Kinematic Linkages - Computer Animation: Algorithms and Techniques - page 184

5.3.4 Summary
Various strategies for IK have been proposed in the literature. Much of this comes from robotics lit-
erature that avoids the expense of computing an inverse [ 1 ] [ 5 ]. Several strategies are presented here.
The most direct solution is by analysis, but many linkages are too complex for such analysis. A numeric
approach is often needed. Trade-offs among the numeric approaches include ease of implementation,
possible real-time behavior, and robustness in the face of singularities. An additional approach is tar-
geted at linkages that are specifically human-like in their DOF and heuristically solves reaching prob-
lems by trying to model human-like reaching; this is discussed in Chapter 9 .
IK, on the surface, promises to solve many animation control problems. However, there is no single,
obvious, and universally attractive solution to IK. There are options, however, and the various
approaches do provide effective tools if used judiciously.
5.4 Chapter summary
Hierarchical models are extremely useful for enforcing certain relationships among the elements so that
the animator can concentrate on just the DOF remaining. Forward kinematics gives the animator
explicit control over each DOF but can become cumbersome when the animation is trying to attain
a specific position or orientation of an element at the end of a hierarchical chain. IK, using the inverse
or pseudoinverse of the Jacobian, allows the animator to concentrate only on the conditions at the end of
such a chain but might produce undesirable configurations. Additional control expressions can be
added to the pseudoinverse Jacobian solution to express a preference for solutions of a certain char-
acter. However, these are all kinematic techniques. Often, more realistic motion is desired and phys-
ically based simulations are needed.
References
[1] Buss S. Introduction to Inverse Kinematics with Jacobian Transpose, Pseudoinverse and Damped Least
Squares Method, Unpublished survey, http://math.ucsd.edu/ sbuss/ResearchWeb/ikmethods/ ; July 2006.
[2] Buss S. Selectively Damped Least Squares for Inverse Kinematics. Journal of Graphics Tools 2005;10
(3):37-49.
[3] Craig J. Introduction to Robotics Mechanics and Control. New York: Addison-Wesley; 1989.
[4] Ribble E. Synthesis of Human Skeletal Motion and the Design of a Special-Purpose Processor for Real-Time
Animation of Human and Animal Figure Motion. Master's thesis. Columbus, Ohio: Ohio State University;
June 1982.
[5] Welman C. Inverse Kinematics and Geometric Constraints for Articulated Figure Manipulation. M.S. Thesis.
Simon Frasier University; 1993.