Optimizing point to point motion of net velocity constrained manipulators

The architecture of many hydraulic manipulators, such as excavators common in the earthmoving industry, have constraints on the net sum of actuator speeds. This paper gives the necessary conditions for minimum-time velocity commands for point to point motion. A kinematic model of the manipulator is used. The optimal solution is not always unique. We propose a particular optimal solution, u*, that is stationary. The optimality of inputs unequal to u* is evaluated by the position of u* in the input domain. Several examples are given to demonstrate the analysis.