Configuration control of seven-degree-of-freedom arms

A seven degree of freedom robot arm with a six degree of freedom end effector is controlled by a processor employing a 6 by 7 Jacobian matrix for defining location and orientation of the end effector in terms of the rotation angles of the joints, a 1 (or more) by 7 Jacobian matrix for defining 1 (or more) user specified kinematic functions constraining location or movement of selected portions of the arm in terms of the joint angles, the processor combining the two Jacobian matrices to produce an augmented 7 (or more) by 7 Jacobian matrix, the processor effecting control by computing in accordance with forward kinematics from the augmented 7 by 7 Jacobian matrix and from the seven joint angles of the arm a set of seven desired joint angles for transmittal to the joint servo loops of the arm. One of the kinematic functions constraints the orientation of the elbow plane of the arm. Another one of the kinematic functions minimizes a sum of gravitational torques on the joints. Still another kinematic function constrains the location of the arm to perform collision avoidance. Generically, one kinematic function minimizes a sum of selected mechanical parameters of at least some of the joints associated with weighting coefficients which may be changed during arm movement. The mechanical parameters may be velocity errors or gravity torques associated with individual joints

Position-based kinematics for 7-DoF serial manipulators with global configuration control, joint limit and singularity avoidance

This paper presents a novel analytic method to uniquely solve inverse kinematics of 7 degrees-of-freedom manipulators while avoiding joint limits and singularities. Two auxiliary parameters are introduced to deal with the self-motion manifolds: the global configuration (GC), which specifies the branch of inverse kinematics solutions; and the arm angle (ψ) that parametrizes the elbow redundancy within the specified branch. The relations between the joint angles and the arm angle are derived, in order to map the joint limits and singularities to arm angle values. Then, intervals of feasible arm angles for the specified target pose and global configuration are determined, taking joint limits and singularities into account. A simple metric is proposed to compute the elbow position according to the feasible intervals. When the arm angle is determined, the joint angles can be uniquely calculated from the position-based inverse kinematics algorithm. The presented method does not exhibit the disadvantages inherent to the use of the Jacobian matrix and can be implemented in real-time control systems. This novel algorithm is the first position-based inverse kinematics algorithm to solve both global and local manifolds, using a redundancy resolution strategy to avoid singularities and joint limits.This work was partially supported by the NETT Project [FP7-PEOPLE-2011-ITN-289146]; and Foundation for Science and Technology, Portugal [grant number SFRH/BD/86499/2012].info:eu-repo/semantics/publishedVersio

Self-motion control of kinematically redundant robot manipulators

Thesis (Master)--Izmir Institute of Technology, Mechanical Engineering, Izmir, 2012Includes bibliographical references (leaves: 88-92)Text in English; Abstract: Turkish and Englishxvi,92 leavesRedundancy in general provides space for optimization in robotics. Redundancy can be defined as sensor/actuator redundancy or kinematic redundancy. The redundancy considered in this thesis is the kinematic redundancy where the total degrees-of-freedom of the robot is more than the total degrees-of-freedom required for the task to be executed. This provides infinite number of solutions to perform the same task, thus, various subtasks can be carried out during the main-task execution. This work utilizes the property of self-motion for kinematically redundant robot manipulators by designing the general subtask controller that controls the joint motion in the null-space of the Jacobian matrix. The general subtask controller is implemented for various subtasks in this thesis. Minimizing the total joint motion, singularity avoidance, posture optimization for static impact force objectives, which include maximizing/minimizing the static impact force magnitude, and static and moving obstacle (point to point) collision avoidance are the subtasks considered in this thesis. New control architecture is developed to accomplish both the main-task and the previously mentioned subtasks. In this architecture, objective function for each subtask is formed. Then, the gradient of the objective function is used in the subtask controller to execute subtask objective while tracking a given end-effector trajectory. The tracking of the end-effector is called main-task. The SCHUNK LWA4-Arm robot arm with seven degrees-of-freedom is developed first in SolidWorks® as a computer-aided-design (CAD) model. Then, the CAD model is converted to MATLAB® Simulink model using SimMechanics CAD translator to be used in the simulation tests of the controller. Kinematics and dynamics equations of the robot are derived to be used in the controllers. Simulation test results are presented for the kinematically redundant robot manipulator operating in 3D space carrying out the main-task and the selected subtasks for this study. The simulation test results indicate that the developed controller’s performance is successful for all the main-task and subtask objectives

