Singular Configuration

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Fumitoshi Matsuno - One of the best experts on this subject based on the ideXlab platform.

  • Control of a Snake Robot on a Cylindrical Surface Based on a Kinematic Model
    IFAC Proceedings Volumes, 2009
    Co-Authors: Hiroaki Tsukano, Motoyasu Tanaka, Fumitoshi Matsuno
    Abstract:

    Abstract In this paper, we propose a trajectory tracking control law for snake robots on a cylindrical surface, which have passive wheels and active joints. Snake robots have kinematic redundancy with introduction of wheelless links. First, we derive a kinematic model of the robot based on non-holonomic constraints that wheels do not sideslip and holonomic constrains that wheels remain in contact with a cylindrical surface at all times. It is necessary to avoid the Singular Configuration of the snake robot to achieve trajectory tracking. We indicate the conditions under which the robot becomes a Singular Configuration by analyzing the kinematic model, and design a trajectory tracking controller that can avoid the Singular Configuration using kinematic redundancy. Simulation results show the validity of the proposed controller.

  • Singular Configuration avoidance of a snake-like robot with screw drive units
    2008 SICE Annual Conference, 2008
    Co-Authors: Yong Gao, Motoyasu Tanaka, Hiroaki Fukushima, Fumitoshi Matsuno
    Abstract:

    In this paper, we propose a control method for a snake-like robot with screw drive units, which aims to achieve Singular Configuration avoidance as well as tracking control of the head position and orientation. A cost function measuring nonSingularity is introduced, and a control input is chosen such that the cost function is increased by using redundant degrees of freedom. The effectiveness of the proposed control law is investigated by simulations and experiments using a 4-link snake-like robot with screw drive units.

  • trajectory tracking control of snake robots based on dynamic model
    International Conference on Robotics and Automation, 2005
    Co-Authors: Fumitoshi Matsuno, H Sato
    Abstract:

    In this paper, we derive a dynamic model and a trajectory tracking control law for snake robots, which have passive wheels and active joints, based on the dynamic model. For a trajectory tracking control of snake robots, it is one of the important problem to avoid the Singular Configuration like a straight line. Using input-ouput linearization for the head position of snake robots based on dynamic model, we can control the head position by PD feedback, but the robot will converge to the Singular Configuration. In order to solve this problem, we propose a control law that controls shape controllable points for avoiding the Singular Configuration. Using the proposed control law, the robot can accomplish trajectory tracking of the head position without converging to the Singular Configuration. Simulation results show the effectiveness of the proposed control law.

  • ICRA - Trajectory Tracking Control of Snake Robots Based on Dynamic Model
    Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 1
    Co-Authors: Fumitoshi Matsuno, H Sato
    Abstract:

    In this paper, we derive a dynamic model and a trajectory tracking control law for snake robots, which have passive wheels and active joints, based on the dynamic model. For a trajectory tracking control of snake robots, it is one of the important problem to avoid the Singular Configuration like a straight line. Using input-ouput linearization for the head position of snake robots based on dynamic model, we can control the head position by PD feedback, but the robot will converge to the Singular Configuration. In order to solve this problem, we propose a control law that controls shape controllable points for avoiding the Singular Configuration. Using the proposed control law, the robot can accomplish trajectory tracking of the head position without converging to the Singular Configuration. Simulation results show the effectiveness of the proposed control law.

H Sato - One of the best experts on this subject based on the ideXlab platform.

  • trajectory tracking control of snake robots based on dynamic model
    International Conference on Robotics and Automation, 2005
    Co-Authors: Fumitoshi Matsuno, H Sato
    Abstract:

    In this paper, we derive a dynamic model and a trajectory tracking control law for snake robots, which have passive wheels and active joints, based on the dynamic model. For a trajectory tracking control of snake robots, it is one of the important problem to avoid the Singular Configuration like a straight line. Using input-ouput linearization for the head position of snake robots based on dynamic model, we can control the head position by PD feedback, but the robot will converge to the Singular Configuration. In order to solve this problem, we propose a control law that controls shape controllable points for avoiding the Singular Configuration. Using the proposed control law, the robot can accomplish trajectory tracking of the head position without converging to the Singular Configuration. Simulation results show the effectiveness of the proposed control law.

