Towards a Socially Acceptable Collision Avoidance for a Mobile Robot Navigating Among Pedestrians Using a Pedestrian Model

Abstract

Safe navigation is a fundamental capability for robots that move among pedestrians. The traditional approach in robotics to attain such a capability has treated pedestrians as moving obstacles and provides algorithms that assure collision-free motion in the presence of such moving obstacles. In contrast, recent studies have focused on providing the robot not only collision-free motion but also a socially acceptable behavior by planning the robot’s path to maintain a “social distance” from pedestrians and respect their personal space. Such a social behavior is perceived as natural by the pedestrians and thus provides them a comfortable feeling, even if it may be considered a decorative element from a strictly safety oriented perspective. In this work we develop a system that realizes human-like collision avoidance in a mobile robot. In order to achieve this goal, we use a pedestrian model from human science literature, a version of the popular Social Force Model that was specifically designed to reproduce conditions similar to those found in shopping malls and other pedestrians facilities. Our findings show that the proposed system, which we tested in 2-h field trials in a real world environment, not only is perceived as comfortable by pedestrians but also yields safer navigation than traditional collision-free methods, since it better fits the behavior of the other pedestrians in the crowd.

Appendix: Background Work: Collision Prediction Social Force Model

1.1 Model Definition

Models of pedestrian collision-avoidance have been developed since the 50 s to deepen understanding of crowd dynamics and design better facilities. The Social Force Model (SFM) [45] is a popular pedestrian model that describes the behavior of pedestrians in a crowd through reaction forces inspired by physics. More than a single model, SFM may be considered as a framework in which the acceleration of a pedestrian $i$ is given by

$$\begin{aligned} \frac{d{\varvec{v}}_i(t)}{dt}= \frac{{\varvec{v}}_i^0-{\varvec{v}}_i{(t)}}{\tau }+\sum _{j\ne i} {\varvec{f}}_{i,j}(t). \end{aligned}$$

(1)

Here ${\varvec{v}}_i(t)$ is the pedestrian velocity at time $t,\,{\varvec{v}}_i^0$ is the pedestrian’s preferred velocity, a vector directed towards the current pedestrian sub-goal and whose magnitude corresponds to the velocity the pedestrian is more comfortable walking at, while $\tau$ is the relaxation time to recover the preferred velocity ($0.66\; \hbox {s}^{-1}$ in [13]). The actual avoidance behavior is determined by the interaction term with the other pedestrians $j$ in the environment, ${\varvec{f}}_{i,j}$, whose precise form determines the SFM specification. The original Circular Specification (CS) of the model was determined by symmetrical repulsive forces as

$$\begin{aligned} {\varvec{f}}_{i,j}(t)=A e^{-d_{i,j}{(t)}/B} \frac{{\varvec{d}}_{i,j}{(t)}}{d_{i,j}{(t)}}, \end{aligned}$$

(2)

where ${\varvec{d}}_{i,j}$ is the distance between the pedestrians, $A$ is the maximum interaction intensity and $B$ determines how the intensity changes with $d$. The model is popular for its simplicity, and it works well at the high densities that describe the egress conditions it has been developed for [46], but it fails in describing lower density regimes and for this reason a few improved specifications, taking in account relative velocities in the computation of ${\varvec{f}}_{i,j}$, have been proposed [47].

Zanlungo et al. [13] compare a few of these specifications to the CP specification that they propose. This model, that develops on ideas originating from Reynold’s boid model [48], uses the relative velocity between the pedestrians to compute how their “future” distance ${\varvec{d}}'_{i,j}$ will vary with time according to the hypothesis that the pedestrians will keep a constant velocity. The time at which the projected distance $d'_{i,j}$ assumes a minimum value is called the “interaction time” $t_i$ for pedestrian $i$ and the value of the corresponding future distance ${\varvec{d}}'_{i,j}(t_i)$ (see Fig. 11) replaces the current distance in the equation for the CS specification force (2) in order to obtain the CP specification equation

$$\begin{aligned} {\varvec{f}}_{i,j}({\varvec{d}}_{i,j},{\varvec{v}}_{i,j},{\varvec{v}}_i)=A \frac{v_i}{t_i} e^{-d{'}_{i,j}/B} \frac{{\varvec{d}}_{i,j}'(t_i)}{d_{i,j}'(t_i)}. \end{aligned}$$

(3)

Here the term $v_i/t_i$ is introduced to modulate the force in such a way that the pedestrian is able to stop in time $t_i$. According to the analysis of [13], the CP-SFM model outperforms the previous SFM specifications in simulating pedestrian collision avoidance in low and average density multi-person settings, a characteristics that makes this model suitable to robot applications.

Fig. 11

Collision prediction among pedestrians with CP-SFM. ${d}'_{ij}$ is the distance between pedestrians at the time of maximum approach $t_i$

[49] compares the performance of CP to other popular pedestrian methods for egress oriented applications.

1.2 Model Calibration

To calibrate and evaluate the CP-SFM model, [13] uses a set of pedestrian trajectories obtained in a controlled experiment to which eight subjects took part. Each subject was given a start and goal point, and was prescribed to walk as naturally as possible towards the goal. The trajectories of pedestrians were tracked in a square area with an 8 meters side. The start and goal points were decided in such a way that the trajectories of all pedestrians will converge, if walking straight to the goal, at the center of the experimental area, creating a potentially complex collision avoiding problem; but the density of the environment was low enough to allow the pedestrians to freely choose their avoidance strategy. The calibration process used a genetic algorithm to minimize a fitness function that consisted in the average distance between the simulated and actual trajectories of pedestrians plus a penalty term assigned to those trajectories that “collided” between them (more exactly, trajectories that reached a minimum distance smaller than the distance between any pair of actual pedestrians during the experiment). The genetic algorithm used 500 genomes per generation, over 1,000 different generations; tournament selection over a pool of five solutions, crossover and random Gaussian mutation with probability 0.1. The solution was determined through 50 independent runs of the algorithm. The CP-SFM method outperformed all the other specifications with an average position error of $30 \pm 1$ centimeters ($55 \pm 1$ for CS-SFM).