Global inverse kinematics solver for linked mechanisms under joint limits and contacts

Abstract

To control the motion of a virtual character with 6-DOF controllers inverse kinematics techniques have to be used. One of these inverse kinematics techniques is the Jacobian method. This report gives a new quaternion based Jacobian method to solve the inverse kinematics problem for the real time motion control of a virtual character. This includes the calculation of the Jacobian matrix which represents the change in end end effector position and orientation given the change in configuration. Here, the configuration is given by the log values of the quaternions which represent the relative orientation between the bones. The method uses the quaternion properties to constrain the rotational freedom of the joints with only three joint limits. Finally, the report proposes some methods to give a response when the virtual character collides with a virtual object.