Fan-Out Measure (Human-Robot Interaction)

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A Fan-Out Measure (Human-Robot Interaction) is a supervision capacity measure of the number of robots that one human operator can effectively operate at once.

  • AKA: Fan-Out.
  • Context:
    • It can typically be measured as a performance plateau, the number of robots beyond which adding another does not improve task effectiveness.
    • It can typically be defined as the reciprocal of the robot attention demand: FO = 1 / RAD = (IE + NT) / IE, where IE is interaction effort and NT is neglect tolerance.
    • It can typically be modeled by the fan-out equation FO = AT / IT, a robot's activity time divided by its interaction time.
    • It can typically increase as neglect tolerance grows relative to interaction effort.
    • ...
    • It can often be measured as the average number of robots operating above an effectiveness threshold when the operator is given more robots than they can use.
    • It can often plateau through task saturation, as when a task has fewer targets than there are robots.
    • It can often be overestimated by models that rely on neglect time, which mixes the robot's ability to operate alone with the operator's estimate of that ability.
    • ...
    • It can range from being a potential fan-out, an upper bound set by the robot's ability, to being an achieved fan-out, which also depends on the human operator.
    • ...
    • It can be used, with measured activity time, to compute the interaction effort of a human-robot interface design.
    • It can rest on independence assumptions about the robots and their tasks when used to predict team performance.
