The inverse kinematic problem requires the solution of a set of n coupled nonlinear equations. Since arm signature models do not possess closed-form inverse kinematics, numerical methods must be applied to solve the nonlinear equations. In this chapter, we describe two algorithms for solving the inverse kinematic problem. The first algorithm, based upon Newton’s method, was originally proposed by Khosla, et al. . We have applied this algorithm in our hardware implementation and evaluation of arm signature identification. The second algorithm is the Jacobi iterative algorithm applied specifically to the inversion of signature models. In the context of this dissertation, we consider the implementation of the inverse kinematic equations to be synonymous with the robot’s kinematic control algorithms. Used by themselves to position the end-effector, the inverse kinematic equations correspond to an open-loop control structure. Closedloop or sensory feedback techniques are more appealing but the real-time measurement of the end-effector’s position and orientation is, in general, impractical with current technologies. In this chapter, the term kinematic control will be used instead of the term inverse kinematics.
KeywordsSine Dinates Verse
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