Rendering of rigid objects with high stiffness while guaranteeing system stability remains a major and challenging issue in haptics. Being a part of the haptic system, the behavior of human operators, represented as the mechanical impedance of arm, has an inevitable influence on system performance. This paper first verified that the human arm impedance can unconsciously be modified through imposing background forces and resist unstable motions arising from external disturbance forces. Then, a reliable impedance tuning (IT) method for improving the stability and performance of haptic systems is proposed, which tunes human arm impedance by superimposing a position-based background force over the traditional haptic workspace. Moreover, an adaptive IT algorithm, adjusting the maximum background force based on the velocity of the human arm, is proposed to achieve a reasonable trade-off between system stability and transparency. Based on a three-degrees-of-freedom haptic device, maximum achievable stiffness and transparency grading experiments are carried out with 12 subjects, which verify the efficacy and advantage of the proposed method.

Existing penalty-based haptic rendering approaches are based on the penetration depth estimation in strictly translational sense and cannot properly take object rotation into account. We propose a new six-degree-of-freedom (6-DOF) haptic rendering algorithm which is based on determining the closest-point projection of the inadmissible configuration onto the set of admissible configurations. Energy is used to define a metric on the configuration space. Once the projection is found the 6-DOF wrench can be computed from the generalized penetration depth. The space is locally represented with exponential coordinates to make the algorithm more efficient. Examples compare the proposed algorithm with the existing approaches and show its advantages.