# A Stackelberg Trust-Based Human-Robot Collaboration Framework for Warehouse Picking
## 5 Experiment
### Human Trust and Evaluation  
This subsection focuses on exploring and quantifying the dynamics of human trust in robots under different scenarios. To achieve this goal, the states in the POSG model were meticulously designed. Specifically, task types were categorized into normal tasks and complex tasks \(\tau_{t}=\big{\{}\tau_{ntrm},\tau_{cpx}\big{\}}\). The normal tasks \(\tau_{ntrm}\) are less challenging, and robots typically achieve high accuracy in completing them. In contrast, complex tasks \(\tau_{cpx}\) are more difficult, and robots demonstrate lower accuracy when handling them. In addition to considering whether the robot executes the task, human behavior was also incorporated into the analysis. These three factors generated six distinct scenarios, which will be explained in detail later.  
To evaluate the impact of these scenarios on human trust, the trust value was set within a range of 1-7, which is inspired by the 7-point Likert scale. This scale, commonly used in psychology, is a questionnaire-based metric that captures varying degrees of human psychological attitudes toward other entities. In this study, it represents the degree of human trust in robots. The dynamic changes in trust were modeled using the linear Gaussian system, where the mean is controlled by parameters \(\alpha_{s}\) and \(\beta_{s}\). Parameter \(\alpha_{s}\) represents the relationship between trust change and initial trust, with larger deviations from the standard indicating more significant trust changes at higher trust levels. Parameter \(\beta_{s}\) adjusts trust change for smaller trust values, exerting greater influence at lower trust levels. The standard deviation \(\sigma_{s}\) controls the uncertainty of trust changes, with higher values indicating broader trust variations and increased uncertainty. The parameters of the linear Gaussian system are referenced from previous studies on human-robot trust, with the data sourced from surveys [20].  
The changes in human trust are represented as a trust transition matrix, as shown in Figure 7. The horizontal axis represents the initial trust value, while the vertical axis represents the updated trust value. Each element of the matrix indicates the probability of trust transitioning from one state to another. The shade of color in different matrix cells indicates the corresponding transition probabilities, with darker colors representing higher probabilities. Additionally, red line segments are used to denote the expected values of trust transitions.  
Furthermore, we implemented the belief space approach described in Section 4.2 within the program. We constructed the belief space and defined the belief update function according to Equation (3). This update mechanism was integrated into the POSG state transition process to enable dynamic belief updates. Additionally, we established the robot's trust evaluation of humans based on Equation (5), with its variations represented by the red line in Figure 7. The experimental results demonstrate that the proposed POSG model effectively models human trust. It also enables real-time robot trust assessment through the Bayesian posterior-based belief space.