US Patent 9321175 Robotic manipulator articulation techniques

A controller determines a set of solutions to an inverse kinematic relationship relating received three axes position and orientation requirements defining a tool control point (TCP) of a robotic manipulator, the robotic manipulator including at least seven revolute joints, to a respective angular position of each of the seven revolute joints. The set of solutions specifies, in terms of an angular position of a first revolute joint proximate to a proximal end of the robotic manipulator, at least one set of angular positions of the second, third, fourth, fifth, sixth and seventh revolute joints. The set of solutions results from solving only closed-form mathematical expressions.