Relevant bibliographies by topics / Non-holonomic constraints

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Non-holonomic constraints'

Author: Grafiati
Published: 9 March 2023
Last updated: 12 June 2025

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Journal articles on the topic "Non-holonomic constraints"

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Ma, Yingchong, Gang Zheng, Wilfrid Perruquetti, and Zhaopeng Qiu. "Local path planning for mobile robots based on intermediate objectives." Robotica 33, no. 4 (2014): 1017–31. http://dx.doi.org/10.1017/s0263574714000186.

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SUMMARYThis paper presents a path planning algorithm for autonomous navigation of non-holonomic mobile robots in complex environments. The irregular contour of obstacles is represented by segments. The goal of the robot is to move towards a known target while avoiding obstacles. The velocity constraints, robot kinematic model and non-holonomic constraint are considered in the problem. The optimal path planning problem is formulated as a constrained receding horizon planning problem and the trajectory is obtained by solving an optimal control problem with constraints. Local minima are avoided by choosing intermediate objectives based on the real-time environment.
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Niu, Xiaoji, You Li, Quan Zhang, Yahao Cheng, and Chuang Shi. "Observability Analysis of Non-Holonomic Constraints for Land-Vehicle Navigation Systems." Journal of Global Positioning Systems 11, no. 1 (2012): 80–88. http://dx.doi.org/10.5081/jgps.11.1.80.

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Arimoto, Suguru, Morio Yoshida, Masahiro Sekimoto, and Kenji Tahara. "A Riemannian-Geometry Approach for Modeling and Control of Dynamics of Object Manipulation under Constraints." Journal of Robotics 2009 (2009): 1–16. http://dx.doi.org/10.1155/2009/892801.

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A Riemannian-geometry approach for modeling and control of dynamics of object manipulation under holonomic or non-holonomic constraints is presented. First, position/force hybrid control of an endeffector of a multijoint redundant (or nonredundant) robot under a holonomic constraint is reinterpreted in terms of “submersion” in Riemannian geometry. A force control signal constructed in the image space of the constraint gradient is regarded as a lifting (or pressing) in the direction orthogonal to the kernel space. By means of the Riemannian distance on the constraint submanifold, stability of position control under holonomic constraints is discussed. Second, modeling and control of two-dimensional object grasping by a pair of multijoint robot fingers are challenged, when the object is of arbitrary shape. It is shown that rolling contact constraints induce the Euler equation of motion, in which constraint forces appear as wrench vectors affecting the object. The Riemannian metric is introduced on a constraint submanifold characterized with arclength parameters. An explicit form of the quotient dynamics is expressed in the kernel space with accompaniment of a pair of first-order differential equations concerning the arclength parameters. An extension of Dirichlet-Lagrange's stability theorem to redundant systems under constraints is suggested by introducing a Morse-Lyapunov function.
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Nakamura, Yoshihiko. "Non-holonomic Robot Systems. Part 5. Motion Control under Dynamical Non-holonomic Constraints." Journal of the Robotics Society of Japan 12, no. 2 (1994): 231–39. http://dx.doi.org/10.7210/jrsj.12.231.

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Dowell, Earl. "Hamilton’s principle and Hamilton’s equations with holonomic and non-holonomic constraints." Nonlinear Dynamics 88, no. 2 (2016): 1093–97. http://dx.doi.org/10.1007/s11071-016-3297-9.

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Shi, Heng, Yanbing Liang, and Zhaohui Liu. "An approach to the dynamic modeling and sliding mode control of the constrained robot." Advances in Mechanical Engineering 9, no. 2 (2017): 168781401769047. http://dx.doi.org/10.1177/1687814017690470.

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An approach to the dynamic modeling and sliding mode control of the constrained robot is proposed in this article. On the basis of the Udwadia–Kalaba approach, the explicit equation of the constrained robot system is obtained first. This equation is applicable to systems with either holonomic or non-holonomic constraints, as well as with either ideal or non-ideal constraint forces. Second, fully considering the uncertainty of the non-ideal force, that is, the dynamic friction in the constrained robot system, the sliding mode control algorithm is put forward to trajectory tracking of the end-effector on a vertical constrained surface to obtain actual values of the unknown constraint force. Moreover, model order reduction method is innovatively used in the Udwadia–Kalaba approach and sliding mode controller to reduce variables and simplify the complexity of the calculation. Based on the demonstration of this novel method, a detailed robot system example is finally presented.
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Chen, B., L. S. Wang, S. S. Chu, and W. T. Chou. "A new classification of non-holonomic constraints." Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 453, no. 1958 (1997): 631–42. http://dx.doi.org/10.1098/rspa.1997.0035.

