General-purpose inverse kinematics transformations for robotic manipulators

Real-time robot control requires efficient inverse kinematics transformations to compute the temporal evolution of the joint coordinates from the motion of the end-effector. The development of a coherent, general-purpose framework, incorporating position, velocity and acceleration transformations, is the theme of this paper. In this framework, the computational requirements of a new inverse kinematic algorithm are delineated. The algorithm is applicable to serial (open-chain) manipulators with arbitrary axes of motion. Comparative evaluations of the computational cost of the algorithm demonstrate its efficacy and feasibility for real-time applications.     

A neuro-simulated annealing approach to the inverse kinematics solution of redundant robotic manipulators

The neural-network-based inverse kinematics solution is one of the recent topics in the robotics because of the fact that many traditional inverse kinematics problem solutions such as geometric, iterative and algebraic are inadequate for redundant robots. However, since the neural networks work with an acceptable error, the error at the end of inverse kinematics learning should be minimized. In this study, simulated annealing (SA) algorithm was used together with the neural-network-based inverse kinematics problem solution robots to minimize the error at the end effector. The solution method is applied to Stanford and Puma 560 six-joint robot models to show the efficiency. The proposed algorithm combines the characteristics of neural network and an optimization technique to obtain the best solution for the critical robotic applications. Three Elman neural networks were trained using separate training sets and different parameters, since one of them can give better results than the others can. The best result is selected within three neural network results by computing the end effector error via direct kinematics equation of the robotic manipulator. The decimal part of the neural network result was improved up to 10 digits using simulated annealing algorithm. The obtained best solution is given to the simulated annealing algorithm to find the best-fitting 10 digits for the decimal part of the solution. The end effector error was reduced significantly.     

A neural-network committee machine approach to the inverse kinematics problem solution of robotic manipulators

In robotics, inverse kinematics problem solution is a fundamental problem in robotics. Many traditional inverse kinematics problem solutions, such as the geometric, iterative, and algebraic approaches, are inadequate for redundant robots. Recently, much attention has been focused on a neural-network-based inverse kinematics problem solution in robotics. However, the result obtained from the neural network requires to be improved for some sensitive tasks. In this paper, a neural-network committee machine (NNCM) was designed to solve the inverse kinematics of a 6-DOF redundant robotic manipulator to improve the precision of the solution. Ten neural networks (NN) were designed to obtain a committee machine to solve the inverse kinematics problem using separately prepared data set since a neural network can give better result than other ones. The data sets for the neural-network training were prepared using prepared simulation software including robot kinematics model. The solution of each neural network was evaluated using direct kinematics equation of the robot to select the best one. As a result, the committee machine implementation increased the performance of the learning.     

基于模糊神经网络的机器人逆运动学问题

针对机器人逆运动学问题，本文指出了基于模糊神经网络（FNN，Fuzzy Neural Network）的解决方案，阐述了基本设计思想和具体算法过程，给出了二自由度刚性机器人的仿真结果，以表明该方案的有效性和可行性。     

Task-directed inverse kinematics for redundant manipulators

This paper presents kinematic algorithms for resolved-rate based inverse kinematics of redundant manipulators. Efficient and robust Jacobian and weighted damped least squares algorithms are given which provide a method that allows full utilization of the redundancy to best achieve task requirements. A nominal set of task space variables is suggested and procedures for modifying this specification or their relative priorities due to changing task requirements or events are discussed. Examples are shown using a simulation of the seven degree-of-freeom Robotics Research manipulator. These simulations demonstrate the singularity robustness of the algorithms and the ability to smoothly transition between task parameterizations and relative priorities.     

A solution to the inverse kinematics of redundant manipulators

A solution to the inverse kinematics is a set of joint coordinates which correspond to a given set of task space coordinates (position and orientation of end effector). For the class of kinematically redundant robots, the solution is generically nonunique such that special methods are required for obtaining a solution. The method addressed in the paper, introduced earlier and termed “generalized inverse,” is based on a certain partitioning of the Jacobian functional corresponding to a nonlinear relationship of the inverse kinematics type. The article presents a new algorithm for solving the inverse kinematics using the method of generalized inverse based on a modified Newton-Raphson iterative technique. The new algorithm is efficient, converges rapidly, and completely generalizes the solution of the inverse kinematics problem for redundant robots. The method is illustrated by numerical examples.     