Local sensory control of a dexterous end effector

A numerical scheme was developed to solve the inverse kinematics for a user-defined manipulator. The scheme was based on a nonlinear least-squares technique which determines the joint variables by minimizing the difference between the target end effector pose and the actual end effector pose. The scheme was adapted to a dexterous hand in which the joints are either prismatic or revolute and the fingers are considered open kinematic chains. Feasible solutions were obtained using a three-fingered dexterous hand. An algorithm to estimate the position and orientation of a pre-grasped object was also developed. The algorithm was based on triangulation using an ideal sensor and a spherical object model. By choosing the object to be a sphere, only the position of the object frame was important. Based on these simplifications, a minimum of three sensors are needed to find the position of a sphere. A two dimensional example to determine the position of a circle coordinate frame using a two-fingered dexterous hand was presented

Coordinated Motion Control of Multiple Robotic Devices for Welding and Redundancy Coordination through Constrained Optimization in Cartesian Space

In this paper we consider the problem of coordinating multiple motion devices for welding. We focus on the problem of coordinating a positioning table and a seven axis manipulator, given the parametric definition of a trajectory on a weld piece. The problem is complex as there are more than nine axis involved and a number of permutations are possible which achieve the same motions of the weld torch. The system is redundant and the robot has singular configurations. As a result, manual programming of the robot system is rather complex. Our approach to the coordination problem is based on subdivision of constraints. The welding table is coordinated to ensure down-handed welding convention, while the seven axis robot (a six axis Cybotech WV15 robot and track) are coordinated to track the weld point. The coordination is achieved by keeping the robot in good maneuverability position, so as to avoid the robots singularity conditions and motion limits of the track. We were able to express the singularity conditions in terms of cartesian coordinates [I]. As a result, we could obtain analytic solution to our optimization of the maneuversability and therefore avoid using known pseudoinverse techniques which are known to exhibit inaccuracies [2]. The output of our optimization process is the positions of the track and the robot end-effector, these positions are used to generate the joint angles of the arm by inverse kinematics

Design, analysis and kinematic control of highly redundant serial robotic arms

The use of robotic manipulators in industry has grown in the last decades to improve and speed up industrial processes. Industrial manipulators started to be investigated for machining tasks since they can cover larger workspaces, increasing the range of achievable operations and improving flexibility. The company Nimbl’Bot developed a new mechanism, or module, to build stiffer flexible serial modular robots for machining applications. This manipulator is a kinematic redundant robot with 21 degrees of freedom. This thesis thoroughly analysis the Nimbl’Bot robot features and is divided into three main topics. The first topic regards using a task priority kinematic redundancy resolution algorithm for the Nimbl’Bot robot tracking trajectory while optimizing its kinetostatic performances. The second topic is the kinematic redundant robot design optimization with respect to a desired application and its kinetostatic performance. For the third topic, a new workspace determination algorithm is proposed for kinematic redundant manipulators. Several simulation tests are proposed and tested on some Nimbl’Bot robot designs for each subjects

Postprocesamiento CAM-ROBOTICA orientado al prototipado y mecanizado en células robotizadas complejas

The main interest of this thesis consists of the study and implementation of postprocessors to adapt the toolpath generated by a Computer Aided Manufacturing (CAM) system to a complex robotic workcell of eight joints, devoted to the rapid prototyping of 3D CAD-defined products. It consists of a 6R industrial manipulator mounted on a linear track and synchronized with a rotary table. To accomplish this main objective, previous work is required. Each task carried out entails a methodology, objective and partial results that complement each other, namely: - It is described the architecture of the workcell in depth, at both displacement and joint-rate levels, for both direct and inverse resolutions. The conditioning of the Jacobian matrix is described as kinetostatic performance index to evaluate the vicinity to singular postures. These ones are analysed from a geometric point of view. - Prior to any machining, the additional external joints require a calibration done in situ, usually in an industrial environment. A novel Non-contact Planar Constraint Calibration method is developed to estimate the external joints configuration parameters by means of a laser displacement sensor. - A first control is originally done by means of a fuzzy inference engine at the displacement level, which is integrated within the postprocessor of the CAM software. - Several Redundancy Resolution Schemes (RRS) at the joint-rate level are compared for the configuration of the postprocessor, dealing not only with the additional joints (intrinsic redundancy) but also with the redundancy due to the symmetry on the milling tool (functional redundancy). - The use of these schemes is optimized by adjusting two performance criterion vectors related to both singularity avoidance and maintenance of a preferred reference posture, as secondary tasks to be done during the path tracking. Two innovative fuzzy inference engines actively adjust the weight of each joint in these tasks.Andrés De La Esperanza, FJ. (2011). Postprocesamiento CAM-ROBOTICA orientado al prototipado y mecanizado en células robotizadas complejas [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/10627Palanci