Energy-based 6-DOF penetration depth computation for penalty-based haptic rendering algorithms

Existing penalty-based haptic rendering approaches compute penetration depth in strictly translational sense and cannot properly take object rotation into account. We aim to provide a theoretical foundation for computing the penetration depth on the group of rigid-body motions SE(3). We propose a penalty-based six-degrees-of-freedom (6-DOF) haptic rendering algorithm based on determining the closest-point projection of the inadmissible configuration onto the set of admissible configurations. Energy is used to define the metric on the configuration space. Once the projection is found the 6-DOF wrench can be computed. The configuration space is locally represented with exponential coordinates to make the algorithm more efficient. Numerical examples compare the proposed algorithm with the existing approaches and show its advantages.