Efficient parallel algorithms and VLSI architectures for manipulator Jacobian computation

Journal Article · Fri Sep 01 00:00:00 EDT 1989 · IEEE Transactions on Systems, Man, and Cybernetics (Institute of Electrical and Electronics Engineers); (USA)

DOI:https://doi.org/10.1109/21.44031· OSTI ID:7184325

Yeung, T B ^[1]; Lee, C S.G. ^[2]

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1. LSI Logic Corp., Milpitas, CA (US)
2. Of Electrical Enginerring, Purdue Univ., West Lafayette, IN (US)

The real-time computation of manipulator Jacobian that relates the manipulator joint velocities to the linear and angular velocities of the manipulator end-effector is pursued. Since the Jacobian can be expressed in the form of the first-order linear recurrence, the time lower bound to complete the Jacobian can be proved to be of order O(N) on uniprocessor computers, and of order O(log{sub 2}N) on both parallel single-instruction-stream multiple-data-stream (SIMD) computers and parallel VLSI pipelines, where N is the number of links of the manipulator. To achieve the computation time lower bound, we developed the generalized-k method on uniprocessor computers, the parallel forward and backward recursive doubling algorithm (PFABRD) on SIMD computers, and a parallel systolic architecture on VLSI pipelines. All the methods are capable of computing the Jacobian at any desired reference coordinate frame k from the base coordinate frame to the end-effector coordinate frame. The computation effort in terms of floating point operations is minimal when k is in the range (4, N {minus} 3) for the generalized-k method, and k = (N + 1)/2 for both the PFABRD algorithm and the parallel pipeline.

• OSTI ID: 7184325
• Journal Information: IEEE Transactions on Systems, Man, and Cybernetics (Institute of Electrical and Electronics Engineers); (USA), Vol. 19:5; ISSN 0018-9472
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
ARRAY PROCESSORS
COMPUTER ARCHITECTURE
PARALLEL PROCESSING
ALGORITHMS
INTEGRATED CIRCUITS
JACOBIAN FUNCTION
REAL TIME SYSTEMS
ELECTRONIC CIRCUITS
FUNCTIONS
MATHEMATICAL LOGIC
MICROELECTRONIC CIRCUITS
PROGRAMMING
990200* - Mathematics & Computers