Parallel Inverse Kinematics for Multithreaded Architectures

Recently, General Purpose Graphical Processing Units (GP-GPUs) have been identified as an intriguing technology to accelerate numerous data-parallel algorithms. Several GPU architectures and programming models are beginning to emerge and establish their niche in the High-Performance Computing (HPC) community. New massively parallel architectures such as the Nvidia’s Fermi and AMD/ATi’s Radeon pack tremendous computing power in their large number of multiprocessors. Their performance is unleashed using one of the two GP-GPU programming models: Compute Unified Device Architecture (CUDA) and Open Computing Language (OpenCL). Both of them offer constructs and features that have direct bearing on the application runtime performance. In this paper, we compare the two GP-GPU architectures and the two programming models using a two-level character recognition network. The two-level network is developed using four different Spiking Neural Network (SNN) models, each with different ratios of computation-to-communication requirements. To compare the architectures, we have chosen the two extremes of the SNN models for implementation of the aforementioned two-level network. An architectural performance comparison of the SNN application running on Nvidia’s Fermi and AMD/ATi’s Radeon is done using the OpenCL programming model exhausting all of the optimization strategies plausible for the two architectures. To compare the programming models, we implement the two-level network on Nvidia’s Tesla C2050 based on the Fermi architecture. We present a hierarchy of implementations, where we successively add optimization techniques associated with the two programming models. We then compare the two programming models at these different levels of implementation and also present the effect of the network size (problem size) on the performance. We report significant application speed-up, as high as 1095× for the most computation intensive SNN neuron model, against a serial implementation on the Intel Core 2 Quad host. A comprehensive study presented in this paper establishes connections between programming models, architectures and applications.

This work proposes several approaches to accelerate the solid---fluid interaction through the use of the Immersed Boundary method on multicore and GPU architectures. Different optimizations on both architectures have been proposed, focusing on memory management and workload mapping. We have chosen two different test scenarios which consist of single-solid and multiple-solid simulations. The performance analysis has been carried out on an intensive set of test cases to analyze the proposed optimizations using multiple CPUs (2) and GPUs (4). An effective performance is obtained for single-solid executions using one CPU (Intel Xeon E5520) achieving a speedup peak equal to 5.5. It is reached a higher benefit on multiple solids obtaining a top speedup of approximately 5.9 and 9 using one CPU (8 cores) and two CPUs (16 cores), respectively. On GPU (Kepler K20c) architecture, two different approaches are presented as the best alternative: one for single-solid executions and one for multiple-solid executions. The best approach obtained for one solid executions achieves a speedup of approximately 17 with respect the sequential counterpart. In contrast, for multiple-solid executions the benefit is much higher, being this type of problems much more suitable for GPU and reaching a peak speedup of 68, 115 and 162 using 1, 2 and 4 GPUs, respectively.

This paper presents inverse position kinematics algorithms with real time capability for Justin, a robotic system with high redundancy and many degrees of freedom. The combination of closed form solutions for parts of the kinematic chain embedded in a nonlinear equation solver is shown to be advantageous. The algorithms are evaluated with DLR's robot Justin both in simulation and reality. Calculation times of 1 ms are achieved, including various optimization criteria for redundancy resolution. In case only a single arm with 7 DoF is considered, a fast calculation time of 250 µs is reached. With inclusion of an iterative step, reachability can be shown in more than 99% of the calculations regardless of the initial guess. The problem of weighting in multi-criteria optimization problems remains, though in the chosen approach the tool tip position is never compromised by other criteria due to the partially closed form solution. The presented algorithm can be applied to inverse position kinematics for all manipulators with serial or tree structure and redundant joints in case closed form solutions are available for parts of the kinematic chain.