Repeatability of inverse kinematics algorithms for mobile manipulators

We introduce and examine the property of repeatability of inverse kinematics algorithms for mobile manipulators. Similarly to stationary manipulators, repeatability of mobile manipulators is defined by requiring that a closed path in the task space should be transformed by the inverse kinematics algorithm into a closed path in the configuration space. In a simply connected, singularity-free region of the task space, a necessary and sufficient condition for repeatability is derived as the integrability condition of a distribution associated with the inverse kinematics algorithm.     

A computer-aided geometric approach to inverse kinematics

This paper presents a geometric approach to solving the inverse kinematics for three-joint placeable robotic manipulators. The distinct feature of this approach is that it uses geometric variables such as length, area ratio, and Pythagoras difference to find the closed form solutions. It is proved here that for any three-joint placeable manipulator there exists a geometric variable that keeps constant during the evolution of the manipulator. With this invariant, a characteristic equation of the manipulator can be derived and can be transformed into a polynomial equation with degree up to four. Therefore the closed form solution of the three-joint placeable manipulator can be obtained. A characteristic equation of the three-revolute-joint manipulator produced by this approach with the assistance of Maple is listed in the Appendix. The possible application of this geometric approach to a six-joint manipulator is also discussed in the paper. © 1998 John Wiley & Sons, Inc. 15: 131–143, 1998     

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.     

A strictly convergent real-time solution for inverse kinematics of robot manipulators

Inverse Kinematics has been recognized as an important problem in robotics applications. A robot independent solution can only be obtained through numerical methods, but most solutions which use this approach have problems with convergence especially near singularity points. This article develops a strictly convergent algorithm and a special-purpose Inverse Kinematics Processor (IKP) to obtain the solution in real time. While the algorithm is based on open-loop integration of rates, the absolute position deviation is used as a criterion to control the iteration, and a feedback mechanism has been especially designed to eliminate problems with long-term drift or with initial errors in the solution. The architecture of the IKP is based on a high-speed floating-point arithmetic processor and is designed to perform the common matrix-vector operations efficiently with a minimum processor cycle time. The algorithm has been simulated on the proposed architecture, and the results show its robustness and real-time capability. For a six degree-of-freedom robot manipulator (for which no closed-form solution exist), the Inverse Kinematics solution may be obtained at an approximate 2 khz rate with an error which is within standard repeatability limits.     

Selection of near-minimum time geometric paths for robotic manipulators

A number of trajectory planning algorithms exist for calculating the joint positions, velocities, and torques which will drive a robotic manipulator along a given geometric path in minimum time. However, the time depends upon the geometric path, so the traversal time of the path should be considered again for geometric planning. There are algorithms available for finding minimum distance paths, but even when obstacle avoidance is not an issue, minimum (Cartesian) distance is not necessarily equivalent to minimum time. In this paper, we have derived a lower bound on the time required to move a manipulator from one point to another, and determined the form of the path which minimizes this lower bound. As numerical examples, we have applied the path solution to the first three joints of the Bendix PACS arm and the Stanford arm. These examples do indeed demonstrate that the derived approximate solutions usually require less time than Cartesian straight-line (minimum-distance) paths and joint-interpolated paths.     

A new inverse kinematics algorithm for binary manipulators with many actuators

In this paper we present a new, and extremely fast, algorithm for the inverse kinematics of discretely actuated manipulator arms with many degrees of freedom. Our only assumption is that the arm is macroscopically serial in structure, meaning that the overall structure is a serial cascade of units with each unit having either a serial or parallel kinematic structure. Our algorithm builds on previous works in which the authors and coworkers have used the workspace density function in a breadthfirst search for solving the inverse kinematics problem. The novelty of the method presented here is that only the 'mean' of this workspace density function is used. Hence the requirement of storing a sampled version of the workspace density function (which is a function on a six-dimensional space in the case of a spatial manipulator) is circumvented. We illustrate the technique with both planar revolute and variable-geometry-truss manipulators, and briefly describe a new manipulator design for which this algorithm is applicable.     

