An efficient method for inverse dynamics of manipulators based on the virtual work principle

The computational efficiency of inverse dynamics of a manipulator is important to the real-time control of the system. For serial manipulators, the recursive Newton-Euler method has been proven to be the most efficient. However, for more general manipulators, such as serial manipulators with closed kinematic loops or parallel manipulators, it must be modified accordingly and the resultant computational efficiency is degraded. This article presents a computationally efficient scheme based on the virtual work principle for inverse dynamics of general manipulators. The present method uses a forward recursive scheme to compute velocities and accelerations, the Newton-Euler equation to calculate inertia forces/torque, and the virtual work principle to formulate the dynamic equations of motion. This method is equally effective for serial and parallel manipulators. For serial manipulators, its computational efficiency is comparable to the recursive Newton-Euler method. For parallel manipulators or serial manipulators with closed kinematic loops, it is more efficient than the existing methods. As an example, the computations of inverse dynamics (including inverse kinematics) of a general Stewart platform require only 842 multiplications, 511 additions, and 12 square roots.     

Computer generation of symbolic kinematics for robot manipulators

Computer generation of symbolic solutions for the direct and inverse robot kinematics is a desired capability not previously available to robotics engineers. In this article, we present a methodology for the design of a software system capable of solving the direct and inverse kinematics for n degree of freedom (dof) manipulators in symbolic form. The inputs to the system are the Denavit-Hartenberg parameters of the manipulator. The outputs of the system are the direct and inverse kinematics solutions in symbolic form. The system consists of a symbolic processor to perform matrix and algebraic manipulations and an expert system to solve the class of nonlinear equations involved in the solution of the inverse kinematics problem. The system can be used to study robot kinematics configurations whose inverse kinematics solutions are not known to exist a priori. Two examples are included to illustrate its capabilities. The first example provides explicit analytical solutions, previously believed nonexistent, for a 3 dof manipulator. A second example is included for a robot whose inverse kinematics solution requires intensive algebraic manipulations.     

Dynamics analysis of the Star parallel manipulator

Matrix relations in kinematics and dynamics of the Star parallel manipulator are established in this paper. The prototype of the manipulator is a three-degree-of-freedom mechanism, which consists of a system of parallel kinematical chains connecting to a moving platform. Knowing the translation motion of the platform, we develop first the inverse kinematics problem and determine the position, velocity and acceleration of each robot’s link. Further, the inverse dynamics problem is solved using an approach based on the principle of virtual work, but it has been verified the results in the framework of the Lagrange equations with their multipliers. Recursive formulae offer expressions and graphs for the power requirement comparison of each of three actuators in two computational complexities: complete dynamic model and simplified dynamic model.     

Extended Jacobian inverse kinematics algorithms for mobile manipulators

We consider the inverse kinematic problem for mobile manipulators consisting of a nonholonomic mobile platform and a holonomic manipulator on board the platform. The kinematics of a mobile manipulator are represented by a driftless control system with outputs together with the associated variational control system. The output reachability map of the driftless control system determines the instantaneous kinematics, while the output reachability map of the variational system plays the role of the analytic Jacobian of the mobile manipulator. Relying on a formal analogy between the kinematics of stationary and mobile manipulators we exploit the extended Jacobian construction in order to design a collection of extended Jacobian inverse kinematics algorithms for mobile manipulators. It has been proved mathematically and confirmed in computer simulations that these algorithms are capable of efficiently solving the inverse kinematic problem. Moreover, a choice of the Jacobian extension may lay down some guidelines for the platform‐manipulator motion coordination. © 2002 Wiley Periodicals, Inc.     

Kinematics analysis of a novel all-attitude flight simulator

To overcome the kinematic singularity limitation of simulator, which is unavoidable in a three-axis architecture, an all-attitude flight simulator in a four-axis architecture is proposed. The simulator can always provide 3DOF motion by applying redundant manipulator mechanism. For direct kinematics of the manipulator, a dual-Euler method is adopted to solve the expressions of attitude angles; thus computation singularity of all- attitude angles is overcome. For inverse kinematics of the manipulator, pseudo-...     