  • ICRA - Trajectory Tracking Control of Snake Robots Based on Dynamic Model
    Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 1
    Co-Authors: Fumitoshi Matsuno, H Sato
    Abstract:

    In this paper, we derive a dynamic model and a trajectory tracking control law for snake robots, which have passive wheels and active joints, based on the dynamic model. For a trajectory tracking control of snake robots, it is one of the important problem to avoid the Singular Configuration like a straight line. Using input-ouput linearization for the head position of snake robots based on dynamic model, we can control the head position by PD feedback, but the robot will converge to the Singular Configuration. In order to solve this problem, we propose a control law that controls shape controllable points for avoiding the Singular Configuration. Using the proposed control law, the robot can accomplish trajectory tracking of the head position without converging to the Singular Configuration. Simulation results show the effectiveness of the proposed control law.

Motoyasu Tanaka - One of the best experts on this subject based on the ideXlab platform.

  • Singularity Analysis of a Snake Robot and an Articulated Mobile Robot With Unconstrained Links
    IEEE Transactions on Control Systems and Technology, 2016
    Co-Authors: Motoyasu Tanaka, Kazuo Tanaka
    Abstract:

    In this paper, we analyze the conditions related to Singular Configurations with unconstrained links and present related theorems and lemmas for a snake robot and an articulated mobile robot. A snake robot and an articulated mobile robot have links that have passive or active wheels and the links are serially connected by active joints. The Singular Configuration should be avoided if the robots are automatically controlled because they cannot execute intended motion when they are in the Singular Configuration. We derive a novel necessary and sufficient condition for the Singular Configurations of the snake robot; this removes some limitations of the traditional condition for a snake robot without unconstrained links. We also derive the necessary and sufficient conditions for the Singular Configurations of the articulated mobile robot, and the structural conditions under which a real articulated mobile robot does not have a Singular Configuration. These conditions are proved by analyzing the elements of matrices included in the kinematic model and considering the geometrical meaning of the elements. In addition, we propose evaluation indices representing the distance from the Singular Configurations of a snake robot. We verify the effectiveness of these indices through simulations.

  • Control of a Snake Robot on a Cylindrical Surface Based on a Kinematic Model
    IFAC Proceedings Volumes, 2009
    Co-Authors: Hiroaki Tsukano, Motoyasu Tanaka, Fumitoshi Matsuno
    Abstract:

    Abstract In this paper, we propose a trajectory tracking control law for snake robots on a cylindrical surface, which have passive wheels and active joints. Snake robots have kinematic redundancy with introduction of wheelless links. First, we derive a kinematic model of the robot based on non-holonomic constraints that wheels do not sideslip and holonomic constrains that wheels remain in contact with a cylindrical surface at all times. It is necessary to avoid the Singular Configuration of the snake robot to achieve trajectory tracking. We indicate the conditions under which the robot becomes a Singular Configuration by analyzing the kinematic model, and design a trajectory tracking controller that can avoid the Singular Configuration using kinematic redundancy. Simulation results show the validity of the proposed controller.

  • Singular Configuration avoidance of a snake-like robot with screw drive units
    2008 SICE Annual Conference, 2008
    Co-Authors: Yong Gao, Motoyasu Tanaka, Hiroaki Fukushima, Fumitoshi Matsuno
    Abstract:

    In this paper, we propose a control method for a snake-like robot with screw drive units, which aims to achieve Singular Configuration avoidance as well as tracking control of the head position and orientation. A cost function measuring nonSingularity is introduced, and a control input is chosen such that the cost function is increased by using redundant degrees of freedom. The effectiveness of the proposed control law is investigated by simulations and experiments using a 4-link snake-like robot with screw drive units.

Alain Fournier - One of the best experts on this subject based on the ideXlab platform.

