arXiv subjects

Anders Robertsson

Publications and source records attributed to Anders Robertsson.

14 recordsLinked to original sources

arXiv2026

On boundedness of solutions of three-state Moore-Greitzer compressor model with nonlinear proportional-integral controller for the surge subsystem

The work focuses on Lagrange stability of the origin for the three-state Moore-Greitzer compressor model in closed loop with a nonlinear PI controller, tuned only to stabilize a lower-dimensional invariant surge-dynamics subsystem.The linearization of the system is not stabilizable but the static nonlinearity satisfies a sector condition, and together with a structural property of the stall-dynamics subsystem, this plays an essential role in the analysis. The main contribution provides explicit conditions on the controller parameters together with analytical arguments that guarantee boundedness of all solutions of the closed-loop system. The analysis employs a non-standard application of circle-criterion-based arguments. Together with the additional arguments developed in the work, this stability test also shows that the closed-loop system is robust to certain perturbations and model uncertainties.

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arXiv2023

A Robust Observer with Gyroscopic Bias Correction for Rotational Dynamics

We propose an observer for rotational dynamics subject to directional and gyroscopic measurements, which simultaneously estimates the gyroscopic biases and attitude rates. We show uniform almost global asymptotic and local exponential stability of the resulting error dynamics, implying robustness against bounded disturbances. This robustness is quantified with respect to a popular nonlinear complementary filter in quantitative simulation studies, and we explore how the measurement noise propagates to the asymptotic errors as a function of tuning. This is an extended version of a paper with the same title (to appear at IFAC WC 2023). Additional mathematical details are provided in this extended version.

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arXiv2022

Cooperative constrained motion coordination of networked heterogeneous vehicles

We consider the problem of cooperative motion coordination for multiple heterogeneous mobile vehicles subject to various constraints. These include nonholonomic motion constraints, constant speed constraints, holonomic coordination constraints, and equality/inequality geometric constraints. We develop a general framework involving differential-algebraic equations and viability theory to determine coordination feasibility for a coordinated motion control under heterogeneous vehicle dynamics and different types of coordination task constraints. If a coordinated motion solution exists for the derived differential-algebraic equations and/or inequalities, a constructive algorithm is proposed to derive an equivalent dynamical system that generates a set of feasible coordinated motions for each individual vehicle. In case studies on coordinating two vehicles, we derive analytical solutions to motion generation for two-vehicle groups consisting of car-like vehicles, unicycle vehicles, or vehicles with constant speeds, which serve as benchmark coordination tasks for more complex vehicle groups. The motion generation algorithm is well-backed by simulation data for a wide variety of coordination situations involving heterogeneous vehicles. We then extend the vehicle control framework to deal with the cooperative coordination problem with time-varying coordination tasks and leader-follower structure. We show several simulation experiments on multi-vehicle coordination under various constraints to validate the theory and the effectiveness of the proposed schemes.

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arXiv2021

Quadrotor Control on $SU(2)\times R^3$ with SLAM Integration

We present a trajectory tracking controller for a quadrotor unmanned aerial vehicle (UAV) configured on $SU(2)\times R^3$, and relate this result to a family of geometric tracking controllers on $SO(3)\times R^3$. The theoretical results are complemented by simulation examples, and the controller is subsequently implemented in practice and integrated with a simultaneous localization and mapping (SLAM) system through an extended Kalman filter (EKF). This facilitates the operation of the UAV without external motion capture systems, and we demonstrate that the proposed control system can be used for inventorying tasks in a supermarket environment without external positioning systems.

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arXiv2021

Distributed adaptive stabilization

In this paper we consider distributed adaptive stabilization for uncertain multivariable linear systems with a time-varying diagonal matrix gain. We show that uncertain multivariable linear systems are stabilizable by diagonal matrix high gains if the system matrix is an H-matrix with positive diagonal entries. Based on matrix measure and stability theory for diagonally dominant systems, we consider two classes of uncertain linear systems, and derive a threshold condition to ensure their exponential stability by a monotonically increasing diagonal gain matrix. When each individual gain function in the matrix gain is updated by state-dependent functions using only local state information, the boundedness and convergence of both system states and adaptive matrix gains are guaranteed. We apply the adaptive distributed stabilization approach to adaptive synchronization control for large-scale complex networks consisting of nonlinear node dynamics and time-varying coupling weights. A unified framework for adaptive synchronization is proposed that includes several general design approaches for adaptive coupling weights to guarantee network synchronization.

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arXiv2019

Segmentation of Robot Movements using Position and Contact Forces

In this paper, a method for autonomous segmentation of demonstrated robot movements is proposed. Position data is clustered into Gaussian mixture models (GMMs), and an initial set of segments is identified from the Gaussian basis functions. A Kalman filter is used to detect sudden changes in the contact force/torque measurements, and this is used to update and verify the initial segmentation points. The segmentation method is verified experimentally on an industrial robot.

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arXiv2019

Autonomous Interpretation of Demonstrations for Modification of Dynamical Movement Primitives

The concept of dynamical movement primitives (DMPs) has become popular for modeling of motion, commonly applied to robots. This paper presents a framework that allows a robot operator to adjust DMPs in an intuitive way. Given a generated trajectory with a faulty last part, the operator can use lead-through programming to demonstrate a corrective trajectory. A modified DMP is formed, based on the first part of the faulty trajectory and the last part of the corrective one. A real-time application is presented and verified experimentally.

