Inverse Kinematics

• Often nonlinear, underdetermined or overdetermined, possibly ill-conditioned.
• Complexity of determining solution proportional to number of free links.
• One free joint between two fixed ones can be solved fairly efficiently, for example, with only one spare degree of freedom.
• Extra constraints may be needed to obtain a unique and stable solution.
  • Example: Requiring a joint to point downwards as a gross approximation to gravity
  • Joint motion constraints (hinge vs. revolute vs. ball) are also useful.
• Additional optimization objectives
  • Resulting optimization problem solved iteratively as an animation proceeds.
  • Example optimization objectives:
    • minimize the kinetic energy of structure;
    • minimize the total elevation of the structure;
    • minimize the maximum (or average) angular torque.