Fast and Accurate Tracking of 3D Curves

This talk considers the use case of cold spray coating of an engine fan blade. Current leading industry deployment involves a dual-robot system, where one robot holds the fan blade and the second robot holds the spray gun to impinge metal powders onto the blade. These robots move together in a fully coordinated 12-degrees-of-freedom (dof) space. The spray task is 5-dof assuming a symmetrical spray pattern, implying 7-dof kinematic redundancy. The problem posed by this application is: How to create high-speed, high-precision, and uniform robot tool motion on a 3D curve using industrial robots with redundant degrees of freedom?

We pose the problem as maximizing the robot path speed subject to the tracking accuracy and speed uniformity constraints. This problem involves multiple challenges: pose optimization (where to place the robots and which robot configuration to use), redundancy resolution (how to choose complete robot configuration subject to the task requirement), joint velocity and acceleration constraints (how to maximize velocity and uniformity subject to the robot joint constraints which may be uncertain or unknown), robot waypoint placement (number and locations of the robot end effector waypoints), and motion segment optimization (which robot motion primitive, moveL, moveJ, or moveC, to use and how to blend them together).

This talk will present a hierarchical optimization approach for this problem. The robot pose and configuration are optimized using a global optimization method (evolutionary optimization) based on local kinematic redundancy resolution along the trajectory. Blending zones are selected to ensure speed uniformity. The motion primitives and waypoints are optimized based on simulated or actual robot motion to minimize the tracking error. The procedure is then repeated until the speed is maximized, subject to the tracking error and speed uniformity constraint.

To assess the efficacy of this methodology, we first use the current practice to develop baseline performance for two sample curves. We then apply our method to industrial robots from multiple vendors, in single and dual-arm configurations, and in simulation and physical experiments, for evaluation and demonstration. The resulting performance improvement over the baseline is at least 3X in all cases.