Parallel algorithms for computation of the manipulator inertia matrix

The development of an O(log2N) parallel algorithm for the manipulator inertia matrix is presented. It is based on the most efficient serial algorithm which uses the composite rigid body method. Recursive doubling is used to reformulate the linear recurrence equations which are required to compute the diagonal elements of the matrix. It results in O(log2N) levels of computation. Computation of the off-diagonal elements involves N linear recurrences of varying-size and a new method, which avoids redundant computation of position and orientation transforms for the manipulator, is developed. The O(log2N) algorithm is presented in both equation and graphic forms which clearly show the parallelism inherent in the algorithm

Efficient Parallel Algorithm for Robot Forward Dynamics Computation

Computing the robot forward dynamics is important for real-time computer simulation of robot arm motion. Two efficient parallel algorithms for computing the forward dynamics for real-time simulation were developed to be implemented on an SIMD computer with n. processors, where h is the number of degrees-of-freedom of the manipulator. The first parallel algorithm, based on the Composite Rigid-Body method, generates the inertia matrix using the parallel Newton-Euler algorithm, the parallel linear recurrence algorithm, and the row-sweep algorithm, and then inverts the inertia matrix to obtain the joint acceleration vector desired at time t. The time complexity of this parallel algorithm is of the order 0(n2) with 0(n) processors. Further reduction of the order of time complexity can be achieved by implementing the Cholesky’s factorization procedure on array processors. The second parallel algorithm, based on the conjugate gradient method, computes the joint accelerations with a time complexity of 0(n) for multiplication operation and 0(nlogn) for addition operation. The proposed parallel computation results are compared with the existing methods

Parallel algorithms and architecture for computation of manipulator forward dynamics

Parallel computation of manipulator forward dynamics is investigated. Considering three classes of algorithms for the solution of the problem, that is, the O(n), the O(n exp 2), and the O(n exp 3) algorithms, parallelism in the problem is analyzed. It is shown that the problem belongs to the class of NC and that the time and processors bounds are of O(log2/2n) and O(n exp 4), respectively. However, the fastest stable parallel algorithms achieve the computation time of O(n) and can be derived by parallelization of the O(n exp 3) serial algorithms. Parallel computation of the O(n exp 3) algorithms requires the development of parallel algorithms for a set of fundamentally different problems, that is, the Newton-Euler formulation, the computation of the inertia matrix, decomposition of the symmetric, positive definite matrix, and the solution of triangular systems. Parallel algorithms for this set of problems are developed which can be efficiently implemented on a unique architecture, a triangular array of n(n+2)/2 processors with a simple nearest-neighbor interconnection. This architecture is particularly suitable for VLSI and WSI implementations. The developed parallel algorithm, compared to the best serial O(n) algorithm, achieves an asymptotic speedup of more than two orders-of-magnitude in the computation the forward dynamics

Model evaluation, recommendation and prioritizing of future work for the manipulator emulator testbed

The Manipulator Emulator Testbed (MET) is to provide a facility capable of hosting the simulation of various manipulator configurations to support concept studies, evaluation, and other engineering development activities. Specifically, the testbed is intended to support development of the Space Station Remote Manipulator System (SSRMS) and related systems. The objective of this study is to evaluate the math models developed for the MET simulation of a manipulator's rigid body dynamics and the servo systems for each of the driven manipulator joints. Specifically, the math models are examined with regard to their amenability to pipeline and parallel processing. Based on this evaluation and the project objectives, a set of prioritized recommendations are offered for future work

Characterization of robotics parallel algorithms and mapping onto a reconfigurable SIMD machine

