A Direct Algorithm to Compute the Switching Curve for Time-Optimal Motion of Cooperative Multi-Manipulators Moving on a Specified Path

For more than two decades it has been known that the solution to the time-optimal problem for a manipulator along a specified path is bang–bang in terms of acceleration along the path and the switching points can be found by phase plane analysis. Despite great advances, no direct method is available for finding the switching points and constructing a switching curve specially for cooperative multi-manipulator systems (CMMSs). So far, all proposed methods are based on search algorithms in which one has to: (i) search the whole phase plane to establish the boundary of the non-feasible area in which the end-effector cannot follow the path and (ii) find the critical points by numerical calculation of the slope of the non-feasible boundary. Although this search algorithm can give the solution, it is very tedious and time consuming, and the problem gets worse for CMMSs. This paper is concerned with developing a direct method to find the critical points and construction of the switching curve for non-redundant CMMSs. To this end, a rigorous study of the characteristics of the critical points and the switching curve is presented, and based on that a direct algorithm is introduced.

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