Advances in Robot Motion and Control—In Memory of Professor Krzysztof Kozlowski

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Robotics and Automation".

Deadline for manuscript submissions: closed (20 November 2022) | Viewed by 32469

Special Issue Editors


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Guest Editor
Department of Control and Systems Engineering, Poznan University of Technology, 60-965 Poznan, Poland
Interests: geometric approach in control of mechanical systems; various applications of robotics, particularly in rehabilitation

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Guest Editor
Institute of Automatic Control and Robotics, Poznan University of Technology, 60-965 Poznan, Poland
Interests: nonlinear systems; robotics; mobile robotics; motion control; motion planning
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue addresses the control and trajectory tracking of different robots, including mobile, walking, and flying robots and sets of mobile robots. All these mechanical systems are described by highly nonlinear differential equations, and the geometric approach and the Lyapunov stability theory seem to be the most appropriate tools to be used to study control and trajectory tracking of these systems. It is highly interesting to know the limitations of these techniques in comparison with simple techniques such as Taylor’s linearization or the first Lyapunov method. At the same time, we want to see their applications in practice; therefore, papers showing good theory with experiments are most welcome. We strongly believe that nontrivial theory supported by good experimental work may add new value and insights into the control of mechanical systems.

Papers submitted to this Special Issue will be reviewed by no less than two independent, internationally recognized experts. Based on the rigorous review process, we will be able to select the best papers to appear in the Special Issue, and we anticipate that they will be of great interest to Applied Sciences readers.

Prof. Dr. Krzysztof Kozlowski
Dr. Dariusz Pazderski
Guest Editors

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Keywords

  • control of mechanical systems
  • differential geometry
  • linearization
  • Lyapunov stability theory
  • trajectory planning
  • multiagent systems

Published Papers (14 papers)

