Efficient modeling and computation of manipulator dynamics using orthogonal Cartesian tensors

The authors use orthogonal second-order Cartesian tensors to formulate the Newton-Euler dynamic equations for a robot manipulator. Based on this formulation, they develop two efficient recursive algorithms for computing the joint actuator torques/forces. The proposed algorithms are applicable to all rigid-link manipulators with open-chain kinematic structures with revolute and/or prismatic joints. An efficient implementation of one of the proposed algorithms shows that the joint torques/forces for a six-degrees-of-freedom manipulator with revolute joints, can be computed in approximately 489 multiplications and 420 additions. For manipulators with zero or 90 degrees twist angles, the required computations are reduced to 388 multiplications and 370 additions. For manipulators with even simpler geometric structures, these arithmetic operations can be further reduced to 277 multiplications and 255 additions.