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.

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.

We consider the problem of creating tighter-fitting bounding volumes (more specifically rectangular swept spheres) when constructing bounding volume hierarchies (BVHs) for complex 3D geometries given in the form of unstructured triangle meshes/soups with the aim of speeding up our IPS Path Planner for rigid bodies, where the triangles often have very different sizes. Currently, the underlying collision and distance computation module (IPS CDC) does not take into account the sizes of the triangles when it constructs BVHs using a top-down strategy. To split triangles in a BVH node into two BVH nodes, IPS CDC has to compute both the split axis and the split position. In this work, we use the principal axes of the tensor of inertia as the potential split axes and the center of mass as the split position, where the computations of both the tensor of inertia and the center of mass require knowledge of the areas of the triangles. We show that our method improves performance (up to 20 % faster) of our IPS Path Planner when it is used to plan collision-free disassembly paths for three different test cases taken from manufacturing industries.

Path planning of an object which is allowed to be in contact with other objects during assembly process is a significant challenge due to the variety of permitted or forbidden collisions between the distinct parts of the objects to be assembled. In order to put objects together in real-life scenarios, parts of assembled objects may be required to flex, whereas other parts may have to fit exactly. Consequently, existing collision checking and distance computation algorithms have to be modified to enable path planning of objects that can be in contact during the assembly process. In this paper, we analyze an improved broad phase proximity query algorithm to enable such contact-based assembly tasks we call CHAT (Contact-based Hierarchy for Assembly Tasks). We demonstrate that, compared to existing approaches, our proposed method is more than an order of magnitude faster for collision queries and up to three times faster for distance queries when the two objects contain a large number of parts (with some parts containing thousands or tens of thousands of triangles). Due to the nature of the algorithm, we expect the performance improvements to increase as the number of parts in an object becomes larger.

Assembly cells, where multiple robots perform sets of tasks, often face the challenge to minimize cycle time and avoid collisions. Collisions are avoided by introducing synchronization schemes among the robots, preventing shared volumes of the workspaces to be simultaneously entered. Synchronization often increases the cycle time and makes the robot programming more difficult to generate, adjust, and maintain. In this paper, we present a novel method to maximize throughput while eliminating all synchronizations among robots. We devise algorithms to minimize cycle time generating no intersection among robots at any time during their paths. First, a surrogate model for minimizing cycle time is provided and solved to optimality: each task is assigned to a robot in a way that no collision occurs. Afterward, the entire workspace is partitioned such that each robot's workspace is separated from the others. Finally, robot paths are generated automatically in order to avoid collisions with the environment and remaining in their precomputed partitions. In the rare cases where some of these steps fail, a feedback procedure redistributing the tasks or modifying the partitions is adopted. Furthermore, since the surrogate model approximates cycle time, several solutions are generated and evaluated based on better approximations of the model. The results are convincing: computational experience on different cases from the automotive industry shows that it is possible to generate programs where the robots never intersect with each other and achieve cycle times comparable to the ones generated allowing synchronization.

This work is inspired by the problem of planning sequences of operations, as welding, in car manufacturing stations where multiple industrial robots cooperate. The goal is to minimize the station cycle time, i.e., the time it takes for the last robot to finish its cycle. This is done by dispatching the tasks among the robots, and by routing and scheduling the robots in a collision-free way, such that they perform all predefined tasks. We propose an iterative and decoupled approach in order to cope with the high complexity of the problem. First, collisions among robots are neglected, leading to a min-max Multiple Generalized Traveling Salesman Problem (MGTSP). Then, when the sets of robot loads have been obtained and fixed, we sequence and schedule their tasks, with the aim to avoid conflicts. The first problem (min-max MGTSP) is solved by an exact branch and bound (B&B) method, where different lower bounds are presented by combining the solutions of a min-max set partitioning problem and of a Generalized Traveling Salesman Problem (GTSP). The second problem is approached by assuming that robots move synchronously: a novel transformation of this synchronous problem into a GTSP is presented. Eventually, in order to provide complete robot solutions, we include path planning functionalities, allowing the robots to avoid collisions with the static environment and among themselves. These steps are iterated until a satisfying solution is obtained. Experimental results are shown for both problems and for their combination. We even show the results of the iterative method, applied to an industrial test case adapted from a stud welding station in a car manufacturing line. This paper is motivated by the problem of planning robot operations in welding applications in the automotive industry. Here, a number of welding tasks have been introduced along the car body: the goal is to let the robots perform such tasks while minimizing the cycle time (or makespan). The main difficulties, from the manufacturing engineer perspective, lie in assigning the tasks to the robots, deciding the order and the timing of the operations, avoiding collisions between the robots and the environment, and among the robots themselves. We present in this work an iterative approach, consisting of two steps: first, sequences for the robot operations are computed in order to minimize the cycle time, while neglecting collisions among robots; then, given the assignment of tasks to robots, the operations are reordered and scheduled while avoiding conflicts among robots. Robot motions are also automatically computed to avoid collisions with the static environment. We show an optimal algorithm, for the first part, based on implicit enumeration (B&B) and introduce a novel suboptimal algorithm, for the second part, to synchronize the robots. These algorithms are iterated while fetching information about the problem that are hard to compute, thus following a lazy approach. Tests on problems adapted from the literature and from the automotive industry, show clear improvements over more sequential approaches and good running times. The algorithms are especially suited for cases with up to 40 tasks and 4 robots, as for typical geometry stations. In future works, we will further investigate efficient heuristic optimization approaches in order to handle larger problems, consisting of more than 100 tasks, as for typical assembly stations.

In this article we present a heuristic algorithm to compute the largest volume of an object in three dimensions that can move collision-free from a start configuration to a goal configuration through a virtual environment. The results presented here provide industrial designers with a framework to reduce the number of design iterations when designing parts to be placed in tight spaces.

We present a resolution complete path planner based on an implicit grid in the configuration space. The planner can be described as a two-level process in which a global planner restricts a local planner to certain subsets of the grid. The global planner starts by letting the local planner search in a coarse subset of the grid, and successively refines the grid until a solution is found. The local planner applies a scheme for lazy evaluation on each subgrid in order to minimize collision checking and thereby increase the performance. Experimental results in an industrial application show that lazy evaluation on a grid is very efficient in practice. The algorithm is particularly useful in high dimensional, relatively uncluttered configuration spaces, especially when collision checking is computationally expensive. Single queries are handled quickly since no preprocessing is required.

Describes an approach to probabilistic roadmap planners (PRMs). The overall theme of the algorithm, called Lazy PRM, is to minimize the number of collision checks performed during planning and hence minimize the running time of the planner. Our algorithm builds a roadmap in the configuration space, whose nodes are the user-defined initial and goal configurations and a number of randomly generated nodes. Neighboring nodes are connected by edges representing paths between the nodes. In contrast with PRMs, our planner initially assumes that all nodes and edges in the roadmap are collision-free, and searches the roadmap at hand for a shortest path between the initial and the goal node. The nodes and edges along the path are then checked for collision. If a collision with the obstacles occurs, the corresponding nodes and edges are removed from the roadmap. Our planner either finds a new shortest path, or first updates the roadmap with new nodes and edges, and then searches for a shortest path. The above process is repeated until a collision-free path is returned. Lazy PRM is tailored to efficiently answer single planning queries, but can also be used for multiple queries. Experimental results presented in the paper show that our lazy method is very efficient in practice.