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Zhao, Yating, Xiaolong Chen, and Han Zhao. "Robust control design for home pension service mobile robots with passive and servo constraints." Science Progress 103, no. 3 (2020): 003685042095221. http://dx.doi.org/10.1177/0036850420952219.

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This paper presents a novel robust control design for a class of home pension service mobile robots (HPSMRs) with non-holonomic passive constraints, based on the Udwadia-Kalaba theory and Udwadia control. The approach has two portions: dynamics modeling and robust control design. The Udwadia-Kalaba theory is employed to deal with the non-holonomic passive constraints. The frame of the Udwadia control is employed to design the robust control to tracking the servo constraints. The designed approach is easy to implement because the analytical solution of the control force can explicitly be obtained even if the non-holonomic passive constraints exists. The uniform boundedness and uniform ultimate boundedness are demonstrated by the theoretical analysis. The effectiveness of the proposed approach is verified through the numerical simulation by a HPSMR.
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Song, Danyang, Jinheng Yang, and Jiancheng Song. "Shearer-Positioning Method Based on Non-Holonomic Constraints." Applied Sciences 12, no. 19 (2022): 10050. http://dx.doi.org/10.3390/app121910050.

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In the traditional shearer-positioning method, an odometer is used to assist the forward velocity correction of the inertial navigation system, but it cannot restrain the system’s error divergence. For this reason, this paper proposes a shearer positioning method based on non-holonomic constraints. In this method, an inertial measurement unit and odometer are installed in the middle of the shearer body and on the traction gear, respectively, the shearer attitude, speed, and position information are calculated through the inertial measurement-unit mechanization, and the shearer’s instantaneous velocity is calculated through the output of the odometer. The mechanization and error transfer process of the inertial navigation system are used to establish a Kalman filtering-state equation. The Kalman filtering observation equation is established through the difference between the projected velocity of the inertial navigation system at the joint and the output velocity of the odometer as the observation vector, and the non-holonomic constraint is introduced. Finally, the error feedback is derived from the results processed by the Kalman filtering algorithm, and the output of the inertial navigation system is corrected to obtain the optimal estimation of the shearer’s attitude, speed and position. The experiment shows that compared with the traditional inertial navigation and odometer combined positioning method, the degree of divergence in the positioning results over time is significantly reduced after adding the non-holonomic constraint. The positioning method has good tracking ability for the trajectory of the shearer. The error of the positioning results in the forward direction is reduced by 66%, the lateral direction is reduced by 62%, and the vertical direction is reduced by 67%.
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Louste, C., and A. Liégeois. "Path planning for non-holonomic vehicles: a potential viscous fluid field method." Robotica 20, no. 3 (2002): 291–98. http://dx.doi.org/10.1017/s0263574701003691.

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This paper deals with the path planning of non-holonomic vehicles on an uneven natural terrain. It uses the properties of incompressible viscous fluid fields. The full configuration is considered including position and orientation. Lanes are computed instead of a single path. Bounds on curvature and constraints on initial and final orientations are also addressed. By using the Keymeulen/Decuyper fluid method and adding friction forces in the Stokes' equations, the shortest paths or the minimum energy ones can be found, even on an uneven terrain. In addition, in order to satisfy the kinematics and dynamics constraints of a non-holonomic robot a local variation of the shear constraint is used to control the upper bound of the trajectory curvature. Adding small corridors at the departure and destination also satisfies initial and final orientation requirements.
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Dissertations / Theses on the topic "Non-holonomic constraints"

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Lonmo, Victor. "Dynamics based control of a mobile robot with non-holonomic constraints." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1996. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq26344.pdf.

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Pasquotti, Maura. "Topics on Optimization Strategies for Constrained Mechanical Systems." Doctoral thesis, Università degli studi di Padova, 2008. http://hdl.handle.net/11577/3425582.

