## 1 Introduction  
The use of industrial robots in manufacturing industry is increasing rapidly [1], and industrial robot-monitoring systems (IRMS) have played an important role in maintaining the normal operation of industrial robots and even the whole factory, most of the IRMSs are based on B/S or C/S architecture remote monitoring by the Internet [2]. With the development of IoT and cloud computing technology, IRMSs based on cloud computing architecture have emerged. For example, [PERSON] et al. [3] implemented a cloud manufacturing monitoring platform based on 5G and SIM (Standard Information Model), [PERSON] et al. [4] implemented a cloud monitoring industrial arm robot based on MQTT protocol. In addition, cloud robotics has become an emerging area of robotics research [5], where the technological key is computational offloading, when the controlroller generates compute-intensive tasks to the cloud in order to reduce the requirements for controller performance and the computational energy consumption of the robot. However, since the robot cannot rely excessively on cloud resources due to its physical bandwidth limitation, computational offloading strategies for cloud robots have become a hot research topic. For example, [PERSON] [6], [PERSON] [7], and [PERSON] [8] offload computationally intensive tasks such as robot grasping, simultaneous localization and mapping (SLAM), and navigation of cloud robots to the cloud. In fact, most tasks in IRMSs, such as fault diagnosis, environmental monitoring, object recognition, and posture awareness, require IRMSs to continuously collect and process large amounts of environmental data in real time to maintain the accuracy of monitoring results; however, the collected data, especially internal and external sensor data, are semi-structured and unstructured [9], with high information redundancy and low value density, if all of them are offloaded to the cloud computing will occupy a large amount of communication bandwidth, and the congestion of data channels may also lead to an increase in latency, then the benefits brought by cloud computing will be greatly reduced. In this context, edge computing [10] as an emerging computing architecture, can place some computing tasks on edge servers close to the devices rather than in distant cloud centers, which can effectively reduce the pressure on the communication bandwidth and reduce the communication latency. In this paper, IRMS is targeted at monitoring fixed-position multi-degree-of-freedom industrial robots which can perform tasks such as handling, palletizing, painting, assembly and welding, and common faulty units include bearings, gearboxes, and motors [11]. cloud-based architecture IRMSs are combined with cloud robotics and edge computing architecture. Edge computing resources can be considered to be an effective complement to cloud resources, reducing both the computational burden of the local monitor and the communication network burden of using cloud computing. The monitor can obtain real-time operation data of a set of industrial robots through internal and external sensors, process the monitoring data and obtain the corresponding monitoring results by executing workflow-based monitoring computation tasks. The monitor can obtain real-time monitoring data of a set of industrial robots through internal and external sensors, process the monitoring data and obtain the corresponding monitoring results by executing workflow-based monitoring computation tasks. To solve the computing resource allocation problem of monitoring workflows, a bi-objective optimization problem of time and monetary cost is modeled, and it can be solved by the proposed genetic algorithm. In experiments on this work, optimal solution of the two optimization objectives obtained by mixed integer quadratic programming (MIQP) technique are used a reference for comparison.