M6-T6 — Social Navigation

Learning objectives

After this lesson, you should be able to:

• Describe personal space and the zones of proxemics, and why the space is not a circle.
• Explain passing-side conventions and why legible, predictable motion matters.
• Describe the freezing-robot problem and its causes and cures.
• Encode social preferences as costs, speed limits and rules, and say what each cannot do.

The intuition

Between strangers in a hospital corridor there is an unwritten contract. Keep to the right. Do not pass closer than an arm’s length unless you must. Slow down near doors. Do not cut between two people who are talking. A nurse follows it without thinking; a robot that does not looks pushy or, worse, frightening.

The anthropologist Edward Hall named the spaces people keep around themselves, proxemics: roughly an intimate zone up to 0.45 m, a personal zone to 1.2 m, a social zone to 3.6 m and a public zone beyond. The zones are not circles: people tolerate others more easily behind them and to the sides than straight in front, where they want room to see and react. A robot that models space as a symmetric disc gets the distances right on average and wrong where it matters.

The mathematics

Three layers of social behaviour

An asymmetric personal-space cost

One simple model, to illustrate the idea, puts a Gaussian cost around each person, with a spread that depends on the angle φ from the person’s facing direction:

r, φ

distance and bearing of the robot from the person, φ = 0 straight ahead of them.

σ_front, σ_back

spread in front of and behind the person (here 1.2 m and 0.6 m).

A

peak cost (here 200 on the costmap scale of 0 to 254).

Real systems fit these shapes to data or learn them; the exact form matters less than three properties: smooth, larger in front, and a cost rather than a wall.

Passing side and legibility

A convention such as “pass on the right” is a cheap way to coordinate with strangers. It works because everyone can predict it. Kruse and colleagues call this human-aware motion: safe, comfortable and legible, meaning that the person can read the robot’s intent early from its motion. A late, sharp swerve is safe but unreadable. An early, gentle one is both.

The freezing-robot problem

In a crowd, the safe space around every person leaves no path for the robot; a planner that keeps a fixed margin around each person concludes that none exists and stops. Trautman and Krause named this the freezing robot problem and showed that it comes from treating people as obstacles that ignore the robot. People do react: a robot that moves, slowly and predictably, gets room.

• Causes: hard thresholds on social cost, no allowance for the people’s cooperation, high speeds that make everything look dangerous.
• Cures: soft costs with a limit on how much the planner may pay; slower speed near people instead of a refusal; a bounded wait followed by a move forward; models in which the robot expects cooperation.

A worked example

Costs around a nurse. A nurse faces +x. With σ_front = 1.2 m, σ_back = 0.6 m and A = 200:

For φ = 0, σ = 1.2: cost = 200 · exp(−1.5² / (2 · 1.2²)) = 200 · exp(−0.781) = 91.6. Passing behind at 1.5 m costs a tenth of passing in front at the same distance, so a planner reading these numbers prefers to pass behind, the polite choice.

Freezing in a corridor. The corridor is 2.4 m wide. A nurse walks down its centre; Scout, 0.4 m wide, hugs the wall with its centre 0.3 m from it, so the lateral gap between their centres is 1.2 − 0.3 = 0.9 m. The cost at that position is 121, about 60% of the peak. If the planner treats any cost above 100 as forbidden, the gap is closed and Scout stops, though the nurse would be glad to let it pass. With a soft cost the planner accepts the 121 at a low speed. A cap on speed, for example 0.4 m/s within 1.5 m of a person, turns the same cost into a polite pass instead of a refusal.

A rule, not a cost. “Pass on the right” is easier to state as a lane than as a cost: add a one-way preference to the lane graph, with a speed limit of 0.5 m/s in the ward corridors.

Engineering implications and limitations

Detect and track people separately

Social costs apply to people, not to carts. A person detector and a tracker give the position, velocity and facing direction (estimated from motion). Do not apply the social layer to unclassified obstacles.

Cap the price of passing

Let the planner pay a bounded amount for closeness, so that the cost of passing never exceeds the cost of waiting forever. Add a timeout after which the robot asks for help (lesson M7-T6).

Slow first, swerve second

Speed is the cheapest way to make a robot safe and the most visible way to make it polite. Scale the speed limit with the distance to people.

Signal intent

Lights, sounds, a short pause before passing and smooth early motion tell people what the robot will do. In a hospital, take extra care around beds, wheelchairs and patients who cannot step aside.

Test with people

Metrics such as minimum distance miss comfort. Evaluate with staff, and log how often people stop or step aside for the robot (lesson M1-T6).

Common misconceptions

Engineering takeaways

1. Proxemics gives zones around a person; the space is larger in front than behind, so a circle is only a rough model.
2. Encode social behaviour as costs, rules and interaction, each in the layer where it is easiest to test.
3. Predictable, early and gentle motion is more comfortable than a late, sharp swerve.
4. The freezing robot comes from hard thresholds and treating people as non-cooperating obstacles.
5. Soft costs, speed limits near people and bounded waiting turn refusals into polite passes.

References and further reading

Proxemics, the crowd-navigation papers and the surveys.

• E. T. Hall, The Hidden Dimension, Doubleday, 1966.
• D. Helbing and P. Molnár, “Social Force Model for Pedestrian Dynamics”, Physical Review E 51, 1995.
• P. Trautman and A. Krause, “Unfreezing the Robot: Navigation in Dense, Interacting Crowds”, IEEE/RSJ IROS, 2010.
• T. Kruse, A. K. Pandey, R. Alami and A. Kirsch, “Human-Aware Robot Navigation: A Survey”, Robotics and Autonomous Systems 61(12), 2013.
• C. Mavrogiannis et al., “Core Challenges of Social Robot Navigation: A Survey”, ACM Transactions on Human-Robot Interaction 12(3), 2023.

Knowledge check

Three conceptual questions. Write an answer, then reveal the explanation. Your answers stay in your browser.

What’s next

Next: the family of local planners compared, and how to choose between them for a given robot.

Related content

Nothing below is required to finish this lesson.

• Before
  M6-T5: Velocity Obstacles, RVO and ORCA

  Build a velocity obstacle and explain how reciprocal avoidance removes oscillation between two robots.