Resolved rate and acceleration control in the presence of actuator constraints

Experimental evaluation of various task-space control algorithms shows that significant deviations from desired trajectories may occur, especially at higher speeds, or in the vicinity of singularities. The experiments on a modular reconfigurable robotic setup confirmed this conclusion: the lateral deviations may range up to several centimeters from the closest point on the desired trajectory. The main reason is that the control output often reaches the saturation value of an actuator. The lateral error is also found to be very dangerous in obstacle-cluttered environments due to possible damage to the manipulator arm while hitting an obstacle at high speed. This article is devoted to solving this problem. Widely used task space control algorithms such as the resolved-rate and the resolved-acceleration algorithms are modified by introducing monitoring on the control output and, accordingly, modifying the commanded control signal so that the end-effector is prevented from leaving the programmed path. As a consequence, the manipulator tip may slow down along the path due to limited actuator power, but it will be accelerated after that to reach the desired position as soon as possible. The algorithms also take into account the presence of singularities to avoid uncontrollable excursions of the manipulator tip. Hundreds of experiments have been carried out to confirm the concept. Some of those with a desired trajectory reaching both the regular and the singular region of the workspace are provided to illustrate the method.