On the Controllability of Single-Step Optimization of Robotic Manipulators

Suboptimal control algorithms have been successfully used for the control of robotic manipulators and spacecraft attitudes. One such suboptimal strategy is single step optimization. This typically involves the numerical solution of a quadratic programming problem at each sampling interval to obtain the acceleration vector for a manipulator. Inverse dynamics are then used to calculate the torque vector. If the feasible region for the acceleration vector does not contain the origin, the method fails. Failure has also resulted when the sampling period was excessively reduced. In this paper, it is shown that failure in both situations is because no feasible acceleration vector exists. Examples and means of avoiding the loss of controllability are also presented.