Force Sensing for Multi-point Contact Using a Constrained, Passive Joint Based on the Moment-Equivalent Point

In this paper, an analyzing method of a constrained joint using the Moment-Equivalent Point (MEP) is introduced that represents the balance between the torques exerted by two end joints in a robotic manipulator and the torque created by multiple-point contact of the flat surface that is in contact with the environment. By construction, the vector representing the summed reactive forces on the center of pressure (CoP) will always pass through the MEP. An important characteristic of the MEP is that it is fixed with respect to the link connecting the two joints if the ratio of the torques exerted at each joint is held constant. Therefore, if the robot has two passive joints that are mechanically constrained such that the ratio of the torques at each joint is constant, the MEP can be treated a single-contact point. Thus, we can model the robot’s behavior as if contacts only with a point on MEP in the environment, even if the actual contact is over multiple points on the flat surface. Such mechanically constrained passive joints and the concept of the MEP result in an approach that is midway between the standard multi-point contact and standard single-point contact in terms of the contact kinematics. One advantage of considering the balance of forces between the robot and the environment based on the MEP is that the tangential force applied to the contact surface can be calculated just from the CoP position and the normal force at the CoP. Experimental results indicate that the tangential force at the foot of the robot can be estimated by measuring only the normal forces applied at the foot.