When a robot moves through a dense crowd, it has two options: wait for people to pass and avoid them (passive collision avoidance), or ask nearby people to make room (active path clearing, e.g., by beeping). Neither is good on its own.

Fig. 1: Left: freezing robot problem, where a robot struggles to find a bypass and as a result takes unnecessary maneuvers, ending in a timeout or a collision. Right: our agent interacts with the crowd by actively clearing a path or passively finding a bypass, balancing the safety-efficiency trade-off.

• Only avoiding keeps everyone safe, but in a crowded scene the robot cannot find a gap. It freezes, takes long detours, and eventually times out or collides (Fig. 1, left).
• Always intervening gets the robot through quickly at first, but pushing people around collapses the natural crowd flow. Once the crowd has no room left to give way, everyone, including the robot, is at higher risk of collision.

We view this as a social dilemma between the robot and the crowd, treated as a single virtual crowd agent. Mutual cooperation $R$ is when both sides make reasonable room for each other. Passive avoidance alone leaves the robot with the sucker outcome $S$, and aggressive path clearing gives the robot a short-term temptation payoff $T$ that turns into mutual defection $P$ once the crowd can no longer make room. L2B learns when to clear a path and when to detour, so the robot stays in $R$ (Fig. 1, right).

L2B augments the navigation reward with a term $R_s$ coming from the crowd. Its first part, weighted by $\beta$, penalizes active path clearing when pedestrians are within the beep range $r^{(b)}$, discouraging the move from $R$ to $T$. Its second part, weighted by $\eta$, penalizes getting closer than a discomfort distance, discouraging the move from $R$ to $S$. Setting $\eta > \beta$ makes getting too close worse than clearing a path, so the policy learns to stay in $R$ by using both actions sparingly. The value network is trained with V-learning on top of SARL.

$$R_s(s_t^{jn}, a_t) = \begin{cases} \beta \, (d_t - r^{(b)}) & \text{if } d_t < r^{(b)} \wedge b_t = 1 \\ \eta \, (d_t - d_{\rm disc}) & \text{else if } d_t < d_{\rm disc} \\ 0 & \text{otherwise} \end{cases}$$

To simulate how a crowd reacts to path clearing, pedestrians follow a simplified Emotional Reciprocal Velocity Obstacles (ERVO) model: everyone inside the half-circle of radius $r^{(b)}$ in front of the robot changes direction when it beeps. The simulator is available at Python-ERVO.

Fig. 2: ERVO-based reactive pedestrians. A circle and triangles represent the robot and pedestrians (left). When the robot executes an active path clearing action, all pedestrians within the half-circle of radius r^(b) (right) change their directions.

In circle-crossing scenarios with N pedestrians, L2B-SARL keeps its success rate around 90% as the crowd grows, while the SARL baseline drops to 70.0% at N = 20, mainly because of timeouts.

Success, collision and timeout rates, and average navigation time

Values in parentheses are differences from SARL (percentage points; seconds for Time).

Qualitative results

L2B-SARL (top) clears its path with a few beeps and goes through the crowd, while SARL (bottom) takes long detours around it.

Fig. 3: (a)-(d) L2B-SARL and (e)-(h) SARL for N = 5, 10, 15, 20. Gray points are pedestrians and filled orange circles are the robot. Bigger orange circles are path clearing (beep) actions.

Balancing path clearing

With too small a penalty $\beta$, the robot beeps too often, confusing the crowd and causing collisions. L2B learns to mix path clearing and collision avoidance.