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Research

16 pages, 1509 KiB  
Article
Differentially-Driven Robots Moving in Formation—Leader–Follower Approach
by Marcin Kiełczewski, Wojciech Kowalczyk and Bartłomiej Krysiak
Appl. Sci. 2022, 12(14), 7273; https://doi.org/10.3390/app12147273 - 20 Jul 2022
Cited by 3 | Viewed by 1167
Abstract
The paper is devoted to the leader–follower approach for multiple mobile robots control and its experimental verification. The formation control of mobile robots is motivated by the concept of virtual leader tracking, which is enhanced by the collision avoidance between the robots proposed [...] Read more.
The paper is devoted to the leader–follower approach for multiple mobile robots control and its experimental verification. The formation control of mobile robots is motivated by the concept of virtual leader tracking, which is enhanced by the collision avoidance between the robots proposed in our previous work. The effectiveness of this approach was verified through realisation of experiments with use of MTracker mobile robots. The OptiTrack vision system was used for robots localization. Software part with control algorithms and communication was prepared with use of the Robot Operating System. Full article
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14 pages, 23646 KiB  
Article
Application of Convolutional Neural Networks in Visual Feedback of Movable Camera Mounting Control
by Rafał Mateusz Sobański, Marta Drążkowska, Maciej Papis and Agata Stankiewicz
Appl. Sci. 2022, 12(10), 5252; https://doi.org/10.3390/app12105252 - 23 May 2022
Cited by 1 | Viewed by 1175
Abstract
The aim of this work is to present an automatic solution to control the surveillance camera merely by the movements of the operator’s head. The method uses convolutional neural networks that work in a course-to-fine manner to estimate head orientation in image data. [...] Read more.
The aim of this work is to present an automatic solution to control the surveillance camera merely by the movements of the operator’s head. The method uses convolutional neural networks that work in a course-to-fine manner to estimate head orientation in image data. First, the image frame of the operator’s head is acquired from the camera on the operator’s side of the system. The exact position of a head, given by its bounding box, is estimated by a Multitask Cascaded Convolutional Network. Second, the customized network for a given scenario is used to classify the orientation of the head-on image data. In particular, the dedicated image dataset was collected for training purposes and was given a discrete set of possible orientations in the vertical and horizontal planes. The accuracy of the estimators is higher than 80%, with an average of 4.12 fps of validation time. Finally, the current head orientation data are converted into a control signal for two degrees of freedom surveillance camera mounting. The feedback response time is 1.5 s, which is sufficient for most real-life surveillance applications. Full article
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23 pages, 3536 KiB  
Article
Application of a Trajectory Tracking Algorithm for Underactuated Underwater Vehicles Using Quasi-Velocities
by Przemyslaw Herman
Appl. Sci. 2022, 12(7), 3496; https://doi.org/10.3390/app12073496 - 30 Mar 2022
Cited by 4 | Viewed by 1306
Abstract
In this work, an application of the trajectory tracking algorithm proposed in the literature for underactuated marine vehicles is presented. The main difference relies on that here the dynamics of the vehicle are expressed in terms of some quasi-velocities (QV). This fact has [...] Read more.
In this work, an application of the trajectory tracking algorithm proposed in the literature for underactuated marine vehicles is presented. The main difference relies on that here the dynamics of the vehicle are expressed in terms of some quasi-velocities (QV). This fact has a double meaning. First of all, it is shown that using the QV, it is possible to control a vehicle in the absence of one variable because the works related to marine vehicles have only concerned fully actuated systems. In addition, a controller using QV provides information that gives some insight into vehicle dynamics and that is not available in classical equations of motion. The simulations done on two 3-DOF models of different underwater vehicles and using two desired trajectories show performance of the considered control strategy. A discussion of the presented control scheme and selected control approaches from recent years was also conducted, and the benefits of the proposed approach were pointed out. Full article
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15 pages, 588 KiB  
Article
Modified Infinite-Time State-Dependent Riccati Equation Method for Nonlinear Affine Systems: Quadrotor Control
by Sławomir Stępień and Paulina Superczyńska
Appl. Sci. 2021, 11(22), 10714; https://doi.org/10.3390/app112210714 - 13 Nov 2021
Cited by 6 | Viewed by 1465
Abstract
This paper presents modeling and infinite-time suboptimal control of a quadcopter device using the state-dependent Riccati equation (SDRE) method. It establishes a solution to the control problem using SDRE and proposes a new procedure for solving the problem. As a new contribution, the [...] Read more.
This paper presents modeling and infinite-time suboptimal control of a quadcopter device using the state-dependent Riccati equation (SDRE) method. It establishes a solution to the control problem using SDRE and proposes a new procedure for solving the problem. As a new contribution, the paper proposes a modified SDRE-based suboptimal control technique for affine nonlinear systems. The method uses a pseudolinearization of the closed-loop system employing Moore–Penrose pseudoinverse. Then, the algebraic Riccati equation (ARE), related to the feedback compensator gain, is reduced to state-independent form, and the solution can be computed only once in the whole control process. The ARE equation is applied to the problem reported in this study that provides general formulation and stability analysis. The effectiveness of the proposed control technique is demonstrated through the use of simulation results for a quadrotor device. Full article