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arXiv2019

Temporally Coupled Dynamical Movement Primitives in Cartesian Space

Control of robot orientation in Cartesian space implicates some difficulties, because the rotation group SO(3) is not contractible, and only globally contractible state spaces support continuous and globally asymptotically stable feedback control systems. In this paper, unit quaternions are used to represent orientations, and it is first shown that the unit quaternion set minus one single point is contractible. This is used to design a control system for temporally coupled dynamical movement primitives (DMPs) in Cartesian space. The functionality of the control system is verified experimentally on an industrial robot.

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arXiv2018

Temporal viability regulation for control affine systems with applications to mobile vehicle coordination under time-varying motion constraints

Controlled invariant set and viability regulation of dynamical control systems have played important roles in many control and coordination applications. In this paper we develop a temporal viability regulation theory for general dynamical control systems, and in particular for control affine systems. The time-varying viable set is parameterized by time-varying constraint functions, with the aim to regulate a dynamical control system to be invariant in the time-varying viable set so that temporal state-dependent constraints are enforced. We consider both time-varying equality and inequality constraints in defining a temporal viable set. We also present sufficient conditions for the existence of feasible control input for the control affine systems. The developed temporal viability regulation theory is applied to mobile vehicle coordination.

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arXiv2018

Feasibility and coordination of multiple mobile vehicles with mixed equality and inequality constraints

We consider the problem of feasible coordination control for multiple homogeneous or heterogeneous mobile vehicles subject to various constraints (nonholonomic motion constraints, holonomic coordination constraints, equality/inequality constraints etc). We develop a general framework involving differential-algebraic equations and viability theory to describe and determine coordination feasibility for a coordinated motion control under heterogeneous vehicle dynamics and different types of coordination constraints. If a solution exists for the derived differential-algebraic equations and/or inequalities, a heuristic algorithm is proposed for generating feasible trajectories for each individual vehicle. In case studies on coordinating two vehicles, we derive analytical solutions to motion generation for two-vehicle groups consisting of car-like vehicles, unicycle vehicles, or vehicles with constant speeds, which serve as benchmark coordination tasks for more complex vehicle groups. We show several simulation experiments on multi-vehicle coordination under various constraints to validate the theory and the effectiveness of the proposed schemes.

eess.SY↗

arXiv2018

Tangent-Space Regularization for Neural-Network Models of Dynamical Systems

This work introduces the concept of tangent space regularization for neural-network models of dynamical systems. The tangent space to the dynamics function of many physical systems of interest in control applications exhibits useful properties, e.g., smoothness, motivating regularization of the model Jacobian along system trajectories using assumptions on the tangent space of the dynamics. Without assumptions, large amounts of training data are required for a neural network to learn the full non-linear dynamics without overfitting. We compare different network architectures on one-step prediction and simulation performance and investigate the propensity of different architectures to learn models with correct input-output Jacobian. Furthermore, the influence of $L_2$ weight regularization on the learned Jacobian eigenvalue spectrum, and hence system stability, is investigated.

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arXiv2018

Identification of LTV Dynamical Models with Smooth or Discontinuous Time Evolution by means of Convex Optimization

We establish a connection between trend filtering and system identification which results in a family of new identification methods for linear, time-varying (LTV) dynamical models based on convex optimization. We demonstrate how the design of the cost function promotes a model with either a continuous change in dynamics over time, or causes discontinuous changes in model coefficients occurring at a finite (sparse) set of time instances. We further discuss the introduction of priors on the model parameters for situations where excitation is insufficient for identification. The identification problems are cast as convex optimization problems and are applicable to, e.g., ARX models and state-space models with time-varying parameters. We illustrate usage of the methods in simulations of jump-linear systems, a nonlinear robot arm with non-smooth friction and stiff contacts as well as in model-based, trajectory centric reinforcement learning on a smooth nonlinear system.

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arXiv2017

On a Feedback Control-based Mechanism of Bidding for Cloud Spot Service

As a cost-effective option for Cloud consumers, spot service has been considered to be a significant supplement for building a full-fledged market economy for the Cloud ecosystem. However, unlike the static and straightforward way of trading on-demand and reserved Cloud services, the market-driven regulations of employing spot service could be too complicated for Cloud consumers to comprehensively understand. In particular, it would be both difficult and tedious for potential consumers to determine suitable bids from time to time. To reduce the complexity in applying spot resources, we propose to use a feedback control to help make bidding decisions. Based on an arccotangent-function-type system model, our novel bidding mechanism imitates fuzzy and intuitive human activities to refine and issue new bids according to previous errors. The validation is conducted by using Amazon's historical spot price trace to perform a set of simulations and comparisons. The result shows that the feedback control-based mechanism obtains a better trade-off between bidding rationality and success rate than the other five comparable strategies. Although this mechanism is only for black-box bidding (price prediction) at this current stage, it can be conveniently and gradually upgraded to take into account external constraints in the future.

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arXiv2017

Using a Predator-Prey Model to Explain Variations of Cloud Spot Price

The spot pricing scheme has been considered to be resource-efficient for providers and cost-effective for consumers in the Cloud market. Nevertheless, unlike the static and straightforward strategies of trading on-demand and reserved Cloud services, the market-driven mechanism for trading spot service would be complicated for both implementation and understanding. The largely invisible market activities and their complex interactions could especially make Cloud consumers hesitate to enter the spot market. To reduce the complexity in understanding the Cloud spot market, we decided to reveal the backend information behind spot price variations. Inspired by the methodology of reverse engineering, we developed a Predator-Prey model that can simulate the interactions between demand and resource based on the visible spot price traces. The simulation results have shown some basic regular patterns of market activities with respect to Amazon's spot instance type m3.large. Although the findings of this study need further validation by using practical data, our work essentially suggests a promising approach (i.e.~using a Predator-Prey model) to investigate spot market activities.

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