Inverse kinematics of planar redundant manipulators via virtual links with configuration index

This article presents a new method for generating inverse kinematic solutions for planar manipulators with large redundancy (hyper-redundant manipulators). The proposed method starts by decomposing a planar redundant manipulator into a series of local planar arms that are either 2-link or 3-link manipulator modules, and connecting the conjunction points between them with virtual links. The manipulator then can be handled by a simple virtual link system, which may be conveniently divided into non-singular and singular cases depending on its configuration. When the virtual link system is no longer effective due to a singular configuration, the displacement of the end-effector is then allocated to virtual links according to a displacement distribution criterion. A dexterity index called the “configuration index” distinguishes the non-singular and singular cases. The concept of virtual link is shown by computer simulations to be simple and effective for the inverse kinematics of a planar hyper-redundant manipulator with a discrete model. In particular, it can be applied to solving the inverse kinematics of a SCARA-type spatial redundant manipulator whose redundancy is included in its planar mechanism. © 1994 John Wiley & Sons, Inc.     

冗余度机器人操作手的运动灵活性测度

本文在速度水平上讨论了机器人操作手的运动灵活性,根据机器人操作手的运动灵活性完全取决于雅可比矩阵列向量的相关性这一分析,提出用雅可比矩阵的子阵 J_m 的总体相关性指标和相对相关性指标作为机器人操作手的运动灵活性测度,定义了运动灵活性的两个度量指标——绝对灵活度 D_α和相对灵活度 D_r;并论证了绝对灵活度 D_α和可操作度 W,相对灵活度 D_r 和可操作度 W、条件数 K 及最小奇异值σ_m 之间的关系;证明了绝对灵活度 D_α和可操作度 W 的等价性,并给出了可操作度的新的定义.从而全面论证了本文提出的操作手的运动灵活性测度的合理性.     

A novel formulation for determining joint constraint loads during optimal dynamic motion of redundant manipulators in DH representation

The kinematic representations of general open-loop chains in many robotic applications are based on the Denavit–Hartenberg (DH) notation. However, when the DH representation is used for kinematic modeling, the relative joint constraints cannot be described explicitly using the common formulation methods. In this paper, we propose a new formulation of solving a system of differential-algebraic equations (DAEs) where the method of Lagrange multipliers is incorporated into the optimization problem for optimal motion planning of redundant manipulators. In particular, a set of fictitious joints is modeled to solve for the joint constraint forces and moments, as well as the optimal dynamic motion and the required actuator torques of redundant manipulators described in DH representation. The proposed method is formulated within the framework of our earlier study on the generation of load-effective optimal dynamic motions of redundant manipulators that guarantee successful execution of given tasks in which the Lagrangian dynamics for general external loads are incorporated. Some example tasks of a simple planar manipulator and a high-degree-of-freedom digital human model are illustrated, and the results show accurate calculation of joint constraint loads without altering the original planned motion. The proposed optimization formulation satisfies the equivalent DAEs.     

Kinematic Analysis of a Macro–Micro Redundantly Actuated Parallel Manipulator

In this paper the kinematic and Jacobian analysis of a macro–micro parallel manipulator is studied in detail. The manipulator architecture is a simplified planar version adopted from the structure of the Large Adaptive Reflector (LAR), the Canadian design of the next generation of giant radio telescopes. This structure is composed of two parallel and redundantly actuated manipulators at the macro and micro level, which both are cable-driven. Inverse and forward kinematic analysis of this structure is presented in this paper. Furthermore, the Jacobian matrices of the manipulator at the macro and micro level are derived, and a thorough singularity and sensitivity analysis of the system is presented. The kinematic and Jacobian analysis of the macro–micro structure is extremely important to optimally design the geometry and characteristics of the LAR structure. The optimal location of the base and moving platform attachment points in both macro and micro manipulators, singularity avoidance of the system in nominal and extreme maneuvers, and geometries that result in high dexterity measures in the design are among the few characteristics that can be further investigated from the results reported in this paper. Furthermore, the availability of the extra degrees of freedom in a macro–micro structure can result in higher dexterity provided that this redundancy is properly utilized. In this paper, this redundancy is used to generate an optimal trajectory for the macro–micro manipulator, in which the Jacobian matrices derived in this analysis are used in a quadratic programming approach to minimize performance indices like minimal micro manipulator motion or singularity avoidance criterion.     

Design optimization of a spatial six degree-of-freedom parallel manipulator based on artificial intelligence approaches

Optimizing the system stiffness and dexterity of parallel manipulators by adjusting the geometrical parameters can be a difficult and time-consuming endeavor, especially when the variables are diverse and the objective functions are excessively complex. However, optimization techniques that are based on artificial intelligence approaches can be an effective solution for addressing this issue. Accordingly, this paper describes the implementation of genetic algorithms and artificial neural networks as an intelligent optimization tool for the dimensional synthesis of the spatial six degree-of-freedom (DOF) parallel manipulator. The objective functions of system stiffness and dexterity are derived according to kinematic analysis of the parallel mechanism. In particular, the neural network-based standard backpropagation learning algorithm and the Levenberg–Marquardt algorithm are utilized to approximate the analytical solutions of system stiffness and dexterity. Subsequently, genetic algorithms are derived from the objective functions described by the trained neural networks, which model various performance solutions. The multi-objective optimization (MOO) of performance indices is established by searching the Pareto-optimal frontier sets in the solution space. Consequently, the effectiveness of this method is validated by simulation.     