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16 pages, 396 KiB  
Article
A Mechanical Feedback Classification of Linear Mechanical Control Systems
by Marcin Nowicki and Witold Respondek
Appl. Sci. 2021, 11(22), 10669; https://doi.org/10.3390/app112210669 - 12 Nov 2021
Cited by 4 | Viewed by 1147
Abstract
We give a classification of linear nondissipative mechanical control system under mechanical change of coordinates and feedback. First, we consider a controllable case that is somehow a mechanical counterpart of Brunovský classification, then we extend the result to all linear nondissipative mechanical systems [...] Read more.
We give a classification of linear nondissipative mechanical control system under mechanical change of coordinates and feedback. First, we consider a controllable case that is somehow a mechanical counterpart of Brunovský classification, then we extend the result to all linear nondissipative mechanical systems (not necessarily controllable) which leads to a mechanical canonical decomposition. The classification of Lagrangian systems is given afterwards. Next, we show an application of the classification results to the stability and stabilization problem and illustrate them with several examples. All presented results in this paper are expressed in terms of objects on the configuration space Rn only, while the state-space of a mechanical control system is Rn×Rn consisting of configurations and velocities. Full article
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16 pages, 401 KiB  
Article
Development of Task-Space Nonholonomic Motion Planning Algorithm Based on Lie-Algebraic Method
by Arkadiusz Mielczarek and Ignacy Dulęba
Appl. Sci. 2021, 11(21), 10245; https://doi.org/10.3390/app112110245 - 01 Nov 2021
Cited by 1 | Viewed by 1169
Abstract
In this paper, a Lie-algebraic nonholonomic motion planning technique, originally designed to work in a configuration space, was extended to plan a motion within a task-space resulting from an output function considered. In both planning spaces, a generalized Campbell–Baker–Hausdorff–Dynkin formula was utilized to [...] Read more.
In this paper, a Lie-algebraic nonholonomic motion planning technique, originally designed to work in a configuration space, was extended to plan a motion within a task-space resulting from an output function considered. In both planning spaces, a generalized Campbell–Baker–Hausdorff–Dynkin formula was utilized to transform a motion planning into an inverse kinematic task known for serial manipulators. A complete, general-purpose Lie-algebraic algorithm is provided for a local motion planning of nonholonomic systems with or without output functions. Similarities and differences in motion planning within configuration and task spaces were highlighted. It appears that motion planning in a task-space can simplify a planning task and also gives an opportunity to optimize a motion of nonholonomic systems. Unfortunately, in this planning there is no way to avoid working in a configuration space. The auxiliary objective of the paper is to verify, through simulations, an impact of initial parameters on the efficiency of the planning algorithm, and to provide some hints on how to set the parameters correctly. Full article
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17 pages, 2165 KiB  
Article
Detection of Pediatric Femur Configuration on X-ray Images
by Marta Drążkowska
Appl. Sci. 2021, 11(20), 9538; https://doi.org/10.3390/app11209538 - 14 Oct 2021
Viewed by 1336
Abstract
In this paper, we present a fully automatic solution for denoting bone configuration on two-dimensional images. A dataset of 300 X-ray images of children’s knee joints was collected. The strict experimental protocol established in this study increased the difficulty of post-processing. Therefore, we [...] Read more.
In this paper, we present a fully automatic solution for denoting bone configuration on two-dimensional images. A dataset of 300 X-ray images of children’s knee joints was collected. The strict experimental protocol established in this study increased the difficulty of post-processing. Therefore, we tackled the problem of obtaining reliable information from medical image data of insufficient quality. We proposed a set of features that unambiguously denoted configuration of the bone on the image, namely the femur. It was crucial to define the features that were independent of age, since age variability of subjects was high. Subsequently, we defined image keypoints directly corresponding to those features. Their positions were used to determine the coordinate system denoting femur configuration. A complex keypoint detector was proposed, composed of two different estimator architectures: gradient-based and based on the convolutional neural network. The positions of the keypoints were used to determine the configuration of the femur on each image frame. The overall performance of both estimators working in parallel was evaluated using X-ray images from the publicly available LERA dataset. Full article
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13 pages, 2882 KiB  
Article
Design of Autonomous Mobile Robot for Cleaning in the Environment with Obstacles
by Arpit Joon and Wojciech Kowalczyk
Appl. Sci. 2021, 11(17), 8076; https://doi.org/10.3390/app11178076 - 31 Aug 2021
Cited by 12 | Viewed by 8596
Abstract
This paper describes the design and development of a cleaning robot, using adaptive manufacturing technology and its use with a control algorithm for which there is a stability proof. The authors’ goal was to fill the gap between theory and practical implementation based [...] Read more.
