Conference Paper

A study of rate coordination algorithm in serial chain redundant manipulators

Dept. of Mech. Eng., Florida Atlantic Univ., Boca Raton, FL
DOI: 10.1109/ICAR.1991.240386 Conference: Advanced Robotics, 1991. 'Robots in Unstructured Environments', 91 ICAR., Fifth International Conference on
Source: IEEE Xplore

ABSTRACT Presents a general algorithm which results in an efficient
solution for the rate coordination problem in redundant manipulators. An
alternative formulation of minimum norm solution is first introduced
based on a geometric interpretation that vectors orthogonal to
constraint space should pass through the origin of the solution space.
It is shown that for any spacial manipulator with 1 or 2 degrees of
redundancy, the minimum norm rate solution can be derived analytically.
The properties of orthogonal vectors are then utilized in formulating
the general solution to incorporate any performance criterion. The
method offers an equivalent but much more efficient alternative to using
the pseudoinverse in redundancy resolution and, in fact, is applicable
to any underdetermined linear system. Analytical as well as numerical
examples are presented to demonstrate the effectiveness of the method

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    ABSTRACT: The redundancy resolution problem for kinematically redundant serial chain manipulators is addressed. In this article we present a generalization of the geometry-based rate allocation algorithm, developed initially for only a minimum norm solution, to obtain the optimal joint rate solution for any specified objective function, with or without weightage. This generalization is made possible through a physial interpretation of the common pseudoinverse-based gradient solution scheme, and by developing a modified formulation for the objective function as a minimum criterion not with respect to the origin of the joint rate space, but with respect to another point in the joint rate space represented by the gradient of the specified objective. Application examples of the algorithm including procedures of solution are demonstrated using 7R manipulators with two generic types of geometry. Moreover, a closed form optimal solution for the class of 7R anthropomorphic arms is also given. © 1995 John Wiley & Sons, Inc.
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