  • High Resolution Flexible 3-RRR Planar Parallel Micro-Stage in Near Singular Configuration for Resolution Improvement
    2005
    Co-Authors: Stéphane Ronchi, Olivier Company, Sébastien Krut, François Pierrot, Alain Fournier
    Abstract:

    We focus on the micro-stage of a new high resolution positioning machine. One of its key features is the use of flexible circular notch hinges for passive joints. After a reminder of the micro-stage architecture and its inverse position and velocity kinematics solutions, a force model is developed for the choice of the actuators. This model takes into account the flexible R (Revolute) joints modeled as torsional springs and the external forces applied on the traveling plate. Simulations are conducted to evaluate both kinds of forces and result in the choice of the appropriate actuator. The final design of the micro-stage is presented as well as the obtained prototype.

  • High resolution flexible 3-RRR planar parallel micro-stage in near Singular Configuration for resolution improvement. Part I
    2005
    Co-Authors: Stéphane Ronchi, Olivier Company, Sébastien Krut, François Pierrot, Alain Fournier
    Abstract:

    The increasing level of requirements in terms of performance, accuracy, repeatability and resolution in the semiconductors industry leads to several technological problems; among them the positioning accuracy and resolution are peculiarly important. In this paper, we address the crucial issue of high resolution and fast positioning mechanisms. We propose a novel type of high resolution and fast positioning mechanism, based on a macro/micro architecture composed of two stages. We focus here on the micro-stage. It is a combination of: a 3-RRR planar parallel structure (3-RRR stands for 3 kinematic chains in parallel, each chain composed of 3 revolute joints R in a serial arrangement) with deported PRR actuation (a rod connected with two revolute joints R to a linear actuator P and to the RRR chain). This architecture provides stiffness, symmetry and interesting thermal properties; Flexible R links (which avoid the drawbacks of conventional links in terms of backlash, friction, wear, stick-slip,...); and near serial-Singular Configuration which results in an improvement of the resolution. A modeling of inverse kinematics for position and velocity is presented. Then, an optimization is run to find the best set of geometrical parameters for the micro-stage. An articulated kinematic scheme is finally presented.

  • IROS - High resolution flexible 3-RRR planar parallel micro-stage in near Singular Configuration for resolution improvement. Part I
    2005 IEEE RSJ International Conference on Intelligent Robots and Systems, 2005
    Co-Authors: Stéphane Ronchi, Sébastien Krut, François Pierrot, Alain Fournier
    Abstract:

    The increasing level of requirements in terms of performance, accuracy, repeatability and resolution in the semiconductors industry leads to several technological problems; among them the positioning accuracy and resolution are peculiarly important. In this paper, we address the crucial issue of high resolution and fast positioning mechanisms. We propose a novel type of high resolution and fast positioning mechanism, based on a macro/micro architecture composed of two stages. We focus here on the micro-stage. It is a combination of: a 3-RRR planar parallel structure (3-RRR stands for 3 kinematic chains in parallel, each chain composed of 3 revolute joints R in a serial arrangement) with deported PRR actuation (a rod connected with two revolute joints R to a linear actuator P and to the RRR chain). This architecture provides stiffness, symmetry and interesting thermal properties; Flexible R links (which avoid the drawbacks of conventional links in terms of backlash, friction, wear, stick-slip,...); and near serial-Singular Configuration which results in an improvement of the resolution. A modeling of inverse kinematics for position and velocity is presented. Then, an optimization is run to find the best set of geometrical parameters for the micro-stage. An articulated kinematic scheme is finally presented.

Zhen Huang - One of the best experts on this subject based on the ideXlab platform.

  • orientation Singularity representation and orientation capability computation of a special class of the gough stewart parallel mechanisms using unit quaternion
    Chinese Journal of Mechanical Engineering, 2012
    Co-Authors: Baokun Li, Qiuju Zhang, Zhen Huang
    Abstract:

