Robotic manipulators are utilized in a wide variety of manufacturing applications. While many industrial robots only have the minimum necessary degrees-of-freedom (dof) that are required for a given task, when working collaboratively on a task, systems of robots typically have more than the minimum required dof and provide an infinite numberofjoint configurations for a given task. This redundancy enables some aspect of the system performance to be optimized. A fundamental challenge with redundant systems, particularly multi-armed systems, is trajectory resolution, namely, the resolution of a single Cartesian trajectory into multiple joint trajectories. In this work, a framework for generating optimal coordinated-trajectories for redundant systems that addresses off-line and real-time trajectory resolution in the context of a machining operation is developed. The exemplar task for this work is robotic sculpting.

Robotic sculpting is a machining operation utilizing coordinated manipulators as the machine tool. When two six-dof manipulators are used, one to move the tool and the other to move the workpiece, the overall system has a high degree of redundancy.

One of the issues with serial link manipulators is that they have a low inherentstiffness due to the cantilever design of the links. Machining forces acting on the end-effectors can result in high bending moments about the joints. Combined with inaccurate models of the manipulators and the machining process, joint actuators can often saturate during operation. Onceajoint is saturated, tool-path tracking maynot be possible and the blank and/or tool may be damaged.

The issue of low stiffness is addressed during off-line planning by minimizing the system compliance in order to produce stiffer trajectories. By choosing stiffer configurations the manipulators can better respond to high machining forces.

In response to unmodeled disturbancesa real-time trajectory re-plannerutilizes a novel time-scaling method to reduce the tool speed, thereby, reducing the demand on the actuator torques. Alternate trajectories are determined such that high inertial torques are reduced and the manipulators continue to follow stiff trajectories. When alternate trajectories are generated, the redundancyis shared between conflicting performance functions.