Vol.:(0123456789) 1 3 Intelligent Service Robotics https://doi.org/10.1007/s11370-019-00275-w ORIGINAL RESEARCH PAPER A mixed integer programming (MIP) model for evaluating navigation and task planning of human–robot interactions (HRI) Mehmet Burak Şenol 1 Received: 14 May 2018 / Accepted: 25 February 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019 Abstract Exercise of robotics in many applications brings in concerns of human–robot interaction. This paper ofers a mathemati- cal model-based mission planning tool for optimizing operator workload and platform utilization in human/multi-robot (H/M-R) teams. None of the earlier methods consistently predicts fan-out (number and confguration of robots that can be operated simultaneously and efectively, a critical H/M-R design decision). In this research, a mixed integer programming (MIP) model and solution framework are proposed to provide better estimates of fan-out while explicitly considering the performance, mission characteristics, objective and task/environment complexity. The extent of each robot’s waiting time is restricted by a utilization threshold in the MIP model. The efect of environment’s complexity on the task efectiveness is considered, where robots’ performances deteriorate during switch and neglect times. Simulation results show that fan-out efect is dependent on interaction efciency, neglect tolerance, as well as other parameters. Performance is most sensitive to environment’s complexity and least sensitive to utilization threshold. In addition, the MIP model reveals optimal control sequence of robots to prevent switching confusions and maximize team performance. Empirical evaluations show that this approach holds great promise for real-world scenarios. Keywords Fan-out · Human–robot interaction (HRI) · Robot efectiveness · Mixed integer programming (MIP) · Optimization · Optimal control sequence · Ergonomics 1 Introduction Robotic applications are prevalent in areas such as defense, security, exploration plus search and rescue. The growing use of robots in complex environments entails motivation for improving the efciency of human/multi-robot (H/M-R) teams. This paper suggests an optimization model related to H/M-R interaction and teaming for quantifying team performance. The modeling approach considers the robots’ autonomous capabilities, task/environment complexity and efectiveness. The output is an H/M-R team policy whether a particular confguration is likely to be feasible. Results show that H/M-R team performance depends not only on autonomy, but also on complexity; however, in actuality, it is most sensitive to the complexity. The similarity in between results and realistic applications reveals the stability and potential of the model for real-world applications. The concurrent existence of robotic research technolo- gies and development programs is growing in many felds. The exercise of robotics in many applications brings with it, concerns of human–robot interaction (HRI). Although these concerns are unique to particular applications, several prin- ciples and issues of HRI surpass situational circumstances in which robotic assets are employed. Automation systems and robotics are also increasingly important in industrial set- tings, e.g., service and inspection robots in manufacturing, assembly lines [1], mineral processing [2], wet stations [3], robotic arms in industry as well as other applications such as educational and therapeutic applications [4], mapping [5] plus the search and rescue robots. But the collaboration between humans and robots is a must since fully robotic sys- tems cannot obtain sufcient fexibility with highly variable interaction scenarios which are strongly situation dependent and extremely dynamic with varying levels of autonomy [6, 7]. Furthermore, the emergent use of unmanned systems in a military capability brings about issues of re-evaluating * Mehmet Burak Şenol mburaksenol@gazi.edu.tr 1 Department of Industrial Engineering, Gazi Universiy, Maltepe, Ankara, Turkey