The kinematics, dynamics, Jacobian, and their corresponding inverse computations are six essential problems in the control of robot manipulators. Efficient parallel algorithms for these computations are discussed and analyzed. Their characteristics are identified and a scheme on the mapping of these algorithms to a reconfigurable parallel architecture is presented. Based on the characteristics including type of parallelism, degree of parallelism, uniformity of the operations, fundamental operations, data dependencies, and communication requirement, it is shown that most of the algorithms for robotic computations possess highly regular properties and some common structures, especially the linear recursive structure. Moreover, they are well-suited to be implemented on a single-instruction-stream multiple-data-stream (SIMD) computer with reconfigurable interconnection network. The model of a reconfigurable dual network SIMD machine with internal direct feedback is introduced. A systematic procedure internal direct feedback is introduced. A systematic procedure to map these computations to the proposed machine is presented. A new scheduling problem for SIMD machines is investigated and a heuristic algorithm, called neighborhood scheduling, that reorders the processing sequence of subtasks to reduce the communication time is described. Mapping results of a benchmark algorithm are illustrated and discussed

Efficient dynamic simulation for multiple chain robotic mechanisms

An efficient O(mN) algorithm for dynamic simulation of simple closed-chain robotic mechanisms is presented, where m is the number of chains, and N is the number of degrees of freedom for each chain. It is based on computation of the operational space inertia matrix (6 x 6) for each chain as seen by the body, load, or object. Also, computation of the chain dynamics, when opened at one end, is required, and the most efficient algorithm is used for this purpose. Parallel implementation of the dynamics for each chain results in an O(N) + O(log sub 2 m+1) algorithm

Dynamics of the Orthoglide parallel robot

Recursive matrix relations for kinematics and dynamics of the Orthoglide parallel robot having three concurrent prismatic actuators are established in this paper. These are arranged according to the Cartesian coordinate system with fixed orientation, which means that the actuating directions are normal to each other. Three identical legs connecting to the moving platform are located on three planes being perpendicular to each other too. Knowing the position and the translation motion of the platform, we develop the inverse kinematics problem and determine the position, velocity and acceleration of each element of the robot. Further, the principle of virtual work is used in the inverse dynamic problem. Some matrix equations offer iterative expressions and graphs for the input forces and the powers of the three actuators

Safe Robotic Grasping: Minimum Impact-Force Grasp Selection

This paper addresses the problem of selecting from a choice of possible grasps, so that impact forces will be minimised if a collision occurs while the robot is moving the grasped object along a post-grasp trajectory. Such considerations are important for safety in human-robot interaction, where even a certified "human-safe" (e.g. compliant) arm may become hazardous once it grasps and begins moving an object, which may have significant mass, sharp edges or other dangers. Additionally, minimising collision forces is critical to preserving the longevity of robots which operate in uncertain and hazardous environments, e.g. robots deployed for nuclear decommissioning, where removing a damaged robot from a contaminated zone for repairs may be extremely difficult and costly. Also, unwanted collisions between a robot and critical infrastructure (e.g. pipework) in such high-consequence environments can be disastrous. In this paper, we investigate how the safety of the post-grasp motion can be considered during the pre-grasp approach phase, so that the selected grasp is optimal in terms applying minimum impact forces if a collision occurs during a desired post-grasp manipulation. We build on the methods of augmented robot-object dynamics models and "effective mass" and propose a method for combining these concepts with modern grasp and trajectory planners, to enable the robot to achieve a grasp which maximises the safety of the post-grasp trajectory, by minimising potential collision forces. We demonstrate the effectiveness of our approach through several experiments with both simulated and real robots.Comment: To be appeared in IEEE/RAS IROS 201

A Novel Approach for Simplification of Industrial Robot Dynamic Model Using Interval Method

This paper proposes a new approach to simplify the dynamic model of industrial robot by means of interval method. Due to strong nonlinearities, some components of robot dynamic model such as the inertia matrix and the vector of centrifugal, Coriolis and gravitational torques, are very complicated for real-time control of industrial robots. Thus, a simplification algorithm is presented in this study in order to reduce the computation time and memory occupation. More importantly, this simplification is suitable for arbitrary trajectories in whole robot workspace. Furthermore, the method devotes to finding negligible inertia parameters, which is useful for robot model identification. A simulation has been carried out on a test trajectory using a 6-DOF industrial robot model, and the results have shown good performance and effectiveness of this method.ANR COROUSS