Classification and characterization of inverse kinematics solutions for anthropomorphic manipulators

Topological properties of the kinematics map are exploited to develop a novel method for redundancy parameterization and extremely fast inverse kinematics solutions for 7-DOF anthropomorphic manipulators and animation characters. The method consists of generating joint angles vectors (configurations) and determining their associated hand position/orientation (pose) via the known forward kinematics. The generated data are classified into various inverse kinematics solutions manifolds. These manifolds are subsequently segmented so that the redundancy can be parameterized and the solutions can be represented by simple equations whose parameters are stored for rapid online computation. During the online phase, given the desired hand pose, the appropriate stored parameters are retrieved and various inverse kinematics solutions are computed. The online time to provide various solutions is of the order of several microseconds, which allow real-time inverse kinematics evaluations for fast moving animation characters or manipulators.     

Overview of damped least-squares methods for inverse kinematics of robot manipulators

In this paper, we present a tutorial report of the literature on the damped-least squares method which has been used for computing velocity inverse kinematics of robotic manipulators. This is a local optimization method that can prevent infeasible joint velocities near singular configurations by using a damping factor to control the norm of the joint velocity vector. However, the exactness of the inverse kinematic solution has to be sacrificed in order to achieve feasibility.The damping factor is an important parameter in this technique since it determines the trade-off between the accuracy and feasibility of the inverse kinematic solution. Various methods that have been proposed to compute an appropriate damping factor are described.Redundant manipulators, possessing extra degrees of freedom, afford more choice of inverse kinematic solutions than do non-redundant ones. The damped least-squares method has been used in conjunction with redundancy resolution schemes to compute feasible joint velocities for redundant arms while performing an additional subtask. We outline the different techniques that have been proposed to achieve this objective. In addition, we introduce an iterative method to compute the optimal damping factor for one of the redundancy resolution techniques.     

Minimum-time control of robotic manipulators with geometric path constraints

Conventionally, robot control algorithms are divided into two stages, namely, path or trajectory planning and path tracking (or path control). This division has been adopted mainly as a means of alleviating difficulties in dealing with complex, coupled manipulator dynamics. Trajectory planning usually determines the timing of manipulator position and velocity without considering its dynamics. Consequently, the simplicity obtained from the division comes at the expense of efficiency in utilizing robot's capabilities. To remove at least partially this inefficiency, this paper considers a solution to the problem of moving a manipulator in minimum time along a specified geometric path subject to input torque/force constraints. We first describe the manipulator dynamics using parametric functions which represent geometric path constraints to be honored for collision avoidance as well as task requirements. Second, constraints on input torques/ forces are converted to those on the parameters. Third, the minimum-time solution is deduced in an algorithm form using phase-plane techniques. Finally, numerical examples are presented to demonstrate utility of the trajectory planning method developed.     

A repeatable inverse kinematics algorithm with linear invariant subspaces for mobile manipulators.

On the basis of a geometric characterization of repeatability we present a repeatable extended Jacobian inverse kinematics algorithm for mobile manipulators. The algorithm's dynamics have linear invariant subspaces in the configuration space. A standard Ritz approximation of platform controls results in a band-limited version of this algorithm. Computer simulations involving an RTR manipulator mounted on a kinematic car-type mobile platform are used in order to illustrate repeatability and performance of the algorithm.     

A geometric optimization method for the trajectory planning of flexible manipulators

Multibody System Dynamics - Lightweight and flexible robots offer an interesting answer to industrial needs for safety and efficiency. The control of such systems should be able to deal properly...     

An improved approach to the solution of inverse kinematics problems for robot manipulators

A structured artificial neural-network (ANN) approach has been proposed here to control the motion of a robot manipulator. Many neural-network models use threshold units with sigmoid transfer functions and gradient descent-type learning rules. The learning equations used are those of the backpropagation algorithm. In this work, the solution of the kinematics of a six-degrees-of-freedom robot manipulator is implemented by using ANN. Work has been undertaken to find the best ANN configurations for this problem. Both the placement and orientation angles of a robot manipulator are used to fin the inverse kinematics solutions.     

Comments on "Selection of near-minimum time geometric paths for robotic manipulators

The paper presented some interesting results on the selection of near-minimum time geometric paths for robotic manipulators. However, there are certain parts of this paper which need to be clarified.