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In the first part of the work we analyze the problem of optimal control of a vehicle along a preassigned trajectory. The vehicle system is studied and simplified in order to obtain a computationally tractable model, which still presents the main characteristics of the real vehicle. The control algorithm, based on MPC techniques, is then explained and its effectiveness is proved through simulation results. The “minimum lap time problem” is afterward considered, which can be considered as an evolution of the trajectory tracking problem; its analysis is presented and is followed by the developed solution, based on pseudospectral methods. In the second part of the thesis the problem of control of underactuated mechanical systems is discussed. The nonholonomic system classically called “rolling disk” is considered as test case; it is a wheel with punctiform contact surface that can roll on the plane without sliding laterally. Differently from the literature we consider the torque as the unique control input signal. This system is modeled through the Lagrangian formalism and then the control strategy, based on backstepping and receding horizon techniques, is shown and proved to be effective.
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Shehadeh, Mhd Ali. "Geometrické řízení hadům podobných robotů." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2020. http://www.nusl.cz/ntk/nusl-417115.

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This master’s thesis describes equations of motion for dynamic model of nonholonomic constrained system, namely the trident robotic snakes. The model is studied in the form of Lagrange's equations and D’Alembert’s principle is applied. Actually this thesis is a continuation of the study going at VUT about the simulations of non-holonomic mechanisms, specifically robotic snakes. The kinematics model was well-examined in the work of of Byrtus, Roman and Vechetová, Jana. So here we provide equations of motion and address the motion planning problem regarding dynamics of the trident snake equipped with active joints through basic examples and propose a feedback linearization algorithm.
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Hosseinyalamdary, Saivash Hosseinyalamdary. "Traffic Scene Perception using Multiple Sensors for Vehicular Safety Purposes." The Ohio State University, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=osu1462803166.

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"Non-holonomic Differential Drive Mobile Robot Control & Design : Critical Dynamics and Coupling Constraints." Master's thesis, 2013. http://hdl.handle.net/2286/R.I.20941.

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abstract: Mobile robots are used in a broad range of application areas; e.g. search and rescue, reconnaissance, exploration, etc. Given the increasing need for high performance mobile robots, the area has received attention by researchers. In this thesis, critical control and control-relevant design issues for differential drive mobile robots is addressed. Two major themes that have been explored are the use of kinematic models for control design and the use of decentralized proportional plus integral (PI) control. While these topics have received much attention, there still remain critical questions which have not been rigorously addressed. In this thesis, answers to the following critical questions are provided: When is 1. a kinematic model sufficient for control design? 2. coupled dynamics essential? 3. a decentralized PI inner loop velocity controller sufficient? 4. centralized multiple-input multiple-output (MIMO) control essential? and how can one design the robot to relax the requirements implied in 1 and 2? In this thesis, the following is shown: 1. The nonlinear kinematic model will suffice for control design when the inner velocity (dynamic) loop is much faster (10X) than the slower outer positioning loop. 2. A dynamic model is essential when the inner velocity (dynamic) loop is less than two times faster than the slower outer positioning loop. 3. A decentralized inner loop PI velocity controller will be sufficient for accomplish- ing high performance control when the required velocity bandwidth is small, rel- ative to the peak dynamic coupling frequency. A rule-of-thumb which depends on the robot aspect ratio is given. 4. A centralized MIMO velocity controller is needed when the required bandwidth is large, relative to the peak dynamic coupling frequency. Here, the analysis in the thesis is sparse making the topic an area for future analytical work. Despite this, it is clearly shown that a centralized MIMO inner loop controller can offer increased performance vis- &#769;a-vis a decentralized PI controller. 5. Finally, it is shown how the dynamic coupling depends on the robot aspect ratio and how the coupling can be significantly reduced. As such, this can be used to ease the requirements imposed by 2 and 4 above.<br>Dissertation/Thesis<br>M.S. Electrical Engineering 2013
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Kun-YaoPeng and 彭錕垚. "The Performance Analysis of an AKF Based Tightly Coupled INS/GNSS Sensor Fusion Scheme with Non-holonomic Constraints." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/10562792501302836886.

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Xu, Ying-Lin, and 許應麟. "A dynamic analysis of non-holonomic constraint rigid body system." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/04058865542816357909.

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Hsu, Ying-Lin, and 許應麟. "A dynamic analysis of non-holonomic constraint rigid body system." Thesis, 1997. http://ndltd.ncl.edu.tw/handle/46205334916940297152.

