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Actuators
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Dynamics and Control of Underactuated Systems
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Dynamics and Control of Underactuated Systems

A special issue of Actuators (ISSN 2076-0825). This special issue belongs to the section "Control Systems".

Deadline for manuscript submissions: 15 April 2025 | Viewed by 4747

Special Issue Editors

Dr. Iacopo Tamellin

E-Mail Website
Guest Editor
Department of Management and Engineering, University of Padova, 36100 Vicenza, Italy
Interests: vibrating systems; dynamic structural modification; dynamic and control of mechatronic systems; multibody systems; underactuated systems; motion planning
Special Issues, Collections and Topics in MDPI journals
Dr. Jason Bettega

E-Mail Website
Guest Editor
Department of Management and Engineering, University of Padova, 36100 Vicenza, Italy
Interests: model predictive control; control of nonminimum-phase systems; control of multibody systems; inverse dynamics; underactuated systems; motion planning

Special Issue Information

Dear Colleagues,

Recently, interest has grown in the research field of underactuated systems. A system is said to be underactuated if the number of degrees of freedom within it is greater than the number of independent actuators. In industrial high-performance applications, this property occurs for several reasons. Firstly, it develops as a consequence of weight- or cost-driven design methodologies that fulfill some predefined specification, leading to a reduction in the number of required motors. Secondly, underactuation can arise due to the failure of one or more actuators. Lastly, in order to lower energy consumption and, for instance, fulfill one of the goals regarding the United Nations 2030 Development Agenda, the mass of the components should be significantly lowered. This yields lightweight, highly flexible components and renders underactuation less negligible. By taking all these possible situations into account in order to ensure good performances in the presence of underactuated systems, proper dynamic modeling and control strategies must be developed.

In this light, this Special Issue aims to present advances in both the dynamic modeling and control of underactuated systems.

Papers are welcome on topics that are related, but not limited, to:

  • Motion planning;
  • Inverse dynamics for underactuated systems;
  • Control of nonminimum-phase mechanical systems;
  • Feedforward control for mechanical systems;
  • Model predictive control for mechanical systems;
  • Active vibration control;
  • Parameter estimation and model updating;
  • Modeling and control of underactuated systems;
  • Modeling and control of flexible systems;
  • Modeling and control of underactuated multibody systems;
  • Underactuated robots;
  • Cable-driven robots.

We look forward to your valuable contribution.

Dr. Iacopo Tamellin
Dr. Jason Bettega
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Actuators is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • underactuated systems
  • motion planning
  • control of underactuated systems
  • dynamics of underactuated systems
  • inverse dynamics
  • flexible systems
  • vibration control

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Published Papers (5 papers)

