# A Stackelberg Trust-Based Human-Robot Collaboration Framework for Warehouse Picking
## 1 Introduction  
### Motivation  
With the rapid advancement of the internet economy and information technology, e-commerce has experienced explosive growth in recent years, which has also driven the expansion of the logistics industry [1]. The logistics system has also become a key factor restricting the development of e-commerce and related industries [2], in which timeliness and cost are major limiting factors [3]. There are two primary activities in the entire logistics process: warehouse picking and logistics distribution. Recently, distribution efficiency hasimproved significantly and has reached a saturation point. Warehouse picking efficiency plays an important role in the entire logistics process [4]. Traditional warehouse picking systems rely on manual labor. Manual picking offers greater flexibility for handling the diversity of goods and requires lower initial investment costs. It is inefficient and unsuitable for large-scale, long-duration operations [5]. Automated warehouse picking systems, such as the pioneering Amazon Kiva system, have clearly improved the efficiency of warehouse picking [6]. However, the growth of e-commerce has introduced diversification, large-scale operations, and the customization of goods, which adds complexity to logistics [7]. Amazon has also indicated that automated technology cannot completely replace human involvement in the picking process. This is due to current technological limitations and humans' superior cognitive abilities in handling complex tasks [8]. Emerging human-robot collaboration systems for warehouse picking combine the low cost, high efficiency, and flexibility of manual and automated picking, which achieves greater accuracy and efficiency [9], increases flexibility, and reduces downtime [10]. However, there are some communication barriers that undermine the effectiveness of current HRC frameworks. First, asymmetric information persists, as robots follow rigid protocols without adapting to human operators' cognitive states [11]. Second, the trust-calibration dilemma stems from missing mutual trust models. This creates polarized behaviors: workers either distrust robots and manually verify outputs or over-trust automation and skip interventions. Systems exacerbate this by failing to quantify trust through measurable signals like intervention frequency [12]. Effective human-robot collaboration requires the modeling of human cognitive processes and complex social attitudes (e.g., trust, guilt, shame). If robots can detect human biases or excessive trust and accurately predict human behavior, collaboration can be significantly improved [13]. To establish more effective collaboration between workers and picking robots, it is essential for robots to understand the level of workers' trust in them and make decisions accordingly. How does trust influence the operational process in human-robot collaborative picking? Low trust in robots leads workers to excessively intervene in their tasks (e.g., checking product labels), which disrupts the workflow and drastically reduces efficiency. This will also cause workers to accumulate fatigue. Conversely, excessive trust can result, in which workers are unwilling or unable to intervene even if it is necessary. This may also cause workers to overestimate the capabilities of automation and neglect the monitoring of robot performance. For instance, if a robot misidentifies an item and the worker does not double-check it, an incorrect product may be delivered to the customer. Therefore, it is crucial to establish a reasonable trust model between humans and robots to model and evaluate human trust levels. This enables robots to appropriately decide when to execute or relinquish tasks during collaboration. Our proposed framework uses the Stackelberg strategy from game theory. This strategy establishes hierarchical decision-making between two agents. The robot acts as the leader, first optimizing its strategy by predicting how the human worker (follower) will respond optimally.