Thanks……. Numerical Example and Verification: "Now, let's dive into a numerical example and verification process. The 1st thing, We considered a GPU assembly process with 12 task sequences, but our focus was on the eight task sequences assigned to humans (H1 to H8). You can see the table 3. These tasks were essential for our HSMM algorithm. The 2nd, We also represented the tasks using hidden state sequences (high risk, moderate risk, low risk) and visible state sequences (fast, moderate, slow) with corresponding durations." Operator Behavior and Risk Perception: Understanding operator behavior and risk perception is crucial in human-robot collaboration. We identified two types of risk perception: rational and irrational. Rational risk perception is based on justifiable reasons, such as being around the reach of the robot trajectory. On the other hand, irrational risk perception is driven by factors like fear, even when the operator is outside the robot's reach. We discussed how risk perception affects assembly rates." So we realized that, the rational risk perception is proportional to the zone of the robot trajectory. However, irrational risk perception still has some probability for those far from the reach region. Let's see the table 4. It talk about the relation ship between risk perception and assembly rate. Whenever the risk perception is high, the operator will have a high probability of a slow assembly rate; conversely, it will have a low probability of a fast assembly rate. On the other hand, when the risk perception is low, the operator will have a high probability of a fast assembly rate; in contrast, it will have a low probability of a slow assembly rate Nếu thuộc có thể bỏ đoạn HSMM Algorithm for HRC: "Now, let's explore the HSMM algorithm and its application in human-robot collaboration. We used a transition matrix with three hidden states (high risk, moderate risk, low risk) and emission probabilities from these hidden states to visible states (Fast-F, Moderate-M, Slow-S). We also considered a scenario where humans and robots work on a workpiece with the possibility of collision, leading to different risk perceptions." So, we have 3 regions: The green region is an autonomous region for humans (low-risk perceptions). The yellow region: the joint region (moderate-risk perceptions) The red reg region: autonomous robotregion (high-risk perceptions) Parameters and Computations: "Moving on, let's discuss the parameters and computations involved in our HSMM algorithm. We tested both discrete and Gaussian emission distributions. In the discrete distribution, all eight tasks were assumed to have the same transition and emission probabilities. Each task had a duration probability matrix, Because The duration probability parameters are estimated based on the maximum possible duration of a specific task compared with the manual operation duration. and the Gaussian emission probability had three separate means. We utilized a Python-based platform for HSMM prediction, ensuring accurate and efficient computations." Computation: "Now, let's delve into the computation process of our HSMM algorithm. We employed a decoding procedure to determine the best-hidden state sequence. Let’s see table 5: In the duration probability matrix for task 1 in a low-risk state, there is a 20 % chance of having a duration equal to 1 and 80 % duration 2. The moderate-risk state had a 100 % chance of a duration of 2. On the other hand, a high-risk state has a 40 % chance of duration two and a 60 % chance of duration three Additionally, we used the expectation-modification algorithm for model inference, adjusting the transition, emission, and duration data to generate an optimal model. This iterative procedure improved the joint probability of hidden and visible state sequences." "Let's take a look at the results of our experiments. We tested both discrete and Gaussian emission distributions. The sample hidden and visible state sequences generated for a 50second time span demonstrated the correlation between risk perception and assembly rates. The discrete distribution has three states: state “0” stands for lowrisk Perception and fast assembly rate; state “1” stands for moderaterisk perception and moderate assembly rate; and state “2” stands for high-risk perception and slow assembly rate. On the other hand, the Gaussian distribution has a separate mean representing the same three states. State “0” “5” “10”. Intuitively, when an operator has a high-risk perception, we assume that he will have a high probability of operating at a low speed. In contrast, when the operator has a low-risk perception, we expect a high probability of a fast operation rate. Thus, the resulting pattern followed by both the Gaussian and discrete distributions goes hand in hand with our intuition, as shown in Fig. 8(a) and (b). The first hidden state starts at “1,” representing medium-risk perception, and the corresponding hidden state is at “0” which indicates a slow assembly rate We observed a strong negative correlation in the Gaussian distribution case, indicating a better fit for our scenario." "In conclusion, our analysis yielded interesting findings regarding operator behavior in the assembly process. Let's summarize the key points." "We observed that operators with a high-risk perception tended to operate at a slower assembly rate, while those with a low-risk perception had a higher probability of operating at a faster rate." "When examining the correlation between hidden and visible state sequences, we found that both the Gaussian and discrete distributions exhibited negative correlations." "However, the Gaussian distribution showed a stronger negative correlation, with a minimum correlation value of σ = -0.92 for all eight tasks. In contrast, the discrete distribution had a maximum correlation value of σ = -0.58, which was lower than the correlation observed in the Gaussian distribution." "Based on these results, we conclude that the Gaussian distribution is more suitable for modeling operator behavior in the assembly process."
