Productivity/energy optimisation of trajectories and coordination for cyclic multi-robot systems

Quality and productivity driven trajectory optimisation for robotic handling of compliant sheet metal parts in multi-press stamping lines

“…The robot motion planning for these material handling systems commonly either ignores the part deformations by assuming that the handled compliant parts are rigid, or focusses on avoiding only plastic deformations. The former was found to be the case through work by Glorieux et al [14,8], which investigated multi-robot motion planning for material handling of sheet metal parts in order to improve productivity and reduce robot wear. The same assumption ("rigid-parts") is made in other studies concerning designing the tool paths, bending sequences and motions for robotic sheet metal part forming [5,15,6,7].…”

“…where Z is the cycle-time with the optimised trajectories, and Z pre is the predefined cycle-time, g 3 is the collision-free multirobot coordination function for the trajectories of the robots in the shared workspace of the robots in set R, and q r J (t) represents the pose of Robot r in time ∀t ∈ [t start , t end ] for the J joints' positions of each Robot r ∈ R. In this work, the collision-free multirobot coordination is not solely realised by tuning the trajectories, but the system also uses an initial waiting-time (∆t r ) to make a robot wait to start its operation so that it will not collide with the robot of the previous operation in the shared workspace [8]. The proposed optimisation model directly calculates the minimal initial waiting-times for collision-free multi-robot coordination based on the robots' trajectories.…”

“…This section describes how the proposed optimisation model represents the problem formulated in Section 2, and how it is parametrised. In order to solve the formulated problem by optimising the multi-robot trajectories, it is modelled as a nonlinear programming (NLP) optimisation problem based on the earlier work by Glorieux et al [8]. The predefined robot paths are first discretised into n segments, which gives the positions q r j,i for each Joint j ∈ J of each Robot r ∈ R, for each Segment i ∈ N = {1, .…”

“…It thus needs to be ensured that the robot joints' velocity and acceleration are zero at the start and end of the operation. This is realised by implementing the following constraints in the NLP modelq r j,1 = 0;q r j,n = 0; q r j,1 = 0;q r j,n = 0; (8) where i = 1 refers to the beginning of the trajectory and i = n to the end. Similar constraints are used to ensure that the robot stands still at the positions for picking or placing the parṫ q r j,pick = 0;q r j,place = 0;…”

“…The optimisation variable t r i determines thus not only the joints velocity and acceleration but also the jerk during Segment i. When the maximum allowed jerk value ... q r j,max is unknown, a good approximation can be obtained by examining the maximum jerk of trajectory generated (at high/maximum robot velocity) by the robot supplier's controller for the specific predefined robot path [8].…”