A method for control of dynamic systems which uses a large table of precomputed data is described. The method was developed in the context of controlling legged systems that balance as they run. The tabular approach takes advantage of the very regular, cyclic character of legged behaviour in order to partition the system state variables into two sets: one set that varies in a relatively fixed way on each cycle, and another set that varies freely from cycle to cycle. Only this second subset of the state variables determines the size of the table. Stored data are computed by numerically simulating a dynamic model of the legged system as it progresses through the stance portion of the running cycle. Repeated simulations are used to characterize the system for different landing conditions. Polynomial surfaces are used to approximate the tabular date. The feasibility of the methods is shown by simulations.