A new Jacobian formulation for general six-revolute manipulators

Conventionally, the kinematics for serial-link manipulators are formed in terms of the joint angles. The author presents an alternative formulation which uses unit vectors along the joint axes as the variables. For the task of updating the manipulator pose for an incremental change in position and orientation, it is shown that the new formulation is approximately equal in computational cost to the traditional method. Compared to the conventional approach, the joint vector formulation has a simple, but larger, sparse Jacobian. Efficiency is achieved by using a sparse matrix solver