methods is hindered by the need to compute the inverse of the manipulator Jacobian at several points.
Linares & Page (1984) and Kazerounian (1987) describe techniques that solve the inverse kinematic problem by varying one joint variable at a time so as to minimize the difference, measured by a defined norm, between the endeffector pose as computed from the current joint variables values and the desired pose. This technique has the
advantages of guaranteed convergence and reliability even at a singular position. This method requires computation of the forward kinematics at each iteration and it has a computational complexity comparable to that of a Modifiedmultidimensional Newton-Raphson.
After reducing the problem to a polynomial system of four equations in only four of the joint variables, Tsai and Morgan (1984) used a homotopy map method, for solving systems of polynomial equations in several variables, to find the solutions of the inverse kinematics problem of revolute five- and six- degree-of-freedom manipulators of* arbitrary architecture. The method finds all solutions but its computational complexity renders it impractical for many applications.
Lumelsky (1984) presented an iterative algorithm that finds estimates for three of the joint variables and solves in closed form for the remaining three variables at each iteration. The method applies to a particular type of arm
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