Straight-Line Single-Step Optimization of Manipulators with a Variable Cost-Weighting Matrix

Single-step optimization is a suboptimal control strategy that has proved useful in robotic manipulator control. A potential problem with the method is that it requires the numerical solution of a quadratic programming problem for each sampling interval. This computational load can be eliminated by preselecting the direction of the acceleration vector along a known straight line in coordinate space. The optimization problem then becomes one-dimensional and can be solved analytically off-line. The results obtained using the straight line approach, as well as earlier single-step formulations, can be significantly improved by the use of a time-varying weighting matrix in the performance measure. This new approach is presented here and applied to a 2-D.O.F. manipulator.