Singular Poses Research Articles

Kinematics inverse solution of assembly robot based on improved particle swarm optimization

AbstractInverse kinematics of robot is the basis of robot assembly, which directly determines the pose of robot. Because the traditional inverse solution algorithm is limited by the robot topology structure, singular pose and inverse solution accuracy, it affects the use of robots. In order to solve the above problems, an improved particle swarm optimization (PSO) algorithm is proposed to solve the inverse problem of robot. This algorithm initializes the particle population based on joint angle limitations, accelerating the convergence speed of the algorithm. In order to avoid falling into local optima and premature convergence, we have proposed a nonlinear weight strategy to update the speed and position of particles, enhancing the algorithm’s search ability, in addition introducing a penalty function to eliminate particles exceeding joint limits. Finally, the positions of common points and singular points are selected on PUMA 560 robot and redundant robot for inverse kinematics simulation verification. The results show that, compared with other algorithms, the improved PSO algorithm has higher convergence accuracy and better convergence speed in solving the inverse solution, and the algorithm has certain universality, which provides a new solution for the inverse kinematics solution of the assembly robot.

Trajectory planning of 3-CRU parallel robot with linear kinematics equation

With advantages of linear kinematics equation, no singular pose, regular workspace, the best motion/force transmission performance, 3-CRU parallel robot is potential to perform better when rapid and repetitive grasping/handling in packaging and medicine industry. For this reason, this paper deals with trajectory planning of the 3-CRU parallel robot. The trajectory planning method of the 3-CRU parallel robot is proposed for the first time whose advantage is the robot can arbitrarily increase the interpolation period in the Cartesian space without a twice interpolation in the joint space. This method simplifies the interpolation process of trajectory planning, reduces the occupation of computational resources, improves the computational efficiency of the controller, and benefits the real-time online control. For the problem of residual vibration when the robot stops, the input shaping technology is adopted and time delay compensation strategy is proposed, which improves the positioning accuracy of the moving platform and ensures fixed running time. This paper lays a theoretical and practical foundation for the application of the 3-CRU parallel robot in the future.

Screw theory based method to formulate local Jacobian’ magnitude estimator contours for 6 DoF robots

Singularity prediction of Jacobian is inherently related to the design of any manipulator. Optimization of Jacobian is known to improve the joint rates and joint torques for the same set of end-effector twists and wrenches. Any mathematical entity which is an estimator of Jacobian can be used as a manifestation of the stated two schemes. It is required that online computation of Jacobian be implemented so that singular poses can be avoided and performance is maximized. We present an algorithm that relates to the determinant of the Jacobian for robotic manipulators. The algorithm developed is quicker to compute, and a strategy is developed to synthesize the local estimator contour. The contours change dynamically, henceforth optimal motor torques (in case of presence of interaction fields or system requiring force control) and optimal joint rates can be defined, depending on the control algorithm. The algorithm developed is independent of the structure of the matrix and is generalized to any six DoF manipulator structure used.

Singularities of a planar 3-RPR parallel manipulator with joint clearance

SUMMARYIf the joint clearances of the joints of a manipulator are considered, an unconstrained motion of the end-effector can be computed. This is true for all poses of the manipulator, even with all actuators locked.This paper presents how this unconstrained motion can be determined for a planar 3-RPR manipulator. The singularities are then studied. It is shown that when clearances are considered, the singularity curves normally found in the workspace of such a manipulator become singular zones. These zones can be significant and greatly reduce the usable workspace of a manipulator. Since a prescribed configuration that would not, in theory, corresponds to a singular pose can become singular due to the unconstrained motion, the results of this paper are relevant to manipulator design and trajectory planning.

Kinematic Analysis of the 3-RPS Cube Parallel Manipulator

The 3-RPS cube parallel manipulator, a three-degree-of-freedom parallel manipulator initially proposed by Huang and Fang (1995, “Motion Characteristics and Rotational Axis Analysis of Three DOF Parallel Robot Mechanisms,” IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century, Vancouver, BC, Canada, Oct. 22–25, pp. 67–71) is analyzed in this paper with an algebraic approach, namely, Study kinematic mapping of the Euclidean group SE(3) and is described by a set of eight constraint equations. A primary decomposition is computed over the set of eight constraint equations and reveals that the manipulator has only one operation mode. Inside this operation mode, it turns out that the direct kinematics of the manipulator with arbitrary values of design parameters and joint variables, has 16 solutions in the complex space. A geometric interpretation of the real solutions is given. The singularity conditions are obtained by deriving the determinant of the Jacobian matrix of the eight constraint equations. All the singular poses are mapped onto the joint space and are geometrically interpreted. By parametrizing the set of constraint equations under the singularity conditions, it is shown that the manipulator is in actuation singularity. The uncontrolled motion gained by the moving platform is also provided. The motion of the moving platform is essentially determined by the fact that three vertices in the moving platform move in three mutually orthogonal planes. The workspace of each point of the moving platform (with exception of the three vertices) is bounded by a Steiner surface. This type of motion has been studied by Darboux in 1897. Moreover, the 3DOF motion of the 3-RPS cube parallel manipulator contains a special one-degree-of-freedom motion, called the vertical Darboux motion (VDM). In this motion, the moving platform can rotate and translate about and along the same axis simultaneously. The surface generated by a line in the moving platform turns out to be a right-conoid surface.

