Efficient parallel algorithms and VLSI architectures for manipulator Jacobian computation

The real-time computation of the 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 a first-order linear recurrence, the time lower bound for computing the Jacobian...

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Veröffentlicht in:IEEE transactions on systems, man, and cybernetics Jg. 19; H. 5; S. 1154 - 1166
Hauptverfasser: Yeung, T.B., Lee, C.S.G.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York, NY IEEE 01.09.1989
Institute of Electrical and Electronics Engineers
Schlagworte:
990200 - Mathematics & Computers
ALGORITHMS
Angular velocity
Applied sciences
ARRAY PROCESSORS
COMPUTER ARCHITECTURE
Computer science; control theory; systems
Concurrent computing
Control theory. Systems
ELECTRONIC CIRCUITS
Exact sciences and technology
FUNCTIONS
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
INTEGRATED CIRCUITS
JACOBIAN FUNCTION
Jacobian matrices
Manipulators
MATHEMATICAL LOGIC
MICROELECTRONIC CIRCUITS
Parallel algorithms
PARALLEL PROCESSING
Pipelines
PROGRAMMING
REAL TIME SYSTEMS
Robot kinematics
Robotics
Vectors
Very large scale integration
Parallel algorithm
VLSI circuit
Jacobi matrix
Real time
Block diagram
Velocity
Calculating method
Robotics
Manipulator
ISSN:0018-9472, 2168-2909
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Zusammenfassung:The real-time computation of the 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 a first-order linear recurrence, the time lower bound for computing the Jacobian can be proved to be of order O(N) on uniprocessor computers and of order O(log/sub 2/ N) on both single-instruction-stream-multiple-data-stream (SIMD) and VLSI pipelined parallel processors, where N is the number of links of the manipulator. To achieve the lower bound, the authors developed a generalized-k method for uniprocessor computers, a parallel forward and backward recursive doubling algorithm (PFABRD) for SIMD computers, and a parallel systolic architecture for 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 computational effort in terms of floating-point operations is minimal when k is in the range (4,N-3) for the generalized-k method, and k=(N+1)/2 for both the PFABRD algorithm and the parallel pipeline.< >
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ISSN:0018-9472
2168-2909
DOI:10.1109/21.44031