    Singular Configuration seriously affects the performance of the Gough-Stewart parallel mechanism and has attracted many researchers’ attentions. However, most of existing topics often focus on the position-Singularity of the mechanism for a constant-orientation, but few reports research the orientation-Singularity for a given position. In order to investigate the orientation-Singularity of the Gough-Stewart parallel mechanisms with two dissimilar semi-regular hexagonal platforms for a given position, after constructing the discrimination matrix of the Singular Configuration of the mechanism and computing the determinant of this matrix by using unit quaternion as the orientation parameters which can avoid the Singularities in parameterization, a general symbolic expression representing the three-dimensional orientation-Singularity locus for a given position is obtained and the three-dimensional view of the orientation-Singularity locus is further described. The orientation-Singularity-free void exists inside the orientation-Singularity locus, but the shape of the orientation-Singularity-free void is irregular and inconvenient for the design of the mechanism. The minimal inscribed sphere of the three-dimensional orientation-Singularity locus namely the orientation-Singularity-free ball is described. The radius of the ball orientation-capability is used as the measurement for the orientation-Singularity-free void size. A new efficient algorithm is proposed for the computation of the orientation-capability. Finally, the influences of the geometry parameters and the different positions of the mechanism on the orientation-capability are discussed. A new method of the Singularity analysis of the Gough-Stewart parallel mechanism is advanced based on the unit quaternion, and the research finds have important referential value for the Configuration parameters optimization of this class of the parallel mechanisms with the goal of having the maximal Singularity-free zone.

  • Mobility analysis of 4-RPRPR and 4-RRRPR parallel mechanisms with bifurcation of Schoenflies motion by screw theory
    2009
    Co-Authors: Qiaohong Chen, Zhen Huang
    Abstract:

    This paper presents the mobility analysis of two parallel mechanisms, 4-RPRPR and 4-RRRRR, by screw theory. It is shown that the two parallel mechanism have the bifurcation of Schoenflies motion. In the Singular Configuration with the moving platform being parallel to the base, the moving platform has three finite translational degrees of freedom (DOFs) and two instantaneous rotational DOFs. The rotation axes can be any two lines parallel to the base. The moving platform can rotate finitely about the u or v axis from the Singular Configuration. After the finite rotation, the moving platform has three finite translational DOFs and one finite rotational DOF about the u or v axis, that is, a Schoenflies Motion. The rotational DOF about the u axis is exclusive to that about the v axis, namely, if the moving platform rotates finitely about the u axis, no finite rotation about the v axis can happen unless the moving platform returns to the Singular posture. To obtain the total control of the change of mobility, five actuators are required to perform redundant actuation.

  • ICRA - Singularity Analysis for a 5-DoF Fully-Symmetrical Parallel Manipulator 5-RRR(RR)
    Proceedings 2007 IEEE International Conference on Robotics and Automation, 2007
    Co-Authors: Si-jun Zhu, Zhen Huang, Ming-yang Zhao
    Abstract:

    A 5-DoF 3R2T (three dimensional rotation and two dimensional translation degrees of freedom) fully-symmetrical parallel manipulator can be adopted in many applications such as simulating the motion of spinal column. However, kinematics of this type parallel manipulator has not been studied enough because of short history. The study of kinematics of the manipulators leads inevitably to the problem of Singular Configuration. Singularity of a 5-DoF 3R2T fully-symmetrical parallel manipulator, 5-RlowbarRI.ubar;RI.ubar;(RR), is illustrated in this study. According to the Singularity classification by Fang and Tsai, both limb Singularity and actuation Singularity are illustrated by screw theory and Grassmann geometry. The result of this study will be helpful for Singularity analysis of 5-DoF 3R2T fully-symmetrical parallel manipulators because of their similar constraint property.

  • Resolution of Singular Configuration Space of 3/6-SPS Parallel Manipulator Using an Equivalent SC Simulation Mechanism
    Volume 7: 29th Mechanisms and Robotics Conference Parts A and B, 2005
    Co-Authors: Zhen Huang
    Abstract:

    The determination of the 6-dimensional Singular Configurations (SC) space of 3/6-SPS Stewart parallel manipulator is a very important and quite complicated problem. For a long time, its developments, however, have been very limited, especially the general-linear complex-SC (GSC). Currently, the Jacobian matrix and the Grassmann line geometry have been used to solve the SC space of the Stewart parallel robot. However, these two approaches are not straightforward. In this paper, a novel computer aided geometric approach is proposed for solving the 6-dimensional SC space of the 3/6-SPS Stewart parallel manipulator. First, a simulation mechanism of the 3/6-SPS parallel manipulator is created. Second, its equivalent SC simulation mechanism is created. Third, from the equivalent SC simulation mechanism, some analytical geometry formulas for solving 6-dimension SC space are derived. Finally, some SC space characteristics are analyzed, and some important developments are achieved.© 2005 ASME