interactions are uncertain. Examples include robots operating in partially-known dynamic environments [5]; legged robots traversing non-smooth terrains [6,7]; quadrotors flying under the influence of uncertain aerodynamic effects [8][9][10][11]; underwater robots affected by uncertain ocean currents [12]; and steerable needles interacting with soft tissue [13]. Thus, employing pre-selected models may restrict the capability to predict actual robot behaviors when operating under uncertainty [14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

“…A different way to address uncertainties in robotenvironment interactions is by extracting dynamics from data. Multiple distinct approaches have been proposedincluding stochastic model extension [17], (deep) reinforcement learning [18], (deep) neural networks [19,20], and spectral methods [21], to name a few-and deployed in robotics (e.g., [11,17,[22][23][24][25]). The advent of data-driven methods for modeling complex dynamical systems creates a need for theoretical safety and/or performance guarantees.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Enhancement for Robustness of Koopman Operator-based Data-driven Mobile Robotic Systems

Shi¹,

Karydis²

2021

Preprint

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Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. Despite its widespread use, research on safety guarantees for systems the dynamics of which are extracted via the Koopman operator, has started receiving attention only recently. In this paper, we propose a way to quantify the prediction error because of noisy measurements when the Koopman operator is approximated via Extended Dynamic Mode Decomposition. We further develop an enhanced robot control strategy to endow robustness to a class of data-driven (robotic) systems that rely on Koopman operator theory, and we show how part of the strategy can happen offline in an effort to make our algorithm capable of real-time implementation. We perform a parametric study to evaluate the (theoretical) performance of the algorithm using a Van der Pol oscillator, and conduct a series of simulated experiments in Gazebo using a non-holonomic wheeled robot.

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Section: Sensitivity Analysis Of Predicted Outputmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Enhancement for Robustness of Koopman Operator-based Data-driven Mobile Robotic Systems

Shi¹,

Karydis²

2021

Preprint

Self Cite

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“…A novel model-free adaptive SMC approach for unknown discrete nonlinear processes was designed [35] by bringing the merits of datadriven control strategy and SMC scheme together, which made the system with model uncertainty of strong robustness. A data-driven hierarchical control (DHC) structure was introduced [36] to ameliorate the performance of systems under the effect of the system uncertainty. e above references demonstrate both robust model predictive control and data-driven strategy which are effective methods to work out the problem of system uncertainty so that it is very important to study the data-driven robust distributed model predictive control with system uncertainty.…”

Section: Introductionmentioning

confidence: 99%

A Distributed Model Predictive Control for Multiple Mobile Robots with the Model Uncertainty

Shang

Zhu

Pan

et al. 2021

Discrete Dynamics in Nature and Society

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In this paper, a distributed predictive control with the model uncertainty which uses the data-driven strategy and robust theory (data-driven RDMPC) is proposed for the formation control of multiple mobile robots. The robust performance objective minimization is applied to replace the quadratic performance objective minimization to establish the optimization problem, where the model uncertainty is considered in the distributed system. The control policy is derived by applying the data-driven strategy, and the future predictive value is obtained by employing the linear law in the historical data. Lyapunov theory is referred to analyze the stability of the mobile robot formation system. The effectiveness of the proposed method is proved by a set of simulation experiments.

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“…In an effort to handle approximate models (or lack thereof) that serve as a target for motion control of (nonlinear) robotic systems, methods based on Koopman operator theory are increasingly used in the context of robotics. Recent examples include modeling and control of a tail-actuated robotic fish [5], trajectory control of micro-aerial vehicles [6], dynamics estimation for a spherical robot [7], model extraction for a simulated lunar lander system [8], as well as model extraction and control for soft robotic arms [9]- [12] and underwater soft robots [13].…”

Section: Introductionmentioning

confidence: 99%

ACD-EDMD: Analytical Construction for Dictionaries of Lifting Functions in Koopman Operator-based Nonlinear Robotic Systems

Shi¹,

Karydis²

2021

Preprint

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Koopman operator theory has been gaining momentum for model extraction, planning, and control of datadriven robotic systems. The Koopman operator's ability to extract dynamics from data depends heavily on the selection of an appropriate dictionary of lifting functions. In this paper we propose ACD-EDMD, a new method for Analytical Construction of Dictionaries of appropriate lifting functions for a range of data-driven Koopman operator based nonlinear robotic systems.The key insight of this work is that information about fundamental topological spaces of the nonlinear system (such as its configuration space and workspace) can be exploited to steer the construction of Hermite polynomial-based lifting functions. We show that the proposed method leads to dictionaries that are simple to implement while enjoying provable completeness and convergence guarantees when observables are weighted bounded. We evaluate ACD-EDMD using a range of diverse nonlinear robotic systems in both simulated and physical hardware experimentation (a wheeled mobile robot, a two-revolute-joint robotic arm, and a soft robotic leg). Results reveal that our method leads to dictionaries that enable high-accuracy prediction and that can generalize to diverse validation sets. The associated GitHub repository of our algorithm can be accessed at https: //github.com/UCR-Robotics/ACD-EDMD.

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A Data-driven Hierarchical Control Structure for Systems with Uncertainty

Cited by 8 publications

References 38 publications

Enhancement for Robustness of Koopman Operator-based Data-driven Mobile Robotic Systems

Enhancement for Robustness of Koopman Operator-based Data-driven Mobile Robotic Systems

A Distributed Model Predictive Control for Multiple Mobile Robots with the Model Uncertainty

ACD-EDMD: Analytical Construction for Dictionaries of Lifting Functions in Koopman Operator-based Nonlinear Robotic Systems

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