Comments on "The control of robot manipulators with bounded input" [with reply]

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Abstract
The present author demonstrates: (1) that the optimal decision strategy (ODS) proposed in the paper by M.W. Spong and J.S. Thorp (IEEE Trans. Automat. Contr. vol.AC-31, p.483-90 (1986)) is in fact a specific case of an optimal aim strategy (OAS) with special aim-state and system-state assignments; and (2) that the primal-dual method employed in the same paper can be replaced by a more direct, more efficient discrete-time control algorithm based on fixed-point iteration or by a more complete, more exact continuous-time control law based on fixed-point feedback. For the class of problems under discussion, however, the authors' special assignments represent a significant application of optimal-aim notions. Spong and Thorp point out that although the optimal decision strategy (ODS) that they use in their paper does not appear to be a special case of OAS as originally defined, it can be included within the framework of more recent formulations of OAS. In fact, it appears that the two methods, as currently defined, are essentially equivalent.

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