An absolute encoder employs multiple sub-encoders of different resolutions and a linking algorithm for combining the sub-encoder outputs to form an accurate, high-resolution position estimate. The sub-encoders can utilize edge modulation of a main grating track, sloped patterns of successively higher periods, and other types of scale patterns. The sub-encoders can also use a variety of detector types suitable for the patterns being used. In one linking approach, pairs of tracks are linked together successively by applying a phase shift to the coarser track and then combining it with the finer track such that the transitions of the coarse track estimates become aligned with those of the finer track, whereupon the values can be combined to form a linked position estimate. In another approach, beat tracks are calculated from physical tracks of similar period, and the beat tracks are used as the coarser tracks in the linking process. A wafer-handling robot employs the absolute encoder for controlling rotation of multiple joints.