Sub-optimal Solution of the Inverse Kinematic Task of Redundant Robots without Using Lagrange Multipliers

In the paper a novel approach is suggested for solving the inverse kinematic task of redundant open kinematic chains. Traditional approaches as the Moore-Penrose generalized inverse-based solutions minimize the sum of squares of the timederivative of the joint coordinates under the constraint that contains the task itself. In the vicinity of kinematic singularities where these solutions are possible the hard constraint terms produce high time-derivatives that can be reduced by the use of a deformation proposed by Levenberg and Marquardt. The novel approach uses the basic scheme of the Receding Horizon Controllers in which the Lagrange multipliers are eliminated by direct application of the kinematic model over the horizon in the role of the ”control force”, and no reduced gradient has to be computed. This fact considerably decreases the complexity of the solution. If the cost function contains penalty for high joint coordinate time-derivatives the kinematic singularities are ab ovo better handled. Simulation examples made for a 7 degree of freedom robot arm demonstrate the operation of the novel approach. The computational need of the method is still considerable but it can be further decreased by the application of complementary tricks.

Accelerated Reduced Gradient Algorithm with Constraint Relaxation in Differential Inverse Kinematics

The Moore-Penrose pseudoinverse-based solution of the differential inverse kinematic task of redundant robots corresponds to the result of a particular optimization underconstraints in which the implementation of Lagrange’s ReducedGradient Algorithm can be evaded simply by considering the zero partial derivatives of the ”Auxiliary Function” associated with this problem. This possibility arises because of the fact that the cost term is built up of quadratic functions of the variable of optimization while the constraint term is linear function of the same variables. Any modification in the cost and/or constraint structure makes it necessary the use of the numerical algorithm. Anyway, the penalty effect of the cost terms is always overridden by the hard constraints that makes practical problems in the vicinity of kinematic singularities where the possible solution stillexists but needs huge joint coordinate time-derivatives. While in the special case the pseudoinverse simply can be deformed, inthe more general one more sophisticated constraint relaxation can be applied. In this paper a formerly proposed acceleratedtreatment of the constraint terms is further developed by the introduction of a simple constraint relaxation. Furthermore, thenumerical results of the algorithm are smoothed by a third order tracking strategy to obtain dynamically implementable solution.The improved method’s operation is exemplified by computation results for a 7 degree of freedom open kinematic chain

DEVELOPMENT OF 5 DOF ROBOTIC ARM PROTOTYPE CONTROL SYSTEM IN BRACHYTHERAPY PREPARATION BASED ON ARTIFICIAL NEURAL NETWORK

Brachytherapy is a cancer treatment that uses radioactive sources with temporary or permanent implantation in cancer tissue. The theraphy uses a radioactive Ir-192 source wrapped in a stainless steel capsule with a diameter of 0.5 mm and a length of 4 mm. The Center for Radioisotopes and Radiopharmaceutical Technology applies a remote manipulator to manufacture microcapsules, which affects the accuracy and risks of the radiation received by the operator. Therefore, to solve this problem, it is necessary to design a 5 DoF robotic arm based on artificial neural networks as a radioactive source transfer tool to improve the precision and safety of operators in preparing the radioactive sources. In developing the 5 DoF robotic arm control system, the NImyRIO was employed, which can control the servo motor, relay pump and valve reality, image processing, and inverse kinematic. The inverse kinematic uses the neural network method with a forward kinematic validation. The inverse kinematic test obtains the RMSE value of 2.78932 for x, 5.05205 for y, and 12.641 for z in the inverse kinematic test of artificial neural networks. Therefore, the inverse kinematic accuracy of the artificial neural network needs to be redeveloped.

Learning Rotations

Many problems in computer vision today are solved via deep learning. Tasks like pose estimation from images, pose estimation from point clouds or structure from motion can all be formulated as a regression on rotations. However, there is no unique way of parametrizing rotations mathematically: matrices, quaternions, axis-angle representation or Euler angles are all commonly used in the field. Some of them, however, present intrinsic limitations, including discontinuities, gimbal lock or antipodal symmetry. These limitations may make the learning of rotations via neural networks a challenging problem, potentially introducing large errors. Following recent literature, we propose three case studies: a sanity check, a pose estimation from 3D point clouds and an inverse kinematic problem. We do so by employing a full geometric algebra (GA) description of rotations. We compare the GA formulation with a 6D continuous representation previously presented in the literature in terms of regression error and reconstruction accuracy. We empirically demonstrate that parametrizing rotations as bivectors outperforms the 6D representation. The GA approach overcomes the continuity issue of representations as the 6D representation does, but it also needs fewer parameters to be learned and offers an enhanced robustness to noise. GA hence provides a broader framework for describing rotations in a simple and compact way that is suitable for regression tasks via deep learning, showing high regression accuracy and good generalizability in realistic high-noise scenarios.

