Minimum-time trajectory planning of spatial cable-suspended robots along a specified path considering both tension and velocity constraints

In this article, minimum-time trajectory planning problems of spatial non-redundant and redundant cable suspended robots are addressed. Both cable tensions and cable velocities are considered to be limited. The equations of motion of such systems are reduced to a system of second order differential equations in terms of path parameter s using the specified desired path. The bounds on the cable tensions and cable velocities are transformed into bounds on the acceleration and velocity along the path. By assuming bang-bang control, the switching points in the ṡ² - s plane are obtained. Then the cable tensions as the inputs are found versus path parameter and subsequently versus time.