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碩士<br>國立臺灣大學<br>應用力學研究所<br>85<br>This paper follows the theories developed by C.O. Chang and V.C. Wang in 1996. They combined Gauss'' Principle of Least Constrain with State Transform to rapidly derive the minimum set of the first order state equations. It is named Constraint-Free State Equations. We apply this method to multi-rigid body nonholonomic constraint in this paper. First, for a double-wheel-roll system, we discuss three situations: non-assigned constraint, assigned track, and assign both track and velocity. Second, for a four-wheel-roll system, we mainly discuss two situations: non-assigned constraint and assigned track. From the above two cases, we conclude that it is a good method for deriving the Constrant-Free State Equations for the systems. However, there are some problems in system control should be solved, and more diecussions will be needed. Hopefully, this paper can provide some easy examples to those who are interesting in Nonholonomic Dynamics. By reading the content, they can understand more and more about this field.
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Books on the topic "Non-holonomic constraints"

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Mann, Peter. Coordinates & Constraints. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0006.

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This short chapter introduces constraints, generalised coordinates and the various spaces of Lagrangian mechanics. Analytical mechanics concerns itself with scalar quantities of a dynamic system, namely the potential and kinetic energies of the particle; this approach is in opposition to Newton’s method of vectorial mechanics, which relies upon defining the position of the particle in three-dimensional space, and the forces acting upon it. The chapter serves as an informal, non-mathematical introduction to differential geometry concepts that describe the configuration space and velocity phase space as a manifold and a tangent, respectively. The distinction between holonomic and non-holonomic constraints is discussed, as are isoperimetric constraints, configuration manifolds, generalised velocity and tangent bundles. The chapter also introduces constraint submanifolds, in an intuitive, graphic format.
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Mann, Peter. Constrained Lagrangian Mechanics. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0008.

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This chapter builds on the previous two chapters to tackle constrained systems, using Lagrangian mechanics and constrained variations. The first section deals with holonomic constraint equations using Lagrange multipliers; these can be used to reduce the number of coordinates until a linearly independent minimal set is obtained that describes a constraint surface within configuration space, so that Lagrange equations can be set up and solved. Motion is understood to be confined to a constraint submanifold. The variational formulation of non-holonomic constraints is then discussed to derive the vakonomic formulation. These erroneous equations are then compared to the central Lagrange equation, and the precise nature of the variations used in each formulation is investigated. The vakonomic equations are then presented in their Suslov form (Suslov–vakonomic form) in an attempt to reconcile the two approaches. In addition, the structure of biological membranes is framed as a constrained optimisation problem.
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Mann, Peter. Virtual Work & d’Alembert’s Principle. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0013.

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This chapter discusses virtual work, returning to the Newtonian framework to derive the central Lagrange equation, using d’Alembert’s principle. It starts off with a discussion of generalised force, applied force and constraint force. Holonomic constraints and non-holonomic constraint equations are then investigated. The corresponding principles of Gauss (Gauss’s least constraint) and Jourdain are also documented and compared to d’Alembert’s approach before being generalised into the Mangeron–Deleanu principle. Kane’s equations are derived from Jourdain’s principle. The chapter closes with a detailed covering of the Gibbs–Appell equations as the most general equations in classical mechanics. Their reduction to Hamilton’s principle is examined and they are used to derive the Euler equations for rigid bodies. The chapter also discusses Hertz’s least curvature, the Gibbs function and Euler equations.
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Book chapters on the topic "Non-holonomic constraints"

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Muniz Oliva, Waldyr. "6. Mechanical systems with non-holonomic constraints." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-540-45795-4_7.

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Azar, Ahmad Taher, Fernando E. Serrano, Nashwa Ahmad Kamal, and Anis Koubaa. "Robust Kinematic Control of Unmanned Aerial Vehicles with Non-holonomic Constraints." In Advances in Intelligent Systems and Computing. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-58669-0_74.

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Tajvar, Pouria, Anastasiia Varava, Danica Kragic, and Jana Tumova. "Robust Motion Planning for Non-holonomic Robots with Planar Geometric Constraints." In Springer Proceedings in Advanced Robotics. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-95459-8_52.

