In recent years, the integration of robot technology into various domains such as healthcare, domestic services, and industrial inspection has highlighted the need for advanced navigation systems. Traditional path planning methods often focus solely on obstacle avoidance, but in dynamic human environments, they fail to account for social behaviors and comfort, leading to inefficient and intrusive interactions. To address this, we propose a pedestrian openness comfort model that enhances robot technology by incorporating dynamic social features. This model leverages asymmetric Gaussian functions, head pose orientation, and arm openness to better predict pedestrian intentions and optimize path planning. By improving the understanding of human-robot interactions, our approach ensures smoother, more natural navigation in crowded settings.
The core of our model lies in extending traditional symmetric Gaussian representations to asymmetric ones, which more accurately capture the dynamic nature of pedestrian comfort spaces. Traditional models, such as the symmetric Gaussian function, represent pedestrian influence as a static field, but they overlook individual variations like gaze direction and arm positions. In contrast, our model integrates these factors to dynamically adjust the comfort space. For instance, the head pose orientation provides insights into a pedestrian’s focus, while arm openness indicates social engagement or personal space boundaries. This allows robots in robot technology applications to anticipate movements and avoid disruptions, enhancing both efficiency and social acceptability.
To formalize this, we define the pedestrian openness comfort model using an asymmetric Gaussian function. The function is divided into four quadrants—front, back, left, and right—based on the pedestrian’s orientation. The variance in each direction is adjusted according to the pedestrian’s velocity, head pose, and arm openness. The general form of the asymmetric Gaussian function is given by:
$$f(x, y) = \begin{cases}
A_f \cdot \exp\left(-\frac{(d \cos \alpha)^2}{2\sigma_f^2} – \frac{(d \sin \alpha)^2}{2\sigma_f^2}\right) & \text{for } \alpha \in [0, \frac{\pi}{2}) \\
A_b \cdot \exp\left(-\frac{(d \cos \alpha)^2}{2\sigma_b^2} – \frac{(d \sin \alpha)^2}{2\sigma_b^2}\right) & \text{for } \alpha \in [\frac{\pi}{2}, \pi) \\
A_l \cdot \exp\left(-\frac{(d \cos \alpha)^2}{2\sigma_l^2} – \frac{(d \sin \alpha)^2}{2\sigma_l^2}\right) & \text{for } \alpha \in [-\frac{\pi}{2}, 0) \\
A_r \cdot \exp\left(-\frac{(d \cos \alpha)^2}{2\sigma_r^2} – \frac{(d \sin \alpha)^2}{2\sigma_r^2}\right) & \text{for } \alpha \in [-\pi, -\frac{\pi}{2})
\end{cases}$$
where \( A \) represents the amplitude, \( \sigma_f, \sigma_b, \sigma_l, \sigma_r \) are the standard deviations for the front, back, left, and right directions, respectively, \( d \) is the Euclidean distance from the pedestrian, and \( \alpha \) is the angle derived from the head pose orientation \( \theta_w \) or movement direction \( \theta_v \). The variances are dynamically computed as:
$$\sigma_f = \sigma \cdot k_f \cdot \left( \frac{v}{1 + v} \right), \quad \sigma_b = \sigma \cdot k_b \cdot \left( \frac{1}{1 + v} \right), \quad \sigma_l = \sigma \cdot k_l \cdot \left( 1 + \text{OpennessL} \right), \quad \sigma_r = \sigma \cdot k_r \cdot \left( 1 + \text{OpennessR} \right)$$
Here, \( v \) is the pedestrian’s velocity, \( \sigma \) is the initial comfort space size, and \( k_f, k_b, k_l, k_r \) are scaling coefficients. The arm openness metrics, OpennessL and OpennessR, are calculated based on joint positions from the shoulders and wrists, providing a measure of how much space the pedestrian occupies laterally. This formulation allows the robot technology system to adapt in real-time to changing social contexts.
