An algorithm based on the Marquardt-Levenberg least-square optimization method has been shown by S. Kollias and D. Anastassiou (IEEE Trans. on Circuits Syst. vol.36, no.8, p.1092-101, Aug. 1989) to be a much more efficient training method than gradient descent, when applied to some small feedforward neural networks. Yet, for many applications, the increase in computational complexity of the method outweighs any gain in learning rate obtained over current training methods. However, the least-squares method can be more efficiently implemented on parallel architectures than standard methods. This is demonstrated by comparing computation times and learning rates for the least-squares method implemented on 1, 2, 4, 8, and 16 processors on an Intel iPSC/2 multicomputer. Two applications which demonstrate the faster real-time learning rate of the last-squares method over than of gradient descent are given

Real time hybrid control results with resolved motion force control (RMFC) and task coordinate pole-placement self-tuning (TST) are given. The control methods calculate corrective forces in a Cartesian coordinate frame to eliminate position and force errors. These forces are transformed to equivalent joint inputs for actuation. RMFC uses stochastic approximation to adapt to changing manipulator dynamics. TST uses self-tuning in the task frame to estimate dynamic system models and place closed loop poles. Results show both methods capable of the hybrid control application but friction has a large effect on the control.

The pole placement self-tuning control method is applied to the control of the manipulators directly in the task coordinate system, which results in highly desirable task-oriented performance characteristics. In the task coordinate, the position control axes and force control axes are orthogonal, therefore, hybrid control can be achieved without degradation in performance of the control system. With the learning mechanism at the task location, dynamic friction and compliant effects are automatically compensated. Simulation results for both position control and hybrid control using the JPL-Stanford Arm demonstrate the effectiveness of the proposed method.