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Research

18 pages, 5132 KiB  
Article
Adaptive Time-Varying Formation Maneuvering Control for Multi-Robot Systems in Complex Obstacle-Rich Environments
by Junmei Zhao, Liping Zhang, Xiao Li, Kewu Li, He Wang and Yeye Liu
Actuators 2024, 13(12), 493; https://doi.org/10.3390/act13120493 - 2 Dec 2024
Viewed by 310
Abstract
To tackle the challenge of time-varying formation control for underactuated robots under model parameter uncertainties and environmental disturbances, this study proposes an affine formation control approach enhanced by an Extended State Observer. Initially, using affine positioning theory and polynomial interpolation, guidelines for selecting [...] Read more.
To tackle the challenge of time-varying formation control for underactuated robots under model parameter uncertainties and environmental disturbances, this study proposes an affine formation control approach enhanced by an Extended State Observer. Initially, using affine positioning theory and polynomial interpolation, guidelines for selecting leader vehicles and trajectory planning methods are established, whereby the trajectory of follower vehicles is uniquely determined through the stress matrix. To address the cumulative disturbances arising from model uncertainties and environmental factors impacting the formation, an Extended State Observer with optimized parameters is introduced. Furthermore, a distributed affine formation control method with disturbance rejection is designed specifically for underactuated robots with “nonlinear, strongly coupled” dynamics, ensuring that the formation system can track the target configuration within bounded error margins. Finally, theoretical analysis and simulation outcomes ultimately confirm the efficacy of the control approach in achieving resilient formation tracking. Full article
(This article belongs to the Special Issue Dynamics and Control of Underactuated Systems)
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22 pages, 4230 KiB  
Article
Active Disturbance Rejection Control for the Trajectory Tracking of a Quadrotor
by Mario Ramírez-Neria, Alberto Luviano-Juárez, Jaime González-Sierra, Rodrigo Ramírez-Juárez, Joaquín Aguerrebere and Eduardo G. Hernandez-Martinez
Actuators 2024, 13(9), 340; https://doi.org/10.3390/act13090340 - 5 Sep 2024
Viewed by 781
Abstract
In the last decade, quadrotors have gained popularity among industry and academia due to their capabilities and the various applications in which they can be found. In addition to the above, because this is an underactuated system, researchers have found it a great [...] Read more.
In the last decade, quadrotors have gained popularity among industry and academia due to their capabilities and the various applications in which they can be found. In addition to the above, because this is an underactuated system, researchers have found it a great challenge to control. Despite this, there is a wide variety of methodologies in the literature to control this type of system. Based on the above, this work proposed an alternative to trajectory tracking control for quadrotor unmanned aerial vehicles (UAV). The problem was divided into two main control loops: an outer control loop for the position coordinates, tackled through linear active disturbance rejection controllers (ADRC), and an inner control loop related to the orientation variables, addressed via robust proportional-integral-differential (PID) controllers. Furthermore, a generalized proportional integral observer (GPIO) was implemented to estimate the velocity and internal and external disturbances; therefore, the control strategy only depended on the attitude (position and orientation) quadrotor measurements. Then, the control performance was tested through numerical simulations and experimental tests, including wind disturbance inputs. Full article
(This article belongs to the Special Issue Dynamics and Control of Underactuated Systems)
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12 pages, 443 KiB  
Article
Two-Stage Control Strategy Based on Motion Planning for Planar Prismatic–Rotational Underactuated Robot
by Dawei Li, Ziang Wei and Zixin Huang
Actuators 2024, 13(8), 278; https://doi.org/10.3390/act13080278 - 25 Jul 2024
Viewed by 862
Abstract
Intelligent robots are often used to explore various areas instead of humans. However, when the driving joint is damaged, the actuated robot degenerates to an underactuated robot, and the traditional control method is not suitable for the underactuated robot. In this work, a [...] Read more.
Intelligent robots are often used to explore various areas instead of humans. However, when the driving joint is damaged, the actuated robot degenerates to an underactuated robot, and the traditional control method is not suitable for the underactuated robot. In this work, a two-stage control approach for a planar prismatic–rotational (PR) underactuated robot is introduced. Firstly, we establish the dynamic model and describe the underactuated constraint between an underactuated rotational joint and active prismatic joint. Secondly, the trajectory with multiple parameters is planned to ensure that the two joints reach the target position. Based on underactuated constraints and the evaluation function, the differential evolution algorithm (DEA) is used to optimize these parameters. After that, in stage 1, we design the controller to move the active prismatic joint to the desired position. Meanwhile, the underactuated rotational joint is rotating freely. In stage 2, we design the controller for the active prismatic joint to track the planned trajectory. By means of this strategy, both joints reach their target locations simultaneously. The final simulation result demonstrates that this strategy is effective. Full article
(This article belongs to the Special Issue Dynamics and Control of Underactuated Systems)