In our experiments, we compared the proposed pedestrian openness comfort model with existing approaches, such as the personal comfort distance model, which relies on symmetric Gaussian functions. We conducted simulations and real-world tests using a differential drive robot equipped with sensors like Kinect V2 and Velodyne-16 LiDAR. The path planning integrated the Dynamic Window Approach (DWA) and A* algorithms for optimization. The results demonstrated that our model significantly reduces motion time and improves path smoothness by avoiding intrusive paths into pedestrian groups.
For simulation, we used MATLAB to create scenarios with static and dynamic pedestrians. In one scenario, a robot navigated through a corridor with pedestrians exhibiting various behaviors, such as discussing in groups or carrying items. The table below summarizes the key results from two simulation scenarios, highlighting the advantages of our model in terms of motion time, iterations, path length, and safety distance.
| Scenario | Model | Motion Time (s) | Iterations | Path Length (m) | Safety Distance (m) |
|---|---|---|---|---|---|
| Scenario 1 | Personal Comfort Distance | 31.68 | 182 | 44.36 | 1.35 |
| Scenario 1 | Pedestrian Openness Comfort | 30.53 | 175 | 43.61 | 1.57 |
| Scenario 2 | Personal Comfort Distance | 142.34 | 531 | 90.08 | 1.96 |
| Scenario 2 | Pedestrian Openness Comfort | 139.92 | 522 | 91.83 | 2.59 |
As shown, the pedestrian openness comfort model reduced motion time by 1.15 seconds in Scenario 1 and 2.42 seconds in Scenario 2, while maintaining a larger safety distance. This indicates better social compliance and efficiency. In real-world tests, we deployed the robot in environments with interacting pedestrians, such as groups discussing or individuals moving toward points of interest. The robot using our model successfully avoided disrupting social interactions by predicting intentions through head pose and arm openness, whereas the traditional model often cut through groups, causing discomfort.
The real-world experiments involved three scenarios: one with a pedestrian attracted to a display, another with a group discussion, and a third with two pedestrians walking side-by-side. The results, summarized in the following table, confirm the practical benefits of our model in robot technology applications, with consistent reductions in motion time and improved navigation fluency.
| Scenario | Model | Motion Time (s) |
|---|---|---|
| Scenario 1 | Personal Comfort Distance | 21.26 |
| Scenario 1 | Pedestrian Openness Comfort | 20.12 |
| Scenario 2 | Personal Comfort Distance | 23.58 |
| Scenario 2 | Pedestrian Openness Comfort | 21.28 |
| Scenario 3 | Personal Comfort Distance | 20.56 |
| Scenario 3 | Pedestrian Openness Comfort | 20.44 |
In conclusion, the pedestrian openness comfort model represents a significant advancement in robot technology for social navigation. By incorporating multi-modal features like head pose and arm openness, it enables robots to better understand and respect human social spaces, leading to more efficient and friendly interactions. Future work could integrate additional sensor data to further enhance the model’s adaptability in diverse environments. This approach not only improves path planning but also fosters greater acceptance of robots in human-centric settings, pushing the boundaries of what robot technology can achieve in daily life.
The mathematical foundation of our model ensures that it can be seamlessly integrated into existing robot technology frameworks. For example, the asymmetric Gaussian function can be combined with cost maps in navigation stacks, allowing robots to dynamically adjust their paths based on real-time pedestrian data. This flexibility is crucial for applications in crowded areas, where robot technology must balance efficiency with social norms. Moreover, the use of head pose estimation and arm openness metrics provides a scalable way to handle complex group dynamics, which are often challenging for traditional models.
Another key aspect is the computational efficiency of our model. By leveraging probabilistic representations, it minimizes the need for extensive computations, making it suitable for real-time applications in robot technology. The variances in the Gaussian function are updated continuously based on pedestrian states, ensuring that the robot responds promptly to changes. This is particularly important in dynamic environments where delays can lead to collisions or social disruptions. Our experiments validated that the model maintains low iteration counts and short motion times, underscoring its practicality.
Overall, the integration of social features into path planning marks a paradigm shift in robot technology. As robots become more prevalent in shared spaces, models like ours will play a vital role in ensuring harmonious human-robot coexistence. The continued evolution of such approaches will undoubtedly expand the capabilities of robot technology, enabling more intelligent and empathetic autonomous systems.