This paper describes the design and development of a cleaning robot, using adaptive manufacturing technology and its use with a control algorithm for which there is a stability proof. The authors’ goal was to fill the gap between theory and practical implementation based on available low-cost components. Adaptive manufacturing was chosen to cut down the cost of manufacturing the robot. Practical verification of the effectiveness of the control algorithm was achieved with the experiments. The robot comprises mainly three assemblies, a four-wheel-drive platform, a four-degrees-of-freedom robotic arm, and a vacuum system. The inlet pipe of the vacuum system was attached to the end effector of the robotic arm, which makes the robot more flexible to clean uneven areas, such as skirting on floors. The robot was equipped with a LIDAR sensor and web camera, giving the opportunity to develop more complex methods. A low-level proportional–integral–derivative (PID) speed controller was implemented, and a high-level controller that uses artificial potential functions to generate repulsive components, which avoids collision with obstacles. Robot operating system (ROS) was installed in the robot’s on-board system. With the help of the ROS node, the high-level controller generates control signals for the low-level controller. Full article
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21 pages, 2229 KiB  
Article
Abstract Rotations for Uniform Adaptive Control and Soft Modeling of Mechanical Devices
by János F. Bitó, Imre J. Rudas, József K. Tar and Árpád Varga
Appl. Sci. 2021, 11(17), 7939; https://doi.org/10.3390/app11177939 - 27 Aug 2021
Cited by 5 | Viewed by 1598
Abstract
The model-based controllers generally suffer from the lack of precise dynamic models. Making reliable analytical models can be evaded by soft modeling techniques, while the consequences of modeling imprecisions are tackled by either robust or adaptive techniques. In robotics, the prevailing adaptive techniques [...] Read more.
The model-based controllers generally suffer from the lack of precise dynamic models. Making reliable analytical models can be evaded by soft modeling techniques, while the consequences of modeling imprecisions are tackled by either robust or adaptive techniques. In robotics, the prevailing adaptive techniques are based on Lyapunov’s “direct method” that normally uses special error metrics and adaptation rules containing fragments of the Lyapunov function. The soft models and controllers need massive parallelism and suffer from the curse of dimensionality. A different adaptive approach based on Banach’s fixed point theorem and using special abstract rotations was recently suggested. Similar rotations were suggested to develop particular neural network-like soft models, too. Presently, via integrating these approaches, a uniform adaptive controlling and modeling methodology is suggested with especial emphasis on the effects of the measurement noises. Its applicability is investigated via simulations for a two degree of freedom mechanical system in which one of the generalized coordinates is under control, while the other one belongs to a coupled parasite dynamical system. The results are promising for allowing the development of relatively coarse soft models and a simple adaptive rule that can be implemented in embedded systems. Full article
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13 pages, 6562 KiB  
Article
Evaluation of Linearization Methods for Control of the Pendubot
by Paweł Parulski, Patryk Bartkowiak and Dariusz Pazderski
Appl. Sci. 2021, 11(16), 7615; https://doi.org/10.3390/app11167615 - 19 Aug 2021
Cited by 7 | Viewed by 2145
Abstract
The aim of this paper is to test the usefulness of a new approach based on partial feedback linearization to control the Pendubot. The control problem stated in the article is to stabilize the Pendubot in the upright position. In particular, properties of [...] Read more.
The aim of this paper is to test the usefulness of a new approach based on partial feedback linearization to control the Pendubot. The control problem stated in the article is to stabilize the Pendubot in the upright position. In particular, properties of the closed-loop system and the zero dynamics are investigated and illustrated by results of simulations. Next, the performance of a hybrid-like controller in the case of input saturation is evaluated by conduction extensive simulation trails. The experimental results suggest that the considered control methodology can be successfully applied for a real system. Full article
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15 pages, 6175 KiB  
Article
Kinematic-Model-Free Redundancy Resolution Using Multi-Point Tracking and Control for Robot Manipulation
by Ahmad AlAttar, Francesco Cursi and Petar Kormushev
Appl. Sci. 2021, 11(11), 4746; https://doi.org/10.3390/app11114746 - 21 May 2021
Cited by 6 | Viewed by 2162
Abstract
Robots have been predominantly controlled using conventional control methods that require prior knowledge of the robots’ kinematic and dynamic models. These controllers can be challenging to tune and cannot directly adapt to changes in kinematic structure or dynamic properties. On the other hand, [...] Read more.
Robots have been predominantly controlled using conventional control methods that require prior knowledge of the robots’ kinematic and dynamic models. These controllers can be challenging to tune and cannot directly adapt to changes in kinematic structure or dynamic properties. On the other hand, model-learning controllers can overcome such challenges. Our recently proposed model-learning orientation controller has shown promising ability to simultaneously control a three-degrees-of-freedom robot manipulator’s end-effector pose. However, this controller does not perform optimally with robots of higher degrees-of-freedom nor does it resolve redundancies. The research presented in this paper extends the state-of-the-art kinematic-model-free controller to perform pose control of hyper-redundant robot manipulators and resolve redundancies by tracking and controlling multiple points along the robot’s serial chain. The results show that with more control points, the controller is able to reach desired poses in fewer steps, yielding an improvement of up to 66%, and capable of achieving complex configurations. The algorithm was validated by running the simulation 100 times, and it was found that, in 82% of the times, the robot successfully reached the desired target pose within 150 steps. Full article