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16 pages, 760 KiB  
Article
Dynamic Output Feedback of Second-Order Systems: An Observer-Based Controller with Linear Matrix Inequality Design
by Danielle Gontijo, José Mário Araújo, Luciano Frezzato and Fernando de Oliveira Souza
Actuators 2024, 13(6), 216; https://doi.org/10.3390/act13060216 - 9 Jun 2024
Viewed by 887
Abstract
This paper presents an observer-based dynamic output-feedback controller design procedure using linear matrix inequality (LMI) optimization for second-order systems with uncertainty and persistent perturbation in the states. Using linear-quadratic criteria, cost functions are minimized in a two-stage procedure to compute optimal state-feedback gains, [...] Read more.
This paper presents an observer-based dynamic output-feedback controller design procedure using linear matrix inequality (LMI) optimization for second-order systems with uncertainty and persistent perturbation in the states. Using linear-quadratic criteria, cost functions are minimized in a two-stage procedure to compute optimal state-feedback gains, and observer gains are coupled into a dynamic output-feedback optimal controller. The LMI set used in the two stages is matrix inversion free, a key issue for polytope formulation when uncertainty is present. The approach is tested in a mobile inverted pendulum robotic platform, and the effectiveness is verified in this underactuated and undesensed case. Full article
(This article belongs to the Special Issue Dynamics and Control of Underactuated Systems)
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21 pages, 7759 KiB  
Article
Trajectory Planning through Model Inversion of an Underactuated Spatial Gantry Crane Moving in Structured Cluttered Environments
by Jason Bettega, Dario Richiedei and Iacopo Tamellin
Actuators 2024, 13(5), 176; https://doi.org/10.3390/act13050176 - 7 May 2024
Viewed by 1061
Abstract
Handling suspended loads in cluttered environments is critical due to the oscillations arising while the load is traveling. Exploiting active control algorithms is often unviable in industrial applications, due to the necessity of installing sensors on the load side, which is expensive and [...] Read more.
Handling suspended loads in cluttered environments is critical due to the oscillations arising while the load is traveling. Exploiting active control algorithms is often unviable in industrial applications, due to the necessity of installing sensors on the load side, which is expensive and often impractical due to technological limitations. In this light, this paper proposes a trajectory planning method for underactuated, non-flat, non-minimum phase spatial gantry crane moving in structured cluttered environments. The method relies on model inversion. First, the system dynamics is partitioned into actuated and unactuated coordinates and then the load displacements are described as a non-linear separable function of these. The unactuated dynamic is unstable; hence, the displacement, velocity, and acceleration references are modified through the output redefinition technique. Finally, platform trajectory is computed, and the desired displacements of the load are obtained. The effectiveness of the proposed method is assessed through numerical and experimental tests performed on a laboratory testbed composed by an Adept Quattro robot moving a pendulum. The load is moved in a cluttered environment, and collisions are avoided while simultaneously tracking the prescribed trajectory effectively. Full article
(This article belongs to the Special Issue Dynamics and Control of Underactuated Systems)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Adaptive PID Control of a Quadrotor using Hybrid Particle Swarm Optimization
Authors: Ishaq Hafez; Rached Dhaouadi
Affiliation: American University of Sharjah, UAE
Abstract: This paper presents a novel solution to enhance quadrotor maneuvering and stabilization using a Hybrid Particle Swarm Optimization with Quasi-Newton (HPSO-QN) method for PID controller design. This advanced technique combines the global search capabilities of Particle Swarm Optimization (PSO) with the local search abilities of the Quasi-Newton (QN) method to estimate the optimal gains for controlling altitude and position trajectories. The tuning process is guided by an objective function that minimizes the mean squared error between the estimated and targeted state references. When compared to standard PSO algorithms, the HPSO-QN method shows significant improvements in terms of robustness and precision. These improvements underscore the effectiveness and potential of the HPSO-QN approach for complex control systems in quadrotors.

Title: Dynamic Output Feedback of Second-Order Systems: An Observer-Based Controller with LMI Design
Authors: Danielle Silva Gontijo; José Mário Araújo; Luciano Antonio Frezatto; Fernando de Oliveira Souza
Affiliation: 1. Universidade Federal de Minas Gerais, Programa de Pós-Graduação em Engenharia Elétrica, Minas Gerais, BR 2. Instituto Federal da Bahia, Grupo de Pesquisa em Sinais e Sistemas, Bahia, BR 3. Universidade Federal de Minas Gerais, Departamento de Engenharia Eletrônica, Minas Gerais, BR
Abstract: In this paper, an LMI design to control uncertain second-order systems subject to perturbation in the state via dynamic output feedback is approached. A Luenberger-like descriptor observer to reconstruct the system state is then introduced, and LMI conditions to robust PD-feedback control using the state estimation are applied to compute an optimal parameterized observer gain. The proposed approach can be applied to complete or underactuated systems under the hypothesis that the mass matrix is non-singular. A numerical example and an experimental implementation for the stabilization of a mini-inverted pendulum are given to show the proposal's effectiveness.

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