A discrete-time robotic command generator

A discrete-time command generator that accepts position and orientation trajectories in Cartesian space and produces position, velocity, and acceleration trajectories in joint space is presented. Discrete-time command generators can be obtained from their continuous-time counterparts by using any standard numerical procedure to solve the nonlinear differential equation at a discrete set of points. However, existing numerical procedures require multiple function evaluations per input point to achieve an accurate solution. A novel technique is presented that achieves an accurate solution with only one function evaluation per input point. The application of the scheme to six degree-of-freedom manipulators is demonstrated through simulation results for a spherical-wrist robot