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Umerez, Jon, and Matteo Mossio. "Constraint, Non-holonomic." In Encyclopedia of Systems Biology. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4419-9863-7_707.

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Zobova, Alexandra A., Kirill V. Gerasimov, and Ivan I. Kosenko. "Adjustment of Non-Holonomic Constraints by Absolutely Inelastic Tangent Impact in the Dynamics of an Omni-Vehicle." In Multibody Dynamics 2019. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-23132-3_62.

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LÜTZEN, JESPER. "A history of non-holonomic constraints." In Mechanistic Images in Geometric Form. Oxford University Press, 2005. http://dx.doi.org/10.1093/acprof:oso/9780198567370.003.0022.

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"The System as an Ecosystem Subject to Non-Holonomic Constraints." In System and Structure. Routledge, 2013. http://dx.doi.org/10.4324/9781315014135-102.

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Alferov, G. V., G. G. Ivanov, P. A. Efimova, and A. S. Sharlay. "Stability of Linear Systems With Multitask Right-Hand Member." In Stochastic Methods for Estimation and Problem Solving in Engineering. IGI Global, 2018. http://dx.doi.org/10.4018/978-1-5225-5045-7.ch004.

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To study the dynamics of mechanical systems and to define the construction parameters and control laws, it is necessary to have computational models accurately describing properties of real mechanisms. From a mathematical point of view, the computational models of mechanical systems are actually the systems of differential equations. These models can contain equations that also describe non-mechanical phenomena. In this chapter, the problems of stability and asymptotic stability conditions for the motion of mechanical systems with holonomic and non-holonomic constraints are under consideration. Stability analysis for the systems of differential equations is given in term of the second Lyapunov's method. With the use of the set-theoretic approach, the necessary and sufficient conditions for stability and asymptotic stability of zero solution of the considered system are formulated. The proposed approaches can be used to study the stability of the motion for robot manipulators, transport, space, and socio-economic systems.
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Sánchez-Sánchez, Pablo, José Daniel Castro-Díaz, Alejandro Gutiérrez-Giles, and Javier Pliego-Jiménez. "A Proposal of Haptic Technology to be Used in Medical Simulation." In Haptic Technology - Intelligent Approach to Future Man-Machine Interaction [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.102508.

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For medical training aims, tele-operation systems have inspired virtual reality systems. Since force sensors placed on the robotic arms provide interaction force information that is transmitted to the human operator, such force produces a tactile sensation that allows feeling some remote or virtual environment properties. However, in the last two decades, researchers have focused on visually simulating the virtual environments present in a surgical environment. This implies that methods that cannot reproduce some characteristics of virtual surfaces, such as the case of penetrable objects, generate the force response. To solve this problem, we study a virtual reality system with haptic feedback using a tele-operation approach. By defining the operator-manipulated interface as the master robot and the virtual environment as the slave robot, we have, by addressing the virtual environment as a restricted motion problem, the force response. Therefore, we implement a control algorithm, based on a tele-operation system, to feedback the corresponding force to the operator. We achieve this through the design of a virtual environment using the dynamic model of the robot in contact with holonomic and non-holonomic constraints. In addition, according to the medical training simulator, before contact, there is always a free movement stage.
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Roy, Abhishek Ghosh, and Pratyusha Rakshit. "Motion Planning of Non-Holonomic Wheeled Robots Using Modified Bat Algorithm." In Nature-Inspired Algorithms for Big Data Frameworks. IGI Global, 2019. http://dx.doi.org/10.4018/978-1-5225-5852-1.ch005.

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The chapter proposes a novel optimization framework to solve the motion planning problem of non-holonomic wheeled mobile robots using swarm algorithms. The specific robotic system considered is a vehicle with approximate kinematics of a car. The configuration of this robot is represented by position and orientation of its main body in the plane and by angles of the steering wheels. Two control inputs are available for motion control including the velocity and the steering angle command. Moreover, the car-like robot is one of the simplest non-holonomic vehicles that displays the general characteristics and constrained maneuverability of systems with non-holonomicity. The control methods proposed in this chapter do not require precise mathematical modeling of every aspect a car-like system. The swarm algorithm-based motion planner determines the optimal trajectory of multiple car-like non-holonomic robots in a given arena avoiding collision with obstacles and teammates. The motion planning task has been taken care of by an adaptive bio-inspired strategy commonly known as Bat Algorithm.
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Conference papers on the topic "Non-holonomic constraints"

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Terze, Zdravko, Joris Naudet, and Dirk Lefeber. "Constraint Gradient Projective Method for Stabilized Dynamic Simulation of Constrained Multibody Systems." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48314.

