Inverse Kinematics Techniques in the BirthPlay Application

Abstract

This research focuses on the manipulation of a virtual character using real-time movement of 6-degree-of-freedom controllers. To this end, several Jacobian-based IK methods were implemented, which use an approximation of the inverse of the Jacobian matrix to calculate changes in DOF values that will lead to the desired position and orientation of the end effector (the last link in the joint chain representing the arm). These methods include the Jacobian Tranpose, Jacobian Pseudoinverse, and Damped Least Squares. Joint limits are enforced through clamping of orientation, as well as the temporary removal of some of the joint's degrees of freedom. Collisions are handled within the Jacobian matrix itself by adding additional effectors for each contact, with a correctional impulse counter to the contact's direction and magnitude based on contact depth. A weight-based approach is used to handle priority of the constraints, those being the end effector's position, its rotation, and contact constraints. The ?final solution is a set of joint angle changes for each frame in the simulation that should result in a realistic motion closely approximating the actual controller's movement, while taking collision constraints into account. The context of the implementation of these techniques is the BirthPlay application, which simulates uncommon or difficult birth operations to train obstetricians in the proper procedures. The implementation produces good solutions for basic inverse kinematics problems, but the collision response method results in extremely slow convergence for configurations with contacts.