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copied!<p>The following resources survey some popular numerical methods for inverse kinematics problems:</p> <ul> <li><p>Samuel R. Buss. <a href="http://math.ucsd.edu/~sbuss/ResearchWeb/ikmethods/iksurvey.pdf" rel="noreferrer">Introduction to Inverse Kinematics with Jacobian Transpose, Pseudoinverse and Damped Least Squares methods</a></p></li> <li><p>Bill Baxter. <a href="http://billbaxter.com/courses/290/html/index.htm" rel="noreferrer">Fast Numerical Methods for Inverse Kinematics</a></p></li> <li><p>Chris Welman. <a href="ftp://fas.sfu.ca/pub/cs/theses/1993/ChrisWelmanMSc.ps.gz" rel="noreferrer">Inverse Kinematics and Geometric Constraints for Articulated Figure Manipulation</a></p></li> </ul> <p>Buss's survey may be particularly interesting, because it explicitly discusses multiple limbs.</p> <p>IK systems for animation must generally support multiple, possibly conflicting, constraints. For example, one arm can hold on to a rail while the other arm reaches for a target.</p> <ul> <li>Jianmin Zhao and Norman Badler. <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.8866" rel="noreferrer">Inverse Kinematics Positioning Using Nonlinear Programming for Highly Articulated Figures</a></li> </ul> <p>6 <em>dof</em> industrial robots generally have closed form IK solutions, as mentioned by Andrew and explained in <em>e.g.</em> <a href="http://rads.stackoverflow.com/amzn/click/0201543613" rel="noreferrer">Craig: <em>Introduction to Robotics</em></a>. More useful for figure animation are methods for 7 <em>dof</em> human-like arms and legs:</p> <ul> <li><p><a href="http://cg.cis.upenn.edu/hms/software/ikan/ikan.html" rel="noreferrer">IKAN: Inverse Kinematics using ANalytical Methods</a></p></li> <li><p>Kulpa and Multon. <a href="http://www.irisa.fr/bunraku/GENS/fmulton/#humanoids05" rel="noreferrer">Fast inverse kinematics and kinetics solver for human-like figures</a></p></li> </ul>

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