Kinematic analysis of a 3-PRS parallel manipulator

Although the current 3-PRS parallel manipulators have different methods on the arrangement of actuators, they may be considered as the same kind of mechanism since they can be treated with the same kinematic algorithm. A 3-PRS parallel manipulator with adjustable layout angle of actuators has been proposed in this paper. The key issues of how the kinematic characteristics in terms of workspace and dexterity vary with differences in the arrangement of actuators are investigated in detail. The mobility of the manipulator is analyzed by resorting to reciprocal screw theory. Then the inverse, forward, and velocity kinematics problems are solved, which can be applied to a 3-PRS parallel manipulator regardless of the arrangement of actuators. The reachable workspace features and dexterity characteristics including kinematic manipulability and global dexterity index are derived by the changing of layout angle of actuators. Simulation results illustrate that different tasks should be taken into consideration when the layout angles of actuators of a 3-PRS parallel manipulator are designed.     

Kinematics analysis of a hybrid manipulator for computer controlled ultra-precision freeform polishing

As one of the final processing steps of precision machining, polishing process is a very key decision for surface quality. This paper presents a novel hybrid manipulator for computer controlled ultra-precision (CCUP) freeform polishing. The hybrid manipulator is composed of a three degree-of-freedom (DOF) parallel module, a two DOF serial module and a turntable providing a redundant DOF. The parallel module gives the workpiece three translations without rotations. The serial module holds the polishing tool and gives it no translations on the polishing contact area due to its particular mechanical design. A detailed kinematics model is established for analyzing the kinematics of the parallel module and the serial module, respectively. For the parallel module, the inverse kinematics, the forward kinematics, the Jacobian matrix, the workspace and the dexterity distribution are analyzed systematically. Workspaces are also investigated for varying structural parameters. For the serial module, the inverse kinematics, the forward kinematics, the workspace and the precession motion analysis are carried out. An example of saddle surface finishing with this manipulator is given and the movement of actuators with respect to this shape is analyzed theoretically. These analysis results illustrate that the proposed hybrid manipulator is a very suitable machine structure for CCUP freeform polishing.     

Inverse Dynamic Model and a Control Application of a Novel 6-DOF Hybrid Kinematics Manipulator

Kinematics with six degrees of freedom can be of several types. This paper describes the inverse dynamic model of a novel hybrid kinematics manipulator. The so-called Epizactor consists of two planar disk systems that together move a connecting element in 6 DOF. To do so each of the disk systems has a linkage point equipped with a homokinetic joint. Each disk system can be described as a serial 3-link planar manipulator with unlimited angles of rotation. To compensate singularities, a kinematic redundancy is introduced via a fourth link. The kinematic concept leads to several technical advantages for compact 6-DOF-manipulators when compared to established parallel kinematics: The ratio of workspace volume and installation space is beneficial, the number of kinematic elements is smaller, and rotating drives are used exclusively. For a singularity-robust control-approach, the inverse dynamic model is derived using the iterative Newton–Euler-method. Feasibility is shown by the application of the model to an example where excessive actuator velocities and torques are avoided.     

Estimation model for kinematic calibration of manipulators with a parallel structure

This article provides an estimation model for calibrating the kinematics of manipulators with a parallel geometrical structure. Parameter estimation for serial link manipulators is well developed, but fail for most structures with parallel actuators, because the forward kinematics is usually not analytically available for these. We extend parameter estimation to such parallel structures by developing an estimation method where errors in kinematical parameters are linearly related to errors in the tool pose, expressed through the inverse kinematics, which is usually well known. The method is based on the work done to calibrate the MultiCraft robot. This robot has five linear actuators built in parallel around a passive serial arm, thus making up a two-layered parallel-serial manipulator, and the unique MultiCraft construction is reviewed. Due to the passive serial arm, for this robot conventional serial calibration must be combined with estimation of the parameters in the parallel actuator structure. The developed kinematic calibration method is verified through simulations with realistic data and real robot kinematics, taking the MultiCraft manipulator as the case. © 1994 John Wiley & Sons, Inc.     