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Constraint gradient projective method for stabilization of constraint violation during integration of constrained multibody systems is in the focus of the paper. Different mathematical models for constrained MBS dynamic simulation on manifolds are surveyed and violation of kinematical constraints is discussed. As an extension of the previous work focused on the integration procedures of the holonomic systems, the constraint gradient projective method for generally constrained mechanical systems is discussed. By adopting differentialgeometric point of view, the geometric and stabilization issues of the method are addressed. It is shown that the method can be applied for stabilization of holonomic and non-holonomic constraints in Pfaffian and general form.
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Terze, Zdravko, Dubravko Matijasˇevic´, Milan Vrdoljak, and Vladimir Koroman. "Differential-Geometric Characteristics of Optimized Generalized Coordinates Partitioned Vectors for Holonomic and Non-Holonomic Multibody Systems." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-86849.

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Differential-geometric characteristics and structure of optimized generalized coordinates partitioned vectors for generally constrained multibody systems are discussed. Generalized coordinates partitioning is well-known procedure that can be applied in the framework of numerical integration of DAE systems. However, although the procedure proves to be a very useful tool, it is known that an optimization algorithm for coordinates partitioning is needed to obtain the best performance. After short presentation of differential-geometric background of optimized coordinates partitioning, the structure of optimally partitioned vectors is discussed on the basis of gradient analysis of separate constraint submanifolds at configuration and velocity level when holonomic and non-holonomic constraints are present in the system. While, in the case of holonomic systems, the vectors of optimally partitioned coordinates have the same structure for generalized positions and velocities, when non-holonomic constraints are present in the system, the optimally partitioned coordinates generally differ at configuration and velocity level and separate partitioned procedure has to be applied. The conclusions of the paper are illustrated within the framework of the presented numerical example.
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Jarzębowska, Elżbieta M., and Vladimir V. Vantsevich. "A Nonlinear Constraint Formulation for Direct and Inverse Vehicle Dynamics Modelling." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-34632.

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The paper presents an analysis of holonomic and non-holonomic material/non-material constrains that may be used in wheeled vehicle dynamics. Based on this analysis, a modified approach to the formulation of vehicle motion constraints is proposed. Specifically, a non-material constraint that limits vehicle kinematic parameters to a required motion, i.e. to a programmable motion that corresponds to required vehicle operational properties including turnability and stability of motion, is introduced. The new concept of constraints put upon wheeled vehicle dynamics makes the resulting direct and inverse dynamic models more oriented towards required vehicle performance and facilitate the control design. The new constraint concept is illustrated by an example of a required vehicle acceleration performance.
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McCann, Brennan S., Morad Nazari, and Firdaus Udwadia. "Analysis of Inequality Constraints Without Using Lagrange Multipliers With Applications to Classical Dynamical Systems." In ASME 2022 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2022. http://dx.doi.org/10.1115/imece2022-94362.

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Abstract The fundamental equation of mechanics (FEM) for constrained motion analysis provides a way to obtain control accelerations necessary to satisfy some set of holonomic or non-holonomic constraints. The methodology provides the control necessary to either perfectly satisfy or minimize the error in all the constraints and does not require computation of Lagrange multipliers. Furthermore, this framework is capable of addressing various types of constraints, and can treat systems that are under-, fully-, or over-constrained, conveniently. The FEM formulation has most commonly been applied to a variety of classes of equality constraints. Some attempts at extending this approach to inequality constraints have been presented in the literature, including applying slack variables to provide freedom in the constraint and diffeomorphisms to map equality constraints to bounded spaces. However, these approaches have different associated advantages and drawbacks. In order to bridge the benefits of both methodologies and mitigate their issues, this work proposes a treatment of holonomic inequality constraints within the framework of the FEM wherea class of functions built on the error and Gaussian distribution functions is leveraged to treat inequality constraints on several classical dynamical case studies. The proposed technique is applied to several classes of holonomic, solitary or one-sided inequalities, and bounding inequalities for a spring-mass-damper, an inverted pendulum, and an inverted pendulum on a cart, illustrating this approach’s broad applicability to mechanical systems.
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Oikonomopoulos, A. S., S. G. Loizou, and K. J. Kyriakopoulos. "Coordination of multiple non-holonomic agents with input constraints." In 2009 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2009. http://dx.doi.org/10.1109/robot.2009.5152397.