DESIGN OF OPTIMAL INVERSE KINEMATIC SOLUTION FOR HUMANOID ROBOTIC ARMS

One of the main problems in robotics is the Inverse Kinematics (IK) problem. In this paper, three optimization algorithms are proposed to solve the IK of Humanoid Robotic Arms (HRAs). A Particle Swarm Optimization (PSO), Social Spider Optimization (SSO), and Black Hole Optimization (BHO) algorithms are proposed in order to optimize the parameters of the proposed IK. Also, in this paper, each optimization method is applied on both right and left arms to find the desired positions and required angles with a minimum error. Denavit-Hartenberg (D-H) method is used to design and simulate the mathematical model of HRAs for both arms in which each arm has five Degree Of Freedom (DOF). The HRAs model is tested for performance by several positions to be reached by both arms in the same time to find which optimization algorithm is better. Optimal solution obtained by SSO, PSO and BHO algorithms are evaluated and listed in comparison table between them. These optimization algorithms are assessed by calculating the Computational Time (CT) and Root Mean Squared Error (RMSE) for the absolute error vector of the positions. Calculation and simulation results showed that BHO algorithm is better than the other optimization algorithms from point of view of CT and RMSE. The worst RMSE is 0.0864 was calculated using PSO algorithm. But longer CT is 7.6521 second, which was calculated using SSO. While the best RMSE and shorter CT.are and 3.0156 second respectively were calculated by BHO algorithm. Moreover, in this paper, the Graphical User Interface (GUI) is designed and built for motional characteristics of the HRAs model in the Forward Kinematics (FK) and IK. The optimization algorithms are designed using MATLAB package facilities to simulate the HRAs model and the solution of IK problem.

Kinematic uncertainty analysis of a cable-driven parallel robot based on an error transfer model

Cable-driven parallel robots (CDPRs) are a kind of mechanism with large workspace, fast response, and low inertia. However, due to the existence of fixed pulleys, it is unavoidable to bring uncertain cable lengths and lead to pose errors of the end-effector (EE). The inverse kinematic model of a CDPR for picking up medicines is established by considering radii of fixed pulleys. The influence of radii of fixed pulleys on errors of cable lengths is explored. Error transfer model of the CPDR is constructed, and uncertain sources of cable lengths are analyzed. Based on evidence theory and error transfer model, an evidence theory-based uncertainty analysis method (ETUAM) is presented. The structural performance function for kinematic response is derived based on error transfer model. Belief and plausibility measures of joint focal elements under the given threshold are obtained. Kinematic error simulations show that errors of cable lengths become larger with the increase of radii of fixed pulleys. Compared with the vertex method and Monte Carlo method, numerical examples demonstrate the accuracy and efficiency of the ETUAM when it comes to the kinematic uncertainty analysis of the CDPR.

Application of Dynamic Input Shaping for a Dual-Mirror System

The task of trajectory planning for a dual-mirror optical pointing system greatly benefits from carefully designed dynamic input signals. This paper summarizes the application of multivariable input shaping (IS) for a dual-mirror system, starting from initial open-loop step-response data. The optical pointing system presented consists of two Fast Steering Mirrors (FSM) for which dynamically coupled input signals are designed, while adhering to mechanical and input signal constraints. For the solution, the planned trajectories for the dual-mirrors are determined via (inverse) kinematic analysis. A linear program (LP) problem is used to compute the dynamic input signal for each of the FSMs, with one of the mirrors acting as an image motion compensation device that guarantees tracking of a planned trajectory within a specified accuracy and the operating constraints of the FSMs.

Kinematic analysis of an augmented 3-RPSP tripod mechanism with six degrees of freedom for bone reduction surgery

Robotic-assisted bone reduction surgery consists in using robots to reconnect patients’ bone fragments prior to fracture healing. The goal of this study is to propose a novel augmented 3-RPSP tripod mechanism with six degree of freedom for longitudinal bone reduction surgery. Its inverse kinematic model is studied and its forward kinematic model is solved by establishing the constraint equations, applying Sylvester’s dialytic method and finding the solutions of the resulting polynomial equation. The velocity model is calculated and its Jacobian matrix is used to identify its singular configurations. In comparison to the Stewart–Gough platform that is a typical mechanism used in this application, the proposed mechanism offers larger reachable workspace which is an important aspect in the femoral shaft bone reduction. A Physiguide and Msc Adams software are used to carry out a simulation of a real femur fracture reduction using the proposed mechanism to validate its suitability. A robotic prototype has been designed and manufactured in order to test its capability of performing diaphyseal femur reduction surgery.