Dynamical System Segmentation for Information Measures in Motion

Berrueta, Thomas A.; Pervan, Ana; Fitzsimons, Kathleen; Murphey, Todd D.

doi:10.1109/lra.2018.2884091

Cited by 10 publications

(9 citation statements)

References 30 publications

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“…Given a candidate control signal, we apply a nonparametric, unsupervised learning algorithm, dynamical system segmentation (DSS), to discover ensemble-level behaviors in relation to the signal. DSS extracts distinct system dynamics from the interactions of internal states and, when present, the effect of candidate control signals on states (45). Initially, the algorithm constructs a set of system models over sequential windows in time-each locally capturing the net effect of interactions between internal states and candidate control signals on the ensemble dynamics.…”

Section: Discovering Emergent Control Authoritymentioning

confidence: 99%

A robot made of robots: Emergent transport and control of a smarticle ensemble

et al. 2019

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Robot locomotion is typically generated by coordinated integration of single-purpose components, like actuators, sensors, body segments, and limbs. We posit that certain future robots could self-propel using systems in which a delineation of components and their interactions is not so clear, becoming robust and flexible entities composed of functional components that are redundant and generic and can interact stochastically. Control of such a collective becomes a challenge because synthesis techniques typically assume known input-output relationships. To discover principles by which such future robots can be built and controlled, we study a model robophysical system: planar ensembles of periodically deforming smart, active particles—smarticles. When enclosed, these individually immotile robots could collectively diffuse via stochastic mechanical interactions. We show experimentally and theoretically that directed drift of such a supersmarticle could be achieved via inactivation of individual smarticles and used this phenomenon to generate endogenous phototaxis. By numerically modeling the relationship between smarticle activity and transport, we elucidated the role of smarticle deactivation on supersmarticle dynamics from little data—a single experimental trial. From this mapping, we demonstrate that the supersmarticle could be exogenously steered anywhere in the plane, expanding supersmarticle capabilities while simultaneously enabling decentralized closed-loop control. We suggest that the smarticle model system may aid discovery of principles by which a class of future “stochastic” robots can rely on collective internal mechanical interactions to perform tasks.

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Section: Discovering Emergent Control Authoritymentioning

confidence: 99%

A robot made of robots: Emergent transport and control of a smarticle ensemble

et al. 2019

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“…There are, of course, a variety of methods that one could use to select an appropriate basis for a given dynamical system. This step is particularly important as selecting a poor basis will quickly degrade the validity of the learned model (Berrueta et al, 2018). One such method is to integrate known information about the system dynamics into the chosen basis functions, such as the relationship between the heading of the lander and the motion generated by the main thruster.…”

Section: Mbscmentioning

confidence: 99%

“…(c) Allocate control to integrate autonomy (gray) and user input (green/red). (Berrueta et al, 2018). One such method is to integrate known information about the system dynamics into the chosen basis functions, such as the relationship between the heading of the lander and the motion generated by the main thruster.…”

Section: Model Learning Via the Koopman Operatormentioning

confidence: 99%

Data-driven Koopman operators for model-based shared control of human–machine systems

Broad

Abraham

Murphey

et al. 2020

The International Journal of Robotics Research

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We present a data-driven shared control algorithm that can be used to improve a human operator’s control of complex dynamic machines and achieve tasks that would otherwise be challenging, or impossible, for the user on their own. Our method assumes no a priori knowledge of the system dynamics. Instead, both the dynamics and information about the user’s interaction are learned from observation through the use of a Koopman operator. Using the learned model, we define an optimization problem to compute the autonomous partner’s control policy. Finally, we dynamically allocate control authority to each partner based on a comparison of the user input and the autonomously generated control. We refer to this idea as model-based shared control (MbSC). We evaluate the efficacy of our approach with two human subjects studies consisting of 32 total participants (16 subjects in each study). The first study imposes a linear constraint on the modeling and autonomous policy generation algorithms. The second study explores the more general, nonlinear variant. Overall, we find that MbSC significantly improves task and control metrics when compared with a natural learning, or user only, control paradigm. Our experiments suggest that models learned via the Koopman operator generalize across users, indicating that it is not necessary to collect data from each individual user before providing assistance with MbSC. We also demonstrate the data efficiency of MbSC and, consequently, its usefulness in online learning paradigms. Finally, we find that the nonlinear variant has a greater impact on a user’s ability to successfully achieve a defined task than the linear variant.

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“…For many systems, due to the presence of friction, this can often be represented as the zerovelocity state. For nonlinear systems with multiple equilibria points, one can use work in [61] to obtain multiple local Koopman representations.…”

Section: B Stability-based Conditions For Koopman Basis Functionsmentioning

confidence: 99%

Learning Stable Models for Prediction and Control

Mamakoukas¹,

Abraham²,

Murphey³

2020

Preprint

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In this paper, we consider the problem of improving the long-term accuracy of data-driven approximations of Koopman operators, which are infinite-dimensional linear representations of general nonlinear systems, by bounding the eigenvalues of the linear operator. We derive a formula for the global error of general Koopman representations and motivate imposing stability constraints on the data-driven model to improve the approximation of nonlinear systems over a longer horizon. In addition, constraints on admissible basis functions for a stable Koopman operator are presented, as well as conditions for constructing a Lyapunov function for nonlinear systems. The modified linear representation is the nearest stable (all eigenvalues are equal or less than 1) matrix solution to a least-squares minimization and bounds the prediction of the system response. We demonstrate the benefit of stable Koopman operators in prediction and control performance using the systems of a pendulum, a hopper, and a quadrotor.

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Dynamical System Segmentation for Information Measures in Motion

Cited by 10 publications

References 30 publications

A robot made of robots: Emergent transport and control of a smarticle ensemble

A robot made of robots: Emergent transport and control of a smarticle ensemble

Data-driven Koopman operators for model-based shared control of human–machine systems

Learning Stable Models for Prediction and Control

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