Geometrically motivated inverse kinematics for an arm with 7 degrees of freedom

The need for robust teleoperated robotic arms is increasing with respect to particular dangerous maritime missions. These missions might include deactivation of underwater mines, underwater salvage, or pipeline repair. In the past, robotic arms with low degrees of freedom were not always feasible for such operations, as the lack of free motion prevented their uses in locations with small space for maneuverability. With higher degrees of freedom, the arms are able to maneuver in tighter spaces and avoid obstacles as well. The increase in the number of degrees of freedom incurs an increase in the computational complexity for determining arm poses. With respect to the 7 degrees of freedom (DOF) Schunk arm, we make observations that allow for the derivation of systems of equations to solve the inverse kinematics problem. Furthermore, we show how to solve the systems such that closed form solutions can be obtained. This approach allows us to give and prove a characterization of the number of solutions with respect to certain conditions. As a surrogate test platform for maritime missions, we have developed a simulation that uses the Robot Operating System (ROS) and ROS visualization (rviz) to simulate the moving of the arm.