Path-constrained trajectory planning for multi-robot manufacturing systems using null-space descent optimization with reduced Hessian

In a multi-robot manufacturing system, several robotic manipulators can be physically coupled and collaborate on a process along a given path. Due to the high degrees of freedom and the high-dimensional constraints for path tracking and physical coupling, it remains challenging to plan the motion trajectories for the robots toward the maximization of their collective capabilities, such as load capacity and stiffness. The state-of-the-art methods face conflicts between the optimality and computational complexity, as well as between constraint satisfaction and convergence speed. To resolve the conflicts, this paper proposes a single-stage optimization method set in order to solve for the optimal robot placement and the joint motion simultaneously under a given manufacturing path on the work-piece. This method set is centered upon a reduced Hessian optimization method that descends orthogonally to all the path and coupling constraints in a robot-specific null-space of reduced dimension, while also considering the motion limits. The convergence of the reduced Hessian method is proved mathematically. Furthermore, we verify the reduced Hessian method statistically against existing methods in numerical experiments of pulling a spring. To make the algorithm applicable to real-world robot-driven manufacturing processes with paths of arbitrary geometric complexity, the method set is extended with a parallel computing technique that deals with multiple connected path segments. Through real-world multi-segment milling experiments, we validate the concept of capability enhancement for the multi-robot manufacturing system under the usage of the proposed method set.