Efficient Computation of Manipulator Inertia Matrix

NASA's Jet Propulsion Laboratory, Pasadena, California

An improved method for the computation of the manipulator inertia matrix has deve!oped, which is based on the concept of the spatial inertia of composite rigi d body (see Figure 1). The computation of the inertia matrix is required for the implementation of the advanced dynamic-control schemes as well as the dynamic simulation of the manipulator motion. The development of this method is motivated by the increasing demand for fast algorithms to provide real-time control and simulation capability and, particularly, the need for faster-than-rea l- time simulation capability, which will be required in many anticipated space teleoperation applications. The work starts by discussing two physical interpretations for elements of the inertia matrix, leading to two distinct previously proposed algorithms: i.e., the Composite Rigid-Body (CRB) algorithm and the Newton-Euler Based (NEB) algorithm, with the CRB algorithm being the most efficient. The redundancy in both algorithms is analyzed, and it is shown that the two algorithms are basicall y equivalent; i.e., they can be transformed to each other. For developing the new algorithm, spatial notation is used, which leads to compact equations and simplifies the algorithmic analysis. Using more classical notation, the final equations of the algorithm are then presented in a coordinate-free form. The choice of optimal frame(s) for projection of the coordinate-free (intrinsic) equations is discussed by analyzing the vectors and the tensors involved in the equations. It is shown that significant efficiency can be achieved by using different frames for projection of different sets of equations. The developed algorithm achieves a greater computational efficiency over the CRB algorithm by eliminating the redundancy in the intrinsic equations as well as by the suitable choice of coordinate frame for their projection. Figure 2 shows a comparison of the efficiency of the developed algorithm (designated as VCRB) and the previously proposed composite rigid-body algorithm (designated as OCRB). The developed algorithm is also more suitable for parallel processing than the CRB algorithm. This is mainly due to the fact th at the algorithm achieves a greater computational efficiency by reducing the data dependency in the computation. In a separate report, it is shown that the developed algorithm can be fully parallelized, leading to the computation of the inertia matrix in a time of O(logn)+O(1) with O(n2) processors.

More details can be found in:

A. Fijany and A.K. Bejczy, RAn Efficient Algorithm for Computation of the Manipulator Inertia Matrix,S Journal of Robotic Systems, Vol. 7, No. 1, pp. 57-80 , Feb. 1990.

Point of Contact:
Antal K. Bejczy
Mail Stop 198-219
Jet Propulsion Laboratory
4800 Oak Grove Drive
Pasadena CA 91109
818-354-4568
bejczy@telerobotics.jpl.nasa.gov

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