Pipelined computation of manipulator modeling matrices

It is essential for the robust control of a dynamic system to employ a characterization of its inertia content in the control formulation. One such characterization is described for the nonlinear time-varying system of a robotic manipulator in the form of pipelined modeling software which is implemented on a medium-sized array processor to run in real time. The time-varying inertia content of the manipulator is expressed in terms of kinematic influence coefficients which are represented by explicit functions of only the generalized coordinates. Properties of these influence coefficients are employed to reduce the computation effort necessary to generate the modeling coefficients. To efficiently pipeline this algorithm, the structure inherent in the problem is exploited to allow extensive use of data-dependent addressing which is employed to compute multiple "small" operations within a single pipeline. The resulting software consists of two portions-- an off-line portion generates integer offset vectors to direct the addressing of the on-line portion in computing the modeling coefficients. The real-time algorithm is fourth-order in the number of links requiring 7.5 ms on a modest-sized array processor to compute the modeling coefficients of a general six-link manipulator.