Efficient computation of manipulator inertia matrices and the direct dynamics problem

A modeling scheme that uses the concepts of generalized and augmented links is proposed for computing joint-space inertia matrices of open-chain rigid body systems. Expressions for evaluating these matrices are derived, utilizing orthogonal Cartesian tensors and the Newton-Euler equations of motion. The resulting recursive algorithm is applicable to all rigid-link manipulators having open-chain kinematic structures with revolute and/or prismatic joints. An efficient implementation of the algorithm shows that the joint-space inertia-matrix of a six degree-of-freedom manipulator with revolute joints can be computed in approximately 420 multiplications and 339 additions. For manipulators with 0° to 90° twist angles, the number of computations is reduced to 271 multiplications and 250 additions