Applications of parallel computing in robotics problems

"December 2013.""A Thesis presented to the Faculty of the Graduate School University of Missouri In Partial Fulfillment Of the Requirements for the Degree Master of Science."Thesis advisor: Dr. Guilherme N. DeSouza.Many typical robotics problems involve search in high-dimensional spaces, where real-time execution is hard to be achieved. This thesis presents two case studies of parallel computation in such robotics problems. More specifically, two problems of motion planning-the Inverse Kinematics of robotic manipulators and Path Planning for mobile robots-are investigated and the contributions of parallel algorithms are highlighted. For the Inverse Kinematics problem, a novel and fast solution is proposed for general serial manipulators. This new approach relies on the computation of multiple (parallel) numerical estimations of the inverse Jacobian while it selects the current best path to the desire con- figuration of the end-effector. Unlike other iterative methods, our method converges very quickly, achieving sub-millimeter accuracy in 20.48ms in average. We demonstrate such high accuracy and the real-time performance of our method by testing it with six different robots, at both non-singular and singular configurations, including a 7-DoF redundant robot. The algorithm is implemented in C/C++ using a configurable number of POSIX threads, and it can be easily expanded to use many-core GPUs. For the Path Planning problem, a solution to the problem of smooth path planning for mobile robots in dynamic and unknown environments is presented. A novel concept of Time-Warped Grids is introduced to predict the pose of obstacles on a grid-based map and avoid collisions. The algorithm is implemented using C/C++ and the CUDA programming environment, and combines stochastic estimation (Kalman filter), Harmonic Potential Fields and a Rubber Band model, and it translates naturally into the parallel paradigm of GPU programing. The proposed method was tested using several simulation scenarios for the Pioneer P3- DX robot, which demonstrated the robustness of the algorithm by finding the optimum path in terms of smoothness, distance, and collision-free either in static or dynamic environments, even with a very large number of obstacles.Includes bibliographical references (pages 70-78)

Parallel algorithm for singular value decomposition as applied to failure tolerant manipulators, A

Includes bibliographical references (pages [348-349]).The system of equations that govern kinematically redundant manipulators is commonly solved by finding the singular value decomposition (SVD) of the corresponding Jacobian matrix. This can require considerable amounts of time to compute, thus a parallel SVD algorithm minimizing execution time is sought. The approach employed here lends itself to parallelization by using Givens rotations and information from previous decompositions. The key contributions of this research include the presentation and implementation of a new variation of a parallel SVD algorithm to compute the SVD for a set of post-fault Jacobians. Results from implementation of the algorithm on a MasPar MP-1 and an IBM SP2 are provided. Specific issues considered for each implementation include how data is mapped to the processing elements, the effect that increasing the number of processing elements has on execution time, and the type of parallel architecture used

Stiffness Analysis of Overconstrained Parallel Manipulators

The paper presents a new stiffness modeling method for overconstrained parallel manipulators with flexible links and compliant actuating joints. It is based on a multidimensional lumped-parameter model that replaces the link flexibility by localized 6-dof virtual springs that describe both translational/rotational compliance and the coupling between them. In contrast to other works, the method involves a FEA-based link stiffness evaluation and employs a new solution strategy of the kinetostatic equations for the unloaded manipulator configuration, which allows computing the stiffness matrix for the overconstrained architectures, including singular manipulator postures. The advantages of the developed technique are confirmed by application examples, which deal with comparative stiffness analysis of two translational parallel manipulators of 3-PUU and 3-PRPaR architectures. Accuracy of the proposed approach was evaluated for a case study, which focuses on stiffness analysis of Orthoglide parallel manipulator

Stiffness modeling for perfect and non-perfect parallel manipulators under internal and external loadings

International audienceThe paper presents an advanced stiffness modeling technique for perfect and non-perfect parallel manipulators under internal and external loadings. Particular attention is paid to the manipulators composed of non-perfect serial chains, whose geometrical parameters differ from the nominal ones and do not allow to assemble manipulator without internal stresses that considerably affect the stiffness properties and also change the end-effector location. In contrast to other works, several types of loadings are considered simultaneously: an external force applied to the end-effector, internal loadings generated by the assembling of non-perfect serial chains and external loadings applied to the intermediate points (auxiliary loading due to the gravity forces and relevant compensator mechanisms, etc.). For this type of manipulators, a non-linear stiffness modeling technique is proposed that allows to take into account inaccuracy in the chains and to aggregate their stiffness models for the case of both small and large deflections. Advantages of the developed technique and its ability to compute and compensate the compliance errors caused by the considered factors are illustrated by an example that deals with parallel manipulators of the Orthoglide family