A planar parallel 3-RRR robot with synchronously driven cranks

This paper focuses on the analysis and synthesis of F-mechanisms, i.e., of planar parallel 3-RRR robots with three synchronously driven cranks. These are high-speed planar mechanisms, which allow modifying the periodical constrained motion by phase shifting during operation. There is a broad variety of obtainable constrained motions — including a permanent stillstand.The velocity analysis reveals that there are poses with either no pole configuration or an infinite number of pole configurations. These singular resp. twofold singular poses can be geometrically characterized. It turns out that in general the singular poses are those where the cranks need to reverse the rotation in order to perform the full motion. At twofold singular poses bifurcations can take place. The constrained motions are algebraic of degree 6. The question of whether the active bars of a given F-mechanism are completely turnable can only be cleared from case to case by a numerical analysis. Here a particular diagram which indicates reverse poses as well as bifurcations is useful.

The 3-RPS parallel manipulator from an algebraic viewpoint

The 3-RPS parallel manipulator is a three degree of freedom parallel manipulator, which was introduced by K. Hunt in 1983 as one of the lower mobility parallel manipulators. Since then the 3-RPS gained a lot of attention in literature, but most of the articles on this manipulator use screw theory to explain its local kinematic behavior. An algebraic approach via Study's kinematic mapping reveals interesting global properties of this type of manipulator. The global kinematic behavior of the manipulator is described by algebraic equations, so called constraint equations. In the kinematic analysis these equations are manipulated using methods of algebraic geometry and are interpreted geometrically. It is shown, that the forward kinematics of the 3-RPS has in general 16 solutions in the field of complex numbers. Its workspace splits into two, essentially different operation modes. A geometric and kinematic interpretation of both modes is given. Furthermore it is shown that a transition between the operation modes is possible under certain circumstances. The operation modes are detected via a primary decomposition of the ideal corresponding to the constraint equations. Conditions for singular poses are derived from the constraint equations by discussing the Jacobian of the set of constraint equations. Finally, for singular poses of each operation mode as well as for singular poses belonging to both operation modes, a mapping into the space of joint parameters will be described. Images of singular poses of the manipulator under the mapping determine algebraic surfaces in the joint space, which are analyzed algebraically.

Study on similarity imitation constraints of biped walking for humanoid robot

Similarity motion imitation on humanoid robot from the captured tracks of human actor has attracted more and more attention. We described the basic system of similarity imitation that was formed by three modules - the image capture, imitation control and imitation on real robot. The similarity degree was analysed by the differences of angle, angular velocity and acceleration between human actor and robot, and the function of spatio-temporal harmony for simultaneous actions was provided as well. In order to make the humanoid robot walk like the human actor by following the captured tracks, the constraints of kinematics and zero moment point ZMP shall be considered. We proposed a method of similarity imitation constraint on biped walking for humanoid robot. The walking process was divided into three phases and the corresponding kinematics and ZMP constraints were set on them. Besides, the trigonometric functions were used to connect the consecutive phases to make the track smooth, and the constraint of avoiding singular pose was also accomplished by making the knee flexible. We applied the constraints of similarity imitation and reached the similar biped walking on the humanoid robot Aldebaran Nao.

Analysis of Bounded Cable Tensions in Cable-Actuated Parallel Manipulators

Cable-actuated parallel manipulators (CPMs) rely on cables instead of rigid links to manipulate the moving platform in the taskspace. Upper and lower bounds imposed on the cable tensions limit the force capability in CPMs and render certain forces infeasible at the end effector. This paper presents a geometrical analysis of the problems to 1) determine whether a CPM is capable of balancing a given wrench within the cable tension limits (feasibility check); 2) minimize the 2-norm of the cable tensions that balance feasible wrenches; and 3) check for the existence of an all-positive nullspace vector, which is a necessary condition to have a wrench-closure configuration in CPMs. The unified approach used in this analysis is systematic and geometrically intuitive that is based on the formulation of the static force equilibrium problem as an intersection between two convex sets and the application of Dykstra's alternating projection algorithm to find the projection of a point onto that intersection. In the case of infeasible wrenches, the algorithm can determine whether the infeasibility is because of the cable tension limits or the non-wrench-closure configuration. For the former case, a method was developed by which this algorithm can be used to extend the cable tension limits to balance infeasible wrenches. In addition, the performance of the algorithm is explained in the case of incompletely restrained cable-driven manipulators and the case of manipulators at singular poses. This paper also discusses the algorithm convergence and termination rule. This geometrical and systematic approach is intended for use as a convenient tool for cable tension analysis during design.

