Cycle time minimization in multi-robot manufacturing stations is computationally challenging. This is due to the many aspects that need to be accounted for, including assigning process tasks to robots, specifying robot configurations at tasks, sequencing, planning motions, and coordinating the robots to avoid collisions. Hence, to find good solutions, often some assumptions are made and/or the problem is divided into subproblems—often limiting the set of solutions with the risk of excluding the best ones. In this study, we generalize the completely disjoint solution method that challenges the so-calledshortest pathassumption, i.e., to let each robot use its shortest collision-free motion between any two configurations, regardless of the other robots. We devise a generalized method calledspatial–temporal load balancing and coordination, which prevents robot–robot collisions by a sequence of disjoint solutions, guiding task assignments, sequences, and robot motions (path and velocity). We study both artificial and industrial instances. For some of them, our suggested method is superior to methods based on the shortest path assumption, with as much as a 28% reduction in cycle time. Moreover, for problem instances with no special structure, we establish that the shortest path assumption is often reasonable.Note to Practitioners—This work is motivated by a particular industrial problem instance of a spot-welding station with two robots and where welds are placed along the edge of a workpiece. Due to the special geometry of the instance one robot can only perform welds in the middle of the edge and the other only at the ends. As a result, if the robots use their shortest motions between welds, then waiting times are required to prevent collisions. Moreover, the tasks are too close to each other to allow for a completely disjoint solution. Hence, we suggest a method based on sequence of disjoint solutions.

Abstract In the presence of uncertainties in the parameters of a mathematical model, optimal solutions using nominal or expected parameter values can be misleading. In practice, robust solutions to an optimization problem are desired. Although robustness is a key research topic within single-objective optimization, little attention is received within multi-objective optimization, i.e. robust multi-objective optimization.This work builds on recent work within robust multi-objective optimization and presents a new robust efficiency concept for bi-objective optimization problems with one uncertain objective. Our proposed concept and algorithmic contribution are tested on a real-world multi-item capacitated resource planning problem, appearing at a large aerospace company manufacturing high precision engine parts. Our algorithm finds all the robust efficient solutions required by the decision-makers in significantly less time than the approach of Kuhn et al. (Eur J Oper Res 252(2):418–431, 2016) on 28 of the 30 industrial instances.

In automotive manufacturing, production systems typically involve multiple robots and, today, are being individualized by utilizing the concept of digital twins. Therefore, the robot programs need to be verified for each individual product. A crucial aspect is to avoid collisions between robots by velocity tuning: This involves an efficient analysis of pairs of robot paths and determining if swept volumes of (sub) paths are disjoint. In general, velocity uncertain motions require disjoint sweep volumes to be safe. We optimize a clearance lower bounding function to provide new sample points for clearance computations. Due to the computational cost of each distance query, our sampling strategy aims to maximize the information gained at each query. The algorithm terminates when robot paths are verified to be disjoint or a collision is detected. Our approach for disjoint paths is inspired by the technique for continuous collision detection known asconservative advancement. Our tests indicate that the proposed sampling method is reliable and computationally much faster than creating and intersecting octrees representing the swept volumes.