In this study, inverse kinematics is solved for the European Robotic Arm. This robot is a type of space manipulator and has seven degrees of freedom. Forward and inverse kinematic is obtained by a new geometrical method. The limitations of robot workspace are calculated for robot joints and grippers. A geometrical inverse kinematic is presented for the first time, and the transferring process for various situations is developed to grasp the object at any position and orientation. Considering multiple missions, for robots in the transferring process, there isn’t a unit method to support all the situations and tasks in the inverse kinematic problem. To determine the workspace of robot, its geometry and object situation (orientation and position) are considered. To this end, using the suggested inverse kinematic algorithm, the target coordinate and orientations are obtained. In the presented inverse kinematic algorithm, an analytical method is used to derive the joint space variables in terms of workspace variables. The European Robotic Arm can move step by step from one target point to the next one. So, a general transferring algorithm is presented to realize the robot’s mission. In the presented algorithm, when the target is unreachable by the one-step operation, the transferring mission is utilized by the robot. Some simulation plans, to validate the proposed algorithms, indicate that the presented method works correctly.

Recently, general purpose GPU (GPGPU) programming has spread rapidly after CUDA was first introduced to write parallel programs in high-level languages for NVIDIA GPUs. While a GPU exploits data parallelism very effectively, task-level parallelism is exploited as a multi-threaded program on a multicore CPU. For such a heterogeneous platform that consists of a multicore CPU and GPU, we propose an automatic code synthesis framework that takes a process network model specification as input and generates a multithreaded CUDA code. With the model based specification, one can explicitly specify both function-level and loop-level parallelism in an application and explore the wide design space in mapping of function blocks and selecting the communication methods between CPU and GPU. The proposed technique is complementary to other high-level methods of CUDA programming.KeywordsGPGPUCUDAmodel-based designautomatic code synthesis

GeoTaichi: A Taichi-powered high-performance numerical simulator for multiscale geophysical problems

Various approaches to solving inverse kinematics implicitly rely on computing forward kinematics in order to obtain an approximate solution. This work proposes an optimised data structure to efficiently compute these equations by avoiding redundant transformations and calculations. This is particulary relevant for highly articulated kinematic models and multiple end effectors with shared joints along their kinematic chains. By integrating the developed OFKT (Optimised Forward Kinematics Tree), less computation time within each iteration is required, which contributes to a significant speedup in convergence. Experiments were conducted using a novel evolutionary approach which was designed for handling complex kinematic geometries.

Collision-free inverse kinematics of the redundant seven-link manipulator used in a cucumber picking robot

The rapid development of artificial intelligence technology makes Robotics more intelligent and flexible. In this context, the kinematics inverse algorithm of the Robotics has become the basis and key technology for the further development of the Robotics. The key point of the inverse algorithm of the Robotics is to coordinate the Robotics operation arm with the corresponding action actuator at the end to realize the space attitude control of the Robotics system, and to make a theoretical basis for the motion analysis of the later Robotics. However, the traditional form of Robotics kinematics inverse algorithm avoids a lot of iterative computational solution process, which increases the complexity of the whole algorithm. Therefore, based on the above situation, this paper proposes a Robotics inverse solution algorithm based on improved BP (back propagation) neural network. In this paper, in the application of the actual algorithm, aiming at the convergence problem of the traditional BP neural network algorithm, an improved BP neural network algorithm based on the excitation function is proposed. By selecting the adaptive processing function in each layer of the neural network, the selection is matched with it. The learning rate, thus improving the accuracy of the entire motion inverse algorithm. At the same time, in order to further reduce the calculation of joint quantification, this paper also creatively introduces the algorithm of plane division auxiliary dynamic model construction. The simulation results show that the inverse kinematics algorithm based on improved BP neural network proposed in this paper has obvious advantages in solving the kinematics inverse problem of six-degree-of-freedom Robotics compared with the traditional inverse solution algorithm.

A GPU-accelerated pseudo-3D vortex method for aerodynamic analysis

The Inverse Kinematics (IK) algorithms implemented in the open-source Orocos Kinematics and Dynamics Library (KDL) are arguably the most widely-used generic IK solvers worldwide. However, KDL's only joint-limit-constrained IK implementation, a pseudoinverse Jacobian IK solver, repeatedly exhibits false-negative failures on various humanoid platforms. In order to find a better IK solver for generic manipulator chains, a variety of open-source, drop-in alternatives have been implemented and evaluated for this paper. This article provides quantitative comparisons, using multiple humanoid platforms, between an improved implementation of the KDL inverse Jacobian algorithm, a set of sequential quadratic programming (SQP) IK algorithms that use a variety of quadratic error metrics, and a combined algorithm that concurrently runs the best performing SQP algorithm and the improved inverse Jacobian implementation. The best alternative IK implementation finds solutions much more often than KDL, is faster on average than KDL for typical manipulation chains, and (when desired) allows tolerances on each Cartesian dimension, further improving speed and convergence when an exact Cartesian pose is not possible and/or necessary.