Singularity loci of an orthogonal spherical two-degree-of-freedom parallel mechanism

Singularity analysis plays an important role in the design of robots, especially for parallel robots. In this paper, the direct and inverse kinematics of an orthogonal spherical two-degree-of-freedom parallel mechanism is proposed based on the modified Euler angles. All the singular poses of the mechanism are achieved through the direct kinematic analysis. Self-motions, which are different from the general spherical 5R parallel mechanisms, are also discussed. Singularity loci in the joint space and Cartesian space are plotted according to the Jacobin of the mechanism. Result shows that the singularity loci at the joint space are two circles and one line, whereas at the Cartesian space are a circle.

On the Singularity Surface of Planar 3-RPR Parallel Mechanisms

This paper investigates the algebraic nature of the singularity surface of 3-RPR planar parallel mechanisms. An old result by Noether shows that the singularity surface in the kinematic image space is rational and hence must consist of a single component. This property implies that if a box can be defined in the workspace of the mechanism such that its faces, edges, and vertices do not contain a singular pose, then there are no singularities inside the box, which is a very useful result in a context of design. The kinematic mapping is first recalled and the equation of the singularity surface is derived in two different ways. The geometric properties of this surface that are essential to derive the rational parametrization are then discussed. Finally, two algorithms to derive parametric representations of the surface are given, which completes the proof.

Discontinuously Movable Seven-Link Mechanisms Via Group-Algebraic Approach

Combining planar and spherical 4R chains generates three kinds of new discontinuously movable (DM) seven-link mechanisms. The mobility analysis is based on algebraic concepts of set theory. These mechanisms are called hybrid planar-spherical 7R, hybrid spherical-spherical 7R, and hybrid planar-planar 6RIP DM mechanisms. Their discontinuous mobility is explained employing the Lie group algebraic properties of the displacement set. Moreover, the same given spatial arrangement of joints can be linked in two ways constituting two distinct chains, which have a quite different mobility. One chain has two global degrees of freedom (d.o.f.), which disobey the general Grubler-Kutzbach mobility criterion. The other chain exhibits a singular pose, which is a bifurcation towards two distinct working modes of mobility with one d.o.f. Then the set of relative motions between any two specific links is not manifold but consists of the union of displacement one-dimensional manifolds. In general, when two or more subgroups are involved in a closed-loop chain, the discontinuous mobility can happen by changing the order of the kinematic pair linking.

Path Tracking of Parallel Manipulators in the Presence of Force Singularity

Parallel manipulators are uncontrollable at force singularities due to the infeasibly high actuator forces required. Existing remedies include the application of actuation redundancy and motion planning for singularity avoidance. While actuation redundancy increases cost and design complexity, singularity avoidance reduces the effective workspace of a parallel manipulator. This article presents a path tracking type of approach to operate parallel manipulators when passing through force singularities. We study motion feasibility in the neighborhood of singularity and conclude that a parallel manipulator may track a path through singular poses if its velocity and acceleration are properly constrained. Techniques for path verification and tracking are presented, and an inverse dynamics algorithm that takes actuator bounds into account is examined. Simulation results for a planar parallel manipulator are given to demonstrate the details of this approach.

Singularities in three-legged platform-type parallel mechanisms

Parallel mechanisms frequently contain an unstable type of singularity that has no counterpart in serial mechanisms. When the mechanism is at or near this type of singularity, it loses the ability to counteract external forces in certain directions. The determination of unstable singular configurations in parallel robots is challenging in general, and is usually tackled via an exhaustive search of the workspace using an accurate analytical model of the mechanism kinematics. This paper considers the singularity determination problem from a geometric perspective for planar and spatial three-legged parallel mechanisms. By using the constraints on the passive joint velocities, we derive a necessary condition for the unstable singularities. Using this condition, certain singularities can be found for certain type of platforms. As an example, new singular poses are discovered using this approach for a six-degree-of-freedom machining center.

Workspace Enlargement for Parallel Kinematic Machines

This paper presents an approach that allows parallel kinematic machines to move through singular poses typically connected with them. Using this the usable workspace of parallel kinematic machines can be significantly increased. This compensates the main disadvantage of parallel kinematic machines, i.e. the sometimes poor ratio of workspace to machine size. Their main advantage, the higher structural stiffness, is maintained. To efficiently apply this to the kinematic design of production machines, different types of workspaces are defined. Finally a robot is presented that passes through singular poses and shows the possibilities in increasing machine performance by applying the presented method.

A study on the kinematics and dynamics of a 3-DOF parallel machine tool

A new kind of 3-DOF parallel machine tool has been developed to apply in billet snag grinding by Northeastern University, China. It has the advantages of simple structure, higher stiffness, higher ratio of force-to-weight, larger working space, simple kinematics equations, no motion coupling and no singular pose. This robot can be used for grinding, milling, polishing and other machining process with suitable tools. In this paper, its structure and degree of freedom, the workspace, the kinematics and accuracy analysis, the static and dynastic analysis, the simple robot and its parameters are introduced.