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20 pages, 2853 KiB  
Article
Sliding Balance Control of a Point-Foot Biped Robot Based on a Dual-Objective Convergent Equation
by Yizhou Lu, Junyao Gao, Xuanyang Shi, Dingkui Tian and Yi Liu
Appl. Sci. 2021, 11(9), 4016; https://doi.org/10.3390/app11094016 - 28 Apr 2021
Cited by 2 | Viewed by 1785
Abstract
The point-foot biped robot is highly adaptable to and can move rapidly on complex, non-structural and non-continuous terrain, as demonstrated in many studies. However, few studies have investigated balance control methods for point-foot sliding on low-friction terrain. This article presents a control framework [...] Read more.
The point-foot biped robot is highly adaptable to and can move rapidly on complex, non-structural and non-continuous terrain, as demonstrated in many studies. However, few studies have investigated balance control methods for point-foot sliding on low-friction terrain. This article presents a control framework based on the dual-objective convergence method and whole-body control for the point-foot biped robot to stabilize its posture balance in sliding. In this control framework, a dual-objective convergence equation is used to construct the posture stability criterion and the corresponding equilibrium control task, which are simultaneously converged. Control tasks are then carried out through the whole-body control framework, which adopts an optimization method to calculate the viable joint torque under the physical constraints of dynamics, friction and contact forces. In addition, this article extends the proposed approach to balance control in standing recovery. Finally, the capabilities of the proposed controller are verified in simulations in which a 26.9-kg three-link point-foot biped robot (1) slides over a 10 trapezoidal terrain, (2) slides on terrain with a sinusoidal friction coefficient between 0.05 and 0.25 and (3) stands and recovers from a center-of-mass offset of 0.02 m. Full article
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18 pages, 1108 KiB  
Article
Transformed Structural Properties Method to Determine the Controllability and Observability of Robots
by Dany Ivan Martinez, José de Jesús Rubio, Victor Garcia, Tomas Miguel Vargas, Marco Antonio Islas, Jaime Pacheco, Guadalupe Juliana Gutierrez, Jesus Alberto Meda-Campaña, Dante Mujica-Vargas and Carlos Aguilar-Ibañez
Appl. Sci. 2021, 11(7), 3082; https://doi.org/10.3390/app11073082 - 30 Mar 2021
Cited by 20 | Viewed by 1951
Abstract
Many investigations use a linearization method, and others use a structural properties method to determine the controllability and observability of robots. In this study, we propose a transformed structural properties method to determine the controllability and observability of robots, which is the combination [...] Read more.
Many investigations use a linearization method, and others use a structural properties method to determine the controllability and observability of robots. In this study, we propose a transformed structural properties method to determine the controllability and observability of robots, which is the combination of the linearization and the structural properties methods. The proposed method uses a transformation in the robot model to obtain a linear robot model with the gravity terms and uses the linearization of the gravity terms to obtain the linear robot model; this linear robot model is used to determine controllability and observability. The described combination evades the structural conditions requirement and decreases the approximation error. The proposed method is better than previous methods because the proposed method can obtain more precise controllability and observability results. The modified structural properties method is compared with the linearization method to determine the controllability and observability of three robots. Full article
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23 pages, 3046 KiB  
Article
Reactive Balance Control for Legged Robots under Visco-Elastic Contacts
by Thomas Flayols, Andrea Del Prete, Majid Khadiv, Nicolas Mansard and Ludovic Righetti
Appl. Sci. 2021, 11(1), 353; https://doi.org/10.3390/app11010353 - 31 Dec 2020
Cited by 3 | Viewed by 3013
Abstract
Contacts between robots and environment are often assumed to be rigid for control purposes. This assumption can lead to poor performance when contacts are soft and/or underdamped. However, the problem of balancing on soft contacts has not received much attention in the literature. [...] Read more.
Contacts between robots and environment are often assumed to be rigid for control purposes. This assumption can lead to poor performance when contacts are soft and/or underdamped. However, the problem of balancing on soft contacts has not received much attention in the literature. This paper presents two novel approaches to control a legged robot balancing on visco-elastic contacts, and compares them to other two state-of-the-art methods. Our simulation results show that performance heavily depends on the contact stiffness and the noises/uncertainties introduced in the simulation. Briefly, the two novel controllers performed best for soft/medium contacts, whereas “inverse-dynamics control under rigid-contact assumptions” was the best one for stiff contacts. Admittance control was instead the most robust, but suffered in terms of performance. These results shed light on this challenging problem, while pointing out interesting directions for future investigation. Full article
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