Analytical equations vs. table look-up for manipulation: A unifying concept

By considering parameterization of the equations of motion for a manipulater, divergent procedures for control involving analytical expressions and table look-up can be examined in the same light. Each approach represents at different point on a continuum characterized by the indicator P, the number of parametric variables. As P increases storage requirements increase, but computational complexity decreases. Typically, for an arm having N degrees of freedom ~(N(3-P/N) operations and ~(MP) stroage cells are required for evaluation of the equations of motion. The State Space Model and the Configuration Space Model, characterized by intermediate values of P, are discussed.