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Koganezawa, Koichi, and Kazuomi Kaneko. "A Method for Constraints Stabilization on Solving Multibody Dynamics." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21322.

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Abstract This paper deals with methods for solving the multibody dynamics with constraints. The problem is considered in the framework of solving the Lagrange multipliers in addition to the system coordinates in the differential and algebraic equation (DAE) governing the dynamics with holonomic or non-holonomic constraints. The proposed methods are originally based on Baumgarte’s work for the holonomic constraints but its extensions to the non-holonomic constraints. Conventionally the Lagrange multipliers are solved algebraically and substituted into the dynamic equations (DAE). This paper, on the other hand, proposes a method to derive the ordinary differential equations with respect to the Lagrange multipliers. One can resort the ordinary numerical integration method to solve the Lagrange multipliers as same as to solve the ODE with respect to the system coordinates. Some examples of numerical solution for the mechanical models having holonomic and non-holonomic constraints shows the excellent stability of the constraints, which is superior to the Baumgarte’s stabilizing method and the penalty method.
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Astolfi, A., R. Ortega, and A. Venkatraman. "Global observer design for mechanical systems with non-holonomic constraints." In 2010 American Control Conference (ACC 2010). IEEE, 2010. http://dx.doi.org/10.1109/acc.2010.5530542.

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Mu¨ller, Andreas. "On the Concept of Mobility Used in Robotics." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87524.

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This paper summarizes the concept of mobility used for holonomic and non-holonomic mechanisms. The mobility of mechanisms is considered from a geometric viewpoint starting with the variety generated by the constraint mapping as configuration space. While the local (finite) mobility is determined by the dimension of the configuration space, the differential mobility may be different. This is so for singular configurations, but also at regular configurations of underconstrained mechanisms. Overconstrained mechanisms are identified as those comprising manifolds of regular configurations that are critical points of the constraint mapping. The considerations include non-holonomic mechanisms. For such mechanisms the configuration space is the integral manifold of the kinematic constraints. Different types of singularities are discussed for non-holonomic mechanisms.
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Terze, Zdravko, and Joris Naudet. "Discrete Mechanical Systems: Projective Constraint Violation Stabilization Method for Numerical Forward Dynamics on Manifolds." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35466.

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During numerical forward dynamics of discrete mechanical systems with constraints, a numerical violation of system kinematical constraints is the basic source of time-integration errors and frequent difficulty that analyst has to cope with. The stabilized time-integration procedure, whose stabilization step is based on projection of the integration results to the underlying constraint manifold via post-integration correction of the selected coordinates, is proposed in the paper. After discussing optimization of the partitioning algorithm, the geometric and stabilization issues of the method are addressed and it is shown that the projective stabilization algorithm can be applied for numerical stabilization of holonomic and non-holonomic constraints in Pfaffian and general form. As a continuation of the previous work, a further elaboration of the projective stabilization method applied on non-holonomic discrete mechanical systems is reported in the paper and numerical example is provided.
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Müller, Andreas. "A Proposal for a Unified Concept of Kinematic Singularities for Holonomic and Non-Holonomic Mechanisms." In ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/detc2012-70649.

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The study of mechanism singularities has traditionally focused on holonomic systems. On the other hand many robotic systems are characterized by non-holonomic constraints, such as mobile platforms and manipulators driven by non-holonomic joints, and a general concept of singularities seems in order. In this paper a possible generalization of the singularity concept is proposed that equally accounts for holonomic and non-holonomic kinematic systems. The central object is the associated kinematic control problem. Singularities are identified as those configurations where the iteration depth of Lie brackets required to compute the accessibility Lie algebra changes. This notion of singularities is applied to serial manipulator and to non-holonomic mobile platforms. It is shown for holonomic manipulators that this is equivalent to the usual Jacobian rank condition. As example the condition is discussed for a Scara manipulator, a 6R manipulator, and for a kinematic car with one or two trailers.
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