Closed-form Solution Of Inverse Kinematics Research Articles

A parallel approach of the inverse kinematics solutions for robots using a transputer network

This article presents parallel method for computing inverse kinematics solitions for robots with closed-form solutions moving along a straight line trajectory specified in Cartesian space. Zhang and Paul's approach 1 is improved for accuracy and speed. Instead of using previous joint positions as proposed by Zhang and Paul, a first order prediction strategy is used to decouple the dependency between joint positions, and a zero order approximation solution is computed. A compensation scheme using Taylor series expansion is applied to obtain the trajectory gradient in joint space to replace the correction scheme proposed by Zhang and Paul. The configuration of a Mitsubishi RV-M1 robot is used for the stimulation of a closed-form inverse kinematics solutions. An Alta SuperLink/XL with four transputer nodes is used for parallel implementation. The stimulation results show a significant improvement in displacement tracking errors and joint configuration errors along the straight line trajectory. The computational latency is reduced as well. The modified approach proposed in this work is more accurate and faster than Zhang and Paul's approach for robots with closed-form inverse kinematics solutions.

Analysis on the Walking Volumes of a Hexapod System with General 3R Link Legs

In order to move the body of a walking robot translationally, and step over the obstacles, the walking robot must have at least 3 degrees of freedom for each leg. Therefore each leg of the general walking robots can be composed of 3-link system with 3 revolute joints. In this paper, the colsed form of inverse kinimatic solutions is shown for this general 3R linkage. Moreover, in order to have efficient walking volume in rough terrain, the workspace of each log is obtained considering the twist angles and the offsets in D-H parameters. When we design a walking robot, the information of the walking volume is needed for planning desired trajectories of the feet effectively. Appropriate knowledge of the walking volume can also be used to maximize linear or angular velocity of minimize power of stress. However, since it is impossible to obrain the information of walking volume in 3-D space directly from the kinematic equations, the walking volume can be searched through the edge detection algorithm using the triangle tracer with closed from inverse kinematic solutions. In this study, we present the closed form inverse kinematic solutions for 3R linkage model, and the walking volume of 6 legged walking robot which is modeled after the darking bettle, Eleodes obscura sulcipennis, through the method of edge detection for an arbitrary 2 dimensional shape using triangle tracer.

A Study of Reactional Force Compensation Based on Three‐Degree‐of Freedom Parallel Platforms

AbstractReaction compensation is necessary for space robot applications because reactional forces/torques will cause undesired movement of the spacecraft. Because the reactional torques can be compensated by the existing torque balancing device in the spacecraft, an additional reaction compensating device is necessary to compensate the reactional forces. In this article we study two types of reactional force compensating devices based on three‐degree‐of freedom, parallel platforms. The first type has three R‐P‐S legs while the second type has three R‐R‐P‐S leg and a passive R‐R‐P leg. A three‐degree of freedom serial manipulator is used to generate reactional forces, which are to be compensated by the paralle platforms. The kinematics and dynamics of both platforms are analyzed and closed form inverse kinematics solutions are derived. We then design a reactional force compensating device that satisfies the strict volume constraint in a spacecraft. The first type of parallel platform is found to require very long legs due to large orientational motion at certain positions. The second type has smooth motion in both position and orientation, and therefore its size can be very compact. It is concluded that the second type of parallel platform has great potential to be used as a compact reactional force compensating device. © 1995 John Wiley & Sons, Inc.

Task decoupling in robot manipulators

Task decoupling in robotic manipulators implies that there is a subset of joints primarily responsible for the completion of a subset of the manipulator task. In this paper, we take a novel and general view of task decoupling in which we identify link subsystems primarily responsible for completion of a subset of the manipulator task components, which is not necessarily position or orientation. Our analysis leads to the discovery of other decoupled manipulator geometries never identified before, wherein the decoupled system is responsible for a subset of degress-of-freedom involving a hybrid combination of both position and orientation. Closed-form inverse kinematic solutions for these manipulator geometries are therefore guaranteed. Task decoupling also implied singularity decoupling wherein singularities of decoupled subsystems are equivalent to the manipulator singularities. The analysis leads to a novel and efficient method for identifying the singularities and solving the inverse kinematics problem of six-axes manipulators with decoupled geometries. The practicality of the concepts introduced is demonstrated through an industrial robot example involving a hybrid position and orientation decoupling.

