An Iterative Approach for Collision Free Routing and Scheduling in Multirobot Stations

Abstract

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.Note to Practitioners-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 i...

A Time-Space Network Model for Collision-Free Routing of Planar Motions in a Multirobot Station

“…At a higher level, task allocation focuses on optimally dispatching tasks to the available robots [5]- [7]. Routing problems typically determine task sequences and the robot route for performing several tasks to be given [2], [8]. Path planning problems compute more detailed paths in the working space subject to collisionaware constraints or physical constraints on the robot [9].…”

“…In manufacturing systems, a robotic assembly line consists of several stations that are placed serially or in parallel to reach production goals [1]. At each station, multiple robots, often sharing the same workspace, work together to carry out complex operations (e.g., stud, welding or sealing) within a predetermined period [2]. High production rates require optimizing the operation and coordination within multi-robot systems of the assemble station to increase productivity.…”

“…To complete the assigned tasks together, the station operation process needs to be optimized. Yet, optimizing this process is a complicated problem and the related decision problems are divided into several subproblems at different levels: task allocation, routing and path planning [2]. These subproblems are typically regarded as operational scheduling and control problems.…”

Opportunistic Planning in Autonomous Underwater Missions

“…The consequence of this approach is that neither the number of actions in a plan, nor the makespan or resource allocation of the plan, are predetermined. This distinguishes planning from scheduling, where the actions to be performed are predetermined but the timing of actions, and the allocation of resources to them, are not [13]- [15].…”

Routing of a Multi-Robot System Using a Time-Space Network Model

“…In [13], the method of separating task allocation and path coordination is adopted, and decoupling is achieved by determining the priority of the delayed start of the manipulator and modifying the path of the manipulator. The iterative decoupling method is proposed in [14], which is to establish the generalized traveling salesman problem for the assigned task, and solve it repeatedly and iteratively through the objective function with no conflict and optimal time until a reliable solution is obtained. In [15], two methods were proposed for the collision-free path planning of multiple manipulators: the concentrating method and the decoupling method.…”