# A Stackelberg Trust-Based Human-Robot Collaboration Framework for Warehouse Picking
## 5 Experiment  
In this section, we conduct experiments to validate our framework. The experiments are completed on an AMD Ryzen 7 5800H CPU with 3.2 GHz and 40 GB memory. The ISTG algorithm is implemented by Python 3.10.9, and the PRISM version is PRISM 4.7 (GUI model). We take the human-robot collaborative picking process in [38; 39] as the case. It uses robot TORU developed by Magazine GmbH in Zalando for human-robot collaborative picking. Unlike other picking robots that can only transport shelves (such as pallets or crates), the mobile TORU utilizes artificial intelligence and a 3D camera to identify, grab, and transport individual items. Furthermore, TORU robots have already been deployed in parallel with workers in the Zalando warehouse. With laser scanners and 3D sensors, TORU can ensure worker safety within the same workspace. It offers higher efficiency and a lower cost compared to traditional shelf-handling robots. However, it is still limited by technological constraints, particularly the robot's ability to handle picking frames with inaccuracies, such as the need to neatly arrange goods. Workers sometimes need to intervene to check tasks, which reduces workflow efficiency. Our framework effectively enhances this human-robot collaboration with robot TORU. We obtained the TORU datasheet from Magazino and collected related simulation data. These datasets were used to configure the experimental parameters. The corresponding models and properties to be verified can be downloaded from [[https://github.com/[PERSON]/HRC_trust_prism](https://github.com/Gyoung/HRC_trust_prism)]([https://github.com/Gyoung/HRC_trust_prism](https://github.com/Gyoung/HRC_trust_prism)) (accessed on 17 February 2025).  
First, a Partially Observable Stochastic Game (POSG) was developed using Python to simulate uncertainty and decision-making interactions in a human-robot collaborative environment. Within this model, human trust is represented as a linear Gaussian system, with parameters derived from prior works on human-robot trust [20]. To enable a real-time evaluation of human trust by the robot, a Bayesian posterior-based belief space representation was employed. The effectiveness of the proposed trust modeling and evaluation approach is experimentally validated in Section 5.1. Second, we generated human strategies using a sigmoid function based on dynamic trust evolution and constructed three different robot strategy models for comparative analysis. These models include the following: (1) a no-trust model that disregards human trust factors; (2) a single-round trust strategy model that considers human trust but optimizes robot decisions based solely on single-round rewards; and (3) a multi-round trust strategy model incorporating multi-round optimization. This part is completed in Section 5.2. Third, we formalized both human and robot strategies as a Partially Observable Markov Decision Process (POMDP) within the PRISM model checker. The extended reward-based PCTL formula was then used to specify and verify the key properties of human-robot collaborative picking. By comparing the three robot strategy models, we analyzed the advantages of our framework in terms of collaboration efficiency, decision-making rationality, and system stability. This part is completed in Section 5.3.