How to calculate inverse kinematics

Question

I want to know how to calculate rotation angles using inverse kinematics. I am planning on using this for real time 3d animation. Anyone know of some good literature that details a specific solution?

Answer 1

The following resources survey some popular numerical methods for inverse kinematics problems:

• Samuel R. Buss. Introduction to Inverse Kinematics with Jacobian Transpose, Pseudoinverse and Damped Least Squares methods

• Bill Baxter. Fast Numerical Methods for Inverse Kinematics

• Chris Welman. Inverse Kinematics and Geometric Constraints for Articulated Figure Manipulation

Buss's survey may be particularly interesting, because it explicitly discusses multiple limbs.

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.

• Jianmin Zhao and Norman Badler. Inverse Kinematics Positioning Using Nonlinear Programming for Highly Articulated Figures

6 dof industrial robots generally have closed form IK solutions, as mentioned by Andrew and explained in e.g. Craig: Introduction to Robotics. More useful for figure animation are methods for 7 dof human-like arms and legs:

• IKAN: Inverse Kinematics using ANalytical Methods

• Kulpa and Multon. Fast inverse kinematics and kinetics solver for human-like figures