Modèles élastiques et élasto‐dynamiques de robots porteurs

The report presents an advanced stiffness modeling technique for parallel manipulators composed of perfect and non-perfect serial chains. The developed technique contributes both to the stiffness modeling of serial and parallel manipulators under internal and external loadings. Particular attention has been done to enhancement of VJM-based stiffness modeling technique for the case of auxiliary loading (applied to the intermediate points). The obtained results allows us to take into account gravity forces induced by the link weights which are assumed to be applied in the intermediate points. In contrast to other works, the developed technique is able to take into account deviation of the end-platform location because of inaccuracy in the geometry of serial chains, which does not allow to assemble manipulator without internal stresses. The developed aggregation procedure combines the chain stiffness models and produces the relevant force-deflection relation, the aggregated Cartesian stiffness matrix and the reference point displacements caused by inaccuracy in kinematic chains. The developed technique can be applied to both over-constrained and under-constrained manipulators, and is suitable for the cases of both small and large deflections.ANR COROUSS

Geometry-aware Manipulability Learning, Tracking and Transfer

Body posture influences human and robots performance in manipulation tasks, as appropriate poses facilitate motion or force exertion along different axes. In robotics, manipulability ellipsoids arise as a powerful descriptor to analyze, control and design the robot dexterity as a function of the articulatory joint configuration. This descriptor can be designed according to different task requirements, such as tracking a desired position or apply a specific force. In this context, this paper presents a novel \emph{manipulability transfer} framework, a method that allows robots to learn and reproduce manipulability ellipsoids from expert demonstrations. The proposed learning scheme is built on a tensor-based formulation of a Gaussian mixture model that takes into account that manipulability ellipsoids lie on the manifold of symmetric positive definite matrices. Learning is coupled with a geometry-aware tracking controller allowing robots to follow a desired profile of manipulability ellipsoids. Extensive evaluations in simulation with redundant manipulators, a robotic hand and humanoids agents, as well as an experiment with two real dual-arm systems validate the feasibility of the approach.Comment: Accepted for publication in the Intl. Journal of Robotics Research (IJRR). Website: https://sites.google.com/view/manipulability. Code: https://github.com/NoemieJaquier/Manipulability. 24 pages, 20 figures, 3 tables, 4 appendice

On the false positives and false negatives of the Jacobian Matrix in kinematically redundant parallel mechanisms

The Jacobian matrix is a highly popular tool for the control and performance analysis of closed-loop robots. Its usefulness in parallel mechanisms is certainly apparent, and its application to solve motion planning problems, or other higher level questions, has been seldom queried, or limited to non-redundant systems. In this paper, we discuss the shortcomings of the use of the Jacobian matrix under redundancy, in particular when applied to kinematically redundant parallel architectures with non-serially connected actuators. These architectures have become fairly popular recently as they allow the end-effector to achieve full rotations, which is an impossible task with traditional topologies. The problems with the Jacobian matrix in these novel systems arise from the need to eliminate redundant variables when forming it, resulting in both situations where the Jacobian incorrectly identifies singularities (false positive), and where it fails to identify singularities (false negative). These issues have thus far remained unaddressed in the literature. We highlight these limitations herein by demonstrating several cases using numerical examples of both planar and spatial architectures

Uncalibrated visual servo for unmanned aerial manipulation

© 20xx IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper addresses the problem of autonomous servoing an unmanned redundant aerial manipulator using computer vision. The overactuation of the system is exploited by means of a hierarchical control law, which allows to prioritize several tasks during flight. We propose a safety-related primary task to avoid possible collisions. As a secondary task, we present an uncalibrated image-based visual servo strategy to drive the arm end-effector to a desired position and orientation by using a camera attached to it. In contrast to the previous visual servo approaches, a known value of camera focal length is not strictly required. To further improve flight behavior, we hierarchically add one task to reduce dynamic effects by vertically aligning the arm center of gravity to the multirotor gravitational vector, and another one that keeps the arm close to a desired configuration of high manipulability and avoiding arm joint limits. The performance of the hierarchical control law, with and without activation of each of the tasks, is shown in simulations and in real experiments confirming the viability of such prioritized control scheme for aerial manipulation.Peer ReviewedPostprint (author's final draft