Resolving the redundancy of a seven DOF wearable robotic system based on kinematic and dynamic constraint

Abstract

According to the seven degrees of freedom (DOFs) human arm model composed of the shoulder, elbow, and wrist joints, positioning of the wrist in space and orientating the palm is a task requiring only six DOFs. Due to this redundancy, a given task can be completed by multiple arm configurations, and there is no unique mathematical solution to the inverse kinematics. The redundancy of a wearable robotic system (exoskeleton) that interacts with the human is expected to be resolved in the same way as that of the human arm. A unique solution to the system's redundancy was introduced by combining both kinematic and dynamic criteria. The redundancy of the arm is expressed mathematically by defining the swivel angle: the rotation angle of the plane including the upper and lower arm around a virtual axis connecting the shoulder and wrist joints which are fixed in space. Two different swivel angles were generated based on kinematic and dynamic constraints. The kinematic criterion is to maximize the projection of the longest principle axis of the manipulability ellipsoid for the human arm on the vector connecting the wrist and the virtual target on the head region. The dynamic criterion is to minimize the mechanical work done in the joint space for each two consecutive points along the task space trajectory. These two criteria were then combined linearly with different weight factors for estimating the swivel angle. Post processing of experimental data collected with a motion capturing system indicated that by using the proposed synthesis of redundancy resolution criteria, the error between the predicted swivel angle and the actual swivel angle adopted by the motor control system was less then five degrees. This result outperformed the prediction based on a single criteria.