Unified Solution of the Baxter Jacobian Matrix

Paper #:
  • 2017-01-0291

Published:
  • 2017-03-28
Abstract:
Robot trajectory represents a set of points determined in the Cartesian coordinate system. In this situation robot controller must have the inverse kinematics solution to allow robot to go through the trajectory. Sometimes robot can run into problems, since the inverse mapping from a Cartesian space to a joint space may cause problems. These are robot positions that are referred to as singularities or degeneracy. For robot manipulators, the Jacobian is defined as the coefficient matrix of any set of equations that relates the velocity state of the end-effector described in the Cartesian space to the actuated joint rates in the joint velocity space. This matrix is important in calculating the singularities of a robot and also in calculating inverse kinematics using Jacobian method. A recent trend in robotics is “collaborative – robots” or cobots who are capable of working with humans sharing the same workspace. The Baxter robot manufactured by Rethink Robotics is a cobot with two arms with a humanoid appearance, each arm consisting of 7 rotational joints. As this is a recently introduced cobot it is important to setup an argument for future references. In this research, the Denavit Hartenberg values for the both arms were validated and used in building the Jacobian Matrix. Two methods were used to calculate the Jacobian which are, Newton Euler method and Vector method. The results from each method were compared with numerical method and validated. Then for both arms a reconfigurable method is proposed unifying both arms simplifying the process and saving time and processing power. So using the reconfigurable model the Jacobian has been calculated and at the end of the process, the values has been applied accordingly. As two armed robots are getting popular in the industry, this reconfigurable method can be used as an important tool to simplify the complex calculations.  
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