The Isotropic Design of Two General Classes of Planar Parallel Manipulators

Manipulator designs with isotropic architectures have a number of advantages, including high servo accuracy and dexterity. Using the isotropy criterion, isotropic designs of two general classes of planar, three-degree-of-freedom, parallel manipulators with three legs are produced. One of these classes comprises 20 manipulators, while the other, 4. As special cases for each class, the complete set of isotropic designs of 2 manipulators is found. The parameter space of isotropic design of these manipulators is a continuum of at least one dimension. © 2995 John Wiley & Sons, Inc.     

Design and analysis of kinematically redundant parallel manipulators with configurable platforms

Redundancy can, in general, improve the ability and performance of parallel manipulators by implementing the redundant degrees of freedom to optimize a secondary objective function. Almost all published researches in the area of parallel manipulators redundancy were focused on the design and analysis of redundant parallel manipulators with rigid (nonconfigurable) platforms and on grasping hands to be attached to the platforms. Conventional grippers usually are not appropriate to grasp irregular or large objects. Very few studies focused on the idea of using a configurable platform as a grasping device. This paper highlights the idea of using configurable platforms in both planar and spatial redundant parallel manipulators, and generalizes their analysis. The configurable platform is actually a closed kinematic chain of mobility equal to the degree of redundancy of the manipulator. The additional redundant degrees of freedom are used in reconfiguring the shape of the platform itself. Several designs of kinematically redundant planar and spatial parallel manipulators with configurable platform are presented. Such designs can be used as a grasping device especially for irregular or large objects or even as a micro-positioning device after grasping the object. Screw algebra is used to develop a general framework that can be adapted to analyze the kinematics of any general-geometry planar or spatial kinematically redundant parallel manipulator with configurable platform.     

A general solution for the position,velocity, and acceleration of hyperredundant planar manipulators

A new approach for the solution of the position, velocity, and acceleration of hyperredundant planar manipulators following any twice‐differentiable desired path is presented. The method is singularity free, and provides a robust solution even in the event of mechanical failure of some of the robot actuators. The approach is based on defining virtual layers, and dividing them into virtual/real three‐link or four‐link subrobots. It starts by solving the inverse kinematic problem for the subrobot located in the lowest virtual layer, which is then used to solve the inverse kinematic equations for the subrobots located in the upper virtual layers. An algorithm is developed that provides a singularity‐free solution up to the full extension through a configuration index. The configuration index can be interpreted as the average of the determinants of the Jacobians of the subrobots. The equations for the velocities and accelerations of the manipulator are solved by extending the same approach, and it is shown that the value of the configuration index is critical in maintaining joint velocity continuity. The inverse dynamic problem of the robot is also solved to obtain the torques required for the robot actuators to accomplish their tasks. Computer simulations of several hyperredundant manipulators using the proposed method are presented as numerical examples. © 2002 John Wiley & Sons, Inc.     

Generation and application of prestress in redundantly full-actuated parallel manipulators

This paper addresses the inverse dynamics of redundantly actuated parallel manipulators. Such manipulators feature advantageous properties, such as a large singularity-free workspace, a high possible acceleration of the moving platform, and higher dexterity and manipulability. Redundant actuation further allows for prestress, i.e., internal forces without generating end-effector wrenches. This prestress can be employed for various goals. It can potentially be used to avoid backlash in the driving units or to generate a desired tangential end-effector stiffness. In this paper, the application of prestress is addressed upon the inverse dynamics solution. A general formulation for the dynamics of redundantly actuated parallel manipulators is given. For the special case of simple redundancy, a closed-form solution is derived in terms of a single prestress parameter. This yields an explicit parametrization of prestress. With this formulation an open-loop prestress control is proposed and applied to the elimination of backlash. Further, the generation of tangential end-effector stiffness is briefly explained. The approach is demonstrated for a planar 4RRR manipulator and a spatial heptapod.     

A systematic method for the hybrid dynamic modeling of open kinematic chains confined in a closed environment

This work presents a systematic method for the dynamic modeling of multi-rigid links confined within a closed environment. The behavior of the system can be completely characterized by two different mathematical models: a set of highly coupled differential equations for modeling the confined multi-link system when it has no impact with surrounding walls; and a set of algebraic equations for expressing the collision of this open kinematic chain system with the confining surfaces. In order to avoid the Lagrangian formulation (which uses an excessive number of total and partial derivatives in deriving the governing equations of multi-rigid links), the motion equations of such a complex system are obtained according to the recursive Gibbs–Appell formulation. The main feature of this paper is the recursive approach, which is used to automatically derive the governing equations of motion. Moreover, in deriving the motion equations, the manipulators are not limited to planar motions only. In fact, for systematic modeling of the motion of a multi-rigid-link system in 3D space, two imaginary links are added to the \(n\)-real links of a manipulator in order to model the spatial rotations of the system. Finally, a 2D and a 3D case studies are simulated to demonstrate the effectiveness of the proposed approach.