Automatic oval hole machining is a great challenge in monolithic wing assembly of aircraft. In this paper, a new six-axis machine tool for oval hole drilling in aircraft wing assembly is developed, and an efficient kinematic modeling and inverse kinematics method for six-axis machine tools is proposed. After a brief structure analysis, necessary coordinate systems are established to build the generalized kinematic model of the six-axis machine tool. Then, with the concept of separation and combination, an inverse kinematics strategy for six-axis machine tools is proposed to improve the accuracy, efficiency, and stability of the algorithm. All motion axes are separated into three groups and their joint coordinates are solved successively based on the joints separation strategy (JSS) for solution. Finally, the inverse kinematic solution of the six-axis machine tool is composed of the prismatic joints with analytical solutions, revolute joints with analytical solutions, and revolute joints with numerical solutions. To verify the validity of the proposed method, numerical and machining experiments have been performed on the developed six-axis machine tool. In the simulation, two error vectors for joint coordinates and the pose of tool tip are presented to evaluate the accuracy of the inverse kinematics algorithm. The simulation results show the great success of the proposed method. Moreover, the position and orientation errors of the drilled oval holes are within 0.093 mm and 0.408°, which is accurate enough to meet the requirement for automatic oval hole machining in aircraft assembly.

This paper describes modeling of the inverse kinematics of a 6-DOF underwater manipulator using closed form solution approach. The manipulator structure is based on puma560 robot with some modification. The manipulator is aimed for underwater operation in water pool. Robotic manipulator is positioning device and its end-effector is required to move in a particular way to accomplish a specific task. The major problem with manipulator is of motion or trajectory planning and its control because execution of any task needs the manipulator to follow a preplanned path. Purpose of trajectory planning is to describe the required motion of the manipulator as a time sequence of locations of joints, links and end-effector and derivatives of their locations. Inverse kinematics solutions can be divided as analytical and numerical. Analytical solutions are preferred because these yield complete computationally fast and reliable solutions. We developed a fast inverse kinematics algorithm with a closed-form solution for a 6-DOF underwater manipulator. The developed algorithm is validated using simulation in Robotic toolbox. Inverse kinematics is calculated and simulation of end effector is done for given joint and link parameters. Finally graphs for motion of manipulator as a time sequence of joints and links are obtained.

Inverse kinematic solutions for a dual redundant camera robot in position are examined in order to alleviate operation difficulty and reduce time. The inverse kinematic algorithm is based on a basic genetic algorithm, and the genetic algorithm which is used to solve the problem of a redundant robot is mainly optimized in the joint space. On this basis, the genetic algorithm improvement strategies are studied. In this paper, a genetic algorithm with constrained 2 redundant degrees of freedom (DOF) is proposed through setting 2 parameter variables, with more flexible structure of optimization objective function and more efficient algorithm than basic genetic algorithm. Finally, the result of inverse kinematic algorithm is achieved in terms of the physical prototype.

The 7R 6‐DOF robots with hollow nonspherical wrist have been proven more suitable for spray painting applications. However, the inverse kinematics of this kind of robot is still imperfect due to the coupling between position and orientation of the end‐effector (EE). In this paper, a new and efficient algorithm for the inverse kinematics of a 7R 6‐DOF robot is proposed. The proposed inverse kinematics algorithm is a two‐step method. The geometry of the 7R 6‐DOF robot is analyzed. A comparison between the 7R 6‐DOF robot and the well‐known equivalent 6R robot is made. Based on this comparison, a rational transformation between these two kinds of robots is constructed. Then the general inverse kinematics algorithm of the equivalent 6R robot is applied to calculate the approximate solutions of the 7R 6‐DOF robot, in the first step. The Damped Least‐Squares (DLS) method is employed to derive the exact solutions, in the second step. The accuracy and efficiency of the algorithm are tested on a 7R 6‐DOF painting robot. The results show that the proposed algorithm is more advantageous in the case without an approximate solution, such as the initial point of a continuous trajectory.