Inverse kinematic solution to a calibrated Puma 560 industrial robot

Robot calibration techniques provide a practical approach to improve the accuracy of industrial robot manipulators. A problem associated with the calibrated results is that the inverse kinematic solution to the calibrated kinematic model becomes difficult to resolve. This paper presents a method for solving the inverse kinematics problem of an S-model calibrated Puma 560 robot. It is a numerical iterative approach based on the closed-form inverse kinematic solution to the nominal Puma kinematic model. The reported method is accurate, efficient and suitable for real-time applications.

Automated inverse-kinematics for robot off-line programming

Automated methods are developed to classify a robot's kinematic type and select an appropriate library inverse-kinematic solution based on this classification. These methods automatically generate DenavitHartenberg joint frame parameters, given any frame representation that can mathematically be represented as a homogeneous transformation.To reduce the number of closed-form inverse-kinematics solutions required for a broad class of serial robots, additional methods account for differences in robot zero state, base frame location, and joint polarity. Further generalization results from using joint frame decoupling to map lower degree-of-freedom robots into the inverse-kinematics solutions of higher degree-offreedom robots.

Design philosophy of an isotropic six-axis serial manipulator

Presented in this paper is the design philosophy employed for the constructtion of DIESTRO, an isotropic, six-axis, serial manipulator. The kinematic criteria applied so far in manipulator design have been based largely on kinematic solvability, in the sense of allowing for closed-form inverse kinematic solutions. As opposed to this rather limiting criterion, DIESTRO was designed kinematically so as to having a set of configurations in which its Jacobian matrix allows its inversion without roundoff error amplification. Although the basic kinematic chain is of the serial type, this design criterion led to an architecture not admitting closed-form inverse kinematic solutions. The central task was to produce an accurate robot under the prescribed specifications. It is believed that, under similar workspace and load specifications, the particularly challenging design of many other serial manipulators with complex architectures can benefit from the design guidelines given here.

A simple method of accuracy enhancement for industrial manipulators

A robot calibration method which includes identification of kinematic parameters and error compensation is presented. The parameter identification process features an easy-to-perform measurement procedure using a low-cost, instrumented, articulated linkage, and with proper planning of the data collection process, the measurement of actual end effector positions can be performed automatically. The basis of the parameter identification approach is akin to that of closed-loop mechanism synthesis. For error compensation, a computation scheme based on the nominal model as opposed to the calibrated one is presented. The resulting algorithm, allowing the exploitation of the closed-form inverse kinematics solutions available for most industrial robots, is computationally efficient and therefore suited for on-line applications. Examples based on simulation studies, devised to include realistic operating conditions, are presented to demonstrate the feasibility of this method. The effects are also investigated of the number of measurements and of the sensor resolution on the overall quality of the identification.

数式処理によるロボットの逆運動学問題の解法 （第１報） 幾何学的な不変量による解法

It is well known that the solution of the inverse kinematics for robotic manipulator requires a lot of labor and time. In this paper, they propose a new method to automatically generate the closed form inverse kinematics solutions for most industrial robots efficiently. This method is based on the subdivision of rigid displacement into elementary subspaces which have invariant geometric properties. Using the invariant geometric properties of the elementary substructures, kinematic invariant relations are obtained, which are independent of the joint variables of the substructures. These relations generate the symbolic inverse kinematic solutions by computer algebra software Mathematica. Their program has successfully solved the inverse kinematics of more than ten typical industrial manipulators.