MODIFICATION OF PSB QUASI-NEWTON UPDATE AND ITS GLOBAL CONVERGENCE FOR SOLVING SYSTEMS OF NONLINEAR EQUATIONS

Nonlinear problems mostly emanate from the work of engineers, physicists, mathematicians and many other scientists. A variety of iterative methods have been developed for solving large scale nonlinear systems of equations. A prominent method for solving such equations is the classical Newton’s method, but it has many shortcomings that include computing Jacobian inverse that sometimes fails. To overcome such drawbacks, an approximation with derivative free line is used on an existing method. The method uses PSB (Powell-Symmetric Broyden) update. The efficiency of the proposed method has been improved in terms of number of iteration and CPU time, hence the aim of this research. The preliminary numerical results show that the proposed method is practically efficient when applied on some benchmark problems.

Implementation and Evaluation of a Semi-Autonomous Hydraulic Dual Manipulator for Cutting Pipework in Radiologically Active Environments

We describe the implementation of a bespoke two arm hydraulically actuated robotic platform which is used to semi-autonomously cut approximately 50 mm diameter pipes of three different materials: cardboard, ABS plastic and aluminium. The system is designed to be utilised within radiologically active environments where human access is limited due to dose limits and thus remote operation is greatly beneficial. The remotely located operator selects the object from an image via a bespoke algorithm featuring a COTS 3 D vision system, along with the desired positions for gripping with one manipulator, and cutting with the other. A pseudo-Jacobian inverse kinematic technique and a programmable automation controller are used to achieve the appropriate joint positions within the dual arm robotic platform. In this article, we present the latest developments to the system and the lessons learnt from the new cutting experiments with a reciprocating saw. A comparison to tele-operated control and manual cutting is also made, with this technique shown to be slower than manual cutting, but faster than pure tele-operational control, where the requirements for highly trained users and operator fatigue are further deleterious factors.

Force Control Improvement in Collaborative Robots through Theory Analysis and Experimental Endorsement

Due to the elasticity of their joints, collaborative robots are seldom used in applications with force control. Besides, the industrial robot controllers are closed and do not allow the user to access the motor torques and other parameters, hindering the possibility of carrying out a customized control. A good alternative to achieve a custom force control is sending the output of the force regulator to the robot controller through motion commands (inner/outer loop control). There are different types of motion commands (e.g., position or velocity). They may be implemented in different ways (Jacobian inverse vs. Jacobian transpose), but this information is usually not available for the user. This article is dedicated to the analysis of the effect of different inner loops and their combination with several external controllers. Two of the most determinant factors found are the type of the inner loop and the stiffness matrix. The theoretical deductions have been experimentally verified on a collaborative robot UR3, allowing us to choose the best behaviour in a polishing operation according to pre-established criteria.

On dynamically consistent Jacobian inverse for non-holonomic robotic systems

This paper presents the dynamically consistent Jacobian inverse for non-holonomic robotic system, and its application to solving the motion planning problem. The system’s kinematics are represented by a driftless control system, and defined in terms of its input-output map in accordance with the endogenous configuration space approach. The dynamically consistent Jacobian inverse (DCJI) has been introduced by means of a Riemannian metric in the endogenous configuration space, exploiting the reduced inertia matrix of the system’s dynamics. The consistency condition is formulated as the commutativity property of a diagram of maps. Singular configurations of DCJI are studied, and shown to coincide with the kinematic singularities. A parametric form of DCJI is derived, and used for solving example motion planning problems for the trident snake mobile robot. Some advantages in performance of DCJI in comparison to the Jacobian pseudoinverse are discovered.