OPTIMAL MECHANISM DESIGN AND DYNAMIC ANALYSIS OF A 3‐LEG 6‐DOF LINEAR MOTOR BASED PARALLEL MANIPULATOR

This paper presents the optimal mechanism design and dynamic analysis of a prototype 3‐leg 6‐DOF (degree‐of‐freedom) parallel manipulator. Inverse kinematics, forward kinematics, inverse dynamics and working space characterizing the platform motion are derived. In the presented architecture, the base platform has three linear slideways individually actuated by a synchronous linear servo motor, and each extensible vertical link connecting the upper and base platforms is actuated by an inductive AC servo motor. The linear motors contribute high‐speed movements to the upper platform. This kind of architecture using hybrid (linear and AC) motors yields high level performance of motions, especially in the working space. The novel result of maximal working angles is the significant contribution of this architecture. The Taguchi Experimental Method is applied to design the optimal mechanism of the platform system, and the result is used as the actual data to build this system.     

Inverse dynamics of redundant manipulators using a minimum number of control forces

The number of the control actuators used by the inverse kinematics and dynamics algorithms that have been developed in the literature for generating redundant robot joint trajectories is equal to the number of the degrees of freedom of the manipulator. In this article, an inverse dynamics algorithm that performs the tasks using only a minimum number of actuators is proposed. The number of actuators is equal to the dimension of the task space, and the control forces are solved simultaneously with the corresponding system motion. It is shown that because all degrees of freedom are not actuated, the control forces may lose the ability to make an instantaneous effect on the end-effector acceleration at certain configurations, yielding the dynamical equation set of the system to be singular. The dynamical equations are modified in the neighborhood of the singular configurations by utilizing higher-order derivative information, so that the singularities in the numerical procedure are avoided. Asymptotically stable inverse dynamics closed-loop control in the presence of perturbations is also discussed. The algorithm is further generalized to closed chain manipulators. Three-link and two-link redundant planar manipulators are analyzed to illustrate the validity of the approach. © 2995 John Wiley & Sons, Inc.     

Design and kinetostatic analysis of a new parallel manipulator

This paper proposes an innovative design for a parallel manipulator that can be applied to a machine tool. The proposed parallel manipulator has three degrees of freedom (DOFs), including the rotations of a moving platform about the x and y axes and a translation of this platform along the z-axis. A passive link is introduced into this new parallel manipulator in order to increase the stiffness of the system and eliminate any unexpected motion. Both direct and inverse kinematic problems are investigated, and a dynamic model using a Newton–Euler approach is implemented. The global system stiffness of the proposed parallel manipulator, which considers the compliance of links and joints, is formulated and the kinetostatic analysis is conducted. Finally, a case study is presented to demonstrate the applications of the kinematic and dynamic models and to verify the concept of the new design.     

Design and control of a 6-degree-of-freedom precision positioning system

This paper presents the design and test of a 6-degree-of-freedom(DOF) precision positioning system, which is assembled by two different 3-DOF precision positioning stages each driven by three piezoelectric actuators (PEAs). Based on the precision PEAs and flexure hinge mechanisms, high precision motion is obtained. The design methodology and kinematic characteristics of the 6-DOF positioning system are investigated. According to an effective kinematic model, the transformation matrices are obtained, which is used to predict the relationship between the output displacement from the system arrangement and the amount of PEAs expansion. In addition, the static and dynamic characteristics of the 6-DOF system have been evaluated by finite element method (FEM) simulation and experiments. The design structure provides a high dynamic bandwidth with the first natural frequency of 586.3 Hz. Decoupling control is proposed to solve the existing coupling motion of the 6-DOF system. Meanwhile, in order to compensate for the hysteresis of PEAs, the inverse Bouc-Wen model was applied as a feedforward hysteresis compensator in the feedforward/feedback hybrid control method. Finally, extensive experiments were performed to verify the tracking performance of the developed mechanism.     

