6,154 research outputs found

    Preliminary Report on High-Performance Computational Structures for Robot Control

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    In this report we present some initial results of our work completed thus far on Computational Structures for Robot Control . A SIMD architecture with the crossbar interprocessor network which achieves the parallel processing execution time lower bound of o( [a1n ]), where a1 is a constant and n is the number of manipulator joints, for the computation of the inverse dynamics problem, is discussed. A novel SIMD task scheduling algorithm that optimizes the parallel processing performance on the indicated architecture is also delineated. Simulations performed on this architecture show speedup factor of 3.4 over previous related work completed for the evaluation of the specified problem, is achieved. Parallel processing of PUMA forward and inverse kinematics solutions is next investigated using a particular scheduling algorithm. In addition, a custom bit-serial array architecture is designed for the computation of the inverse dynamics problem within the bit-serial execution time lower bound of o(c1k + c2kn), where c1 and c2 are specified constants, k is the word length, and n is the number of manipulator joints. Finally, mapping of the Newton-Euler equations onto a fixed systolic array is investigated. A balanced architecture for the inverse dynamics problem which achieves the systolic execution time lower bound for the specified problem is depicted. Please note again that these results are only preliminary and improvements to our algorithms and architectures are currently still being made

    Dynamics of the Orthoglide parallel robot

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    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

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

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    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

    Parallel algorithms for computation of the manipulator inertia matrix

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    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

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

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    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

    Kinematically optimal hyper-redundant manipulator configurations

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    “Hyper-redundant” robots have a very large or infinite degree of kinematic redundancy. This paper develops new methods for determining “optimal” hyper-redundant manipulator configurations based on a continuum formulation of kinematics. This formulation uses a backbone curve model to capture the robot's essential macroscopic geometric features. The calculus of variations is used to develop differential equations, whose solution is the optimal backbone curve shape. We show that this approach is computationally efficient on a single processor, and generates solutions in O(1) time for an N degree-of-freedom manipulator when implemented in parallel on O(N) processors. For this reason, it is better suited to hyper-redundant robots than other redundancy resolution methods. Furthermore, this approach is useful for many hyper-redundant mechanical morphologies which are not handled by known methods

    Efficient mapping algorithms for scheduling robot inverse dynamics computation on a multiprocessor system

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    Two efficient mapping algorithms for scheduling the robot inverse dynamics computation consisting of m computational modules with precedence relationship to be executed on a multiprocessor system consisting of p identical homogeneous processors with processor and communication costs to achieve minimum computation time are presented. An objective function is defined in terms of the sum of the processor finishing time and the interprocessor communication time. The minimax optimization is performed on the objective function to obtain the best mapping. This mapping problem can be formulated as a combination of the graph partitioning and the scheduling problems; both have been known to be NP-complete. Thus, to speed up the searching for a solution, two heuristic algorithms were proposed to obtain fast but suboptimal mapping solutions. The first algorithm utilizes the level and the communication intensity of the task modules to construct an ordered priority list of ready modules and the module assignment is performed by a weighted bipartite matching algorithm. For a near-optimal mapping solution, the problem can be solved by the heuristic algorithm with simulated annealing. These proposed optimization algorithms can solve various large-scale problems within a reasonable time. Computer simulations were performed to evaluate and verify the performance and the validity of the proposed mapping algorithms. Finally, experiments for computing the inverse dynamics of a six-jointed PUMA-like manipulator based on the Newton-Euler dynamic equations were implemented on an NCUBE/ten hypercube computer to verify the proposed mapping algorithms. Computer simulation and experimental results are compared and discussed

    Computational structures for robotic computations

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    The computational problem of inverse kinematics and inverse dynamics of robot manipulators by taking advantage of parallelism and pipelining architectures is discussed. For the computation of inverse kinematic position solution, a maximum pipelined CORDIC architecture has been designed based on a functional decomposition of the closed-form joint equations. For the inverse dynamics computation, an efficient p-fold parallel algorithm to overcome the recurrence problem of the Newton-Euler equations of motion to achieve the time lower bound of O(log sub 2 n) has also been developed

    Parallel algorithms and architecture for computation of manipulator forward dynamics

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    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

    Kinematics, controls, and path planning results for a redundant manipulator

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    The inverse kinematics solution, a modal position control algorithm, and path planning results for a 7 degree of freedom manipulator are presented. The redundant arm consists of two links with shoulder and elbow joints and a spherical wrist. The inverse kinematics problem for tip position is solved and the redundant joint is identified. It is also shown that a locus of tip positions exists in which there are kinematic limitations on self-motion. A computationally simple modal position control algorithm has been developed which guarantees a nearly constant closed-loop dynamic response throughout the workspace. If all closed-loop poles are assigned to the same location, the algorithm can be implemented with very little computation. To further reduce the required computation, the modal gains are updated only at discrete time intervals. Criteria are developed for the frequency of these updates. For commanding manipulator movements, a 5th-order spline which minimizes jerk provides a smooth tip-space path. Schemes for deriving a corresponding joint-space trajectory are discussed. Modifying the trajectory to avoid joint torque saturation when a tip payload is added is also considered. Simulation results are presented
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