Determining the initial configuration of uninterrupted redundant manipulator trajectories in a manufacturing environment

Authors:
Zan Mi;Jingzhou (James) Yang;Joo H. Kim;Karim Abdel-Malek
Affiliations:
Machine Research, Caterpillar Inc., Peoria, IL 61629, USA;Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA;Polytechnic Institute of New York University Brooklyn, NY 11201, USA;Center for Computer-Aided Design, The University of Iowa, Iowa City, IA 52242-1000, USA
Venue:
Robotics and Computer-Integrated Manufacturing
Year:
2011

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Abstract

In a manufacturing environment where a redundant manipulator is programmed to follow a specific trajectory such as welding, painting, and soldering, it is often the case that the manipulator reaches a singular configuration where the program is stopped, the manipulator has to be switched to a new configuration, and the motion continued. This paper presents a method of determining the initial configuration of robotic manipulators to traverse a path trajectory without halting the motion. The method consists of: (1) identifying singular curves/surfaces using the Jacobian rank deficiency method; (2) determining non-crossable curves/surfaces using acceleration-based crossability criteria; (3) finding if the path intersects any non-crossable singular curve/surface. If there is not any intersection, the manipulator does not interrupt with any initial configuration on the trajectory. Otherwise, the intersection is determined, and the non-crossable singular configuration at the intersection point is determined; (4) solving the differential algebraic system of equations (DAE) of index 2 using the Runge-Kutta method; and (5) solving the optimization problem. The method is illustrated through examples.