Inverse Kinematics of Binary Manipulators Using a Continuum Model

Binary actuators have only two discrete states, both of which are stable without feedback. As a result, manipulators with binary actuators have a finite number of states. The major benefits of binary actuation are that extensive feedback control is not required, reliability and task repeatability are very high, and two-state actuators are generally very inexpensive, resulting in low cost robotic mechanisms. These manipulators have great potential for use in both the manufacturing and service sectors, where the cost of high performance robotic manipulators is often difficult to justify. The most difficult challenge with a binary manipulator is to achieve relatively continuous end-effector trajectories given the discrete nature of binary actuation. Since the number of configurations attainable by binary manipulators grows exponentially in the number of actuated degrees of freedom, calculation of inverse kinematics by direct enumeration of joint states and calculation of forward kinematics is not feasible in the highly actuated case. This paper presents an efficient method for performing binary manipulator inverse kinematics and trajectory planning based on having the binary manipulator shape adhere closely to a time-varying curve. In this way the configuration of the arm does not exhibit drastic changes as the end effector follows a discrete trajectory.     

Neural networks and the inverse kinematics problem

Inverse kinematics is a fundamental problem in robotics. Past solutions for this problem have been realized through the use of various algebraic or algorithmic procedures. In this paper the use of feedforward neural networks to solve the inverse kinematics problem is examined for three different cases. A closed kinematic linkage is used for mapping input joint angles to output joint angles. A three-degree-of-freedom manipulator in 3D space is used to test mappings from both cartesian and spherical coordinates to manipulator joint coordinates. A majority of the results have average errors which fall below 1% of the robot workspace. The accuracy indicates that neural networks are an alternate method for performing the inverse kinematics estimation, thus introducing the fault-tolerant and high-speed advantages of neural networks to the inverse kinematics problem.This paper also shows the use of a new technique which reduces neural network mapping errors with the use of error compensation networks. The results of the work are put in perspective with a survey of current applications of neural networks in robotics.     

Matrix modelling in dynamics of a 2-DOF orienting gear train

Recursive matrix relations for kinematics and dynamics analysis of a 2-DOF orienting gear train are established in this paper. The mechanism is a parallel system with five moving links and three bevel gear pairs controlled by two electric motors. Knowing the rotation motion of the end-effector, the inverse dynamic problem is solved using an approach based on the principle of virtual work and have verified the results in the framework of the Lagrange equations of the second kind. Finally, some graphs for the input angles of rotation, the forces and the powers of the actuators are obtained.     

Inverse dynamics of a parallel manipulator

Presented is an analysis of the kinematics and the inverse dynamics of a proposed three degree of freedom (dof) parallel manipulator resembling the Stewart platform in a general form. In the kinematic analysis, the inverse kinematics, velocity, and acceleration analyses are performed, respectively, using vector analysis and general homogeneous transformations. An algorithm to solve the inverse dynamics of the proposed parallel manipulator is then presented using a Lagrangian technique. In this case, it is found that one should introduce and subsequently eliminate Lagrange multipliers to arrive at the governing equations. Numerical examples are finally carried out to examine the validity of the approach and the accuracy of the numerical technique employed. The trajectory of motion of the manipulator is also performed using a cubic spline. © 1994 John Wiley & Sons, Inc.     

仿人机器人轻型高刚性手臂设计及运动学分析

重点研究了7自由度轻型高刚性作业型仿人机器人手臂的机构设计和运动学分析方法.首先使用动力学仿真、有限元分析与实验测试相结合的方法,设计了仿人机器人手臂,该机械臂结构紧凑、质量轻、刚度高.同时,提出结合查询数据库和逆运动学计算去模仿人类手臂姿态,从而获得逆运动学最优解的方法.该方法不仅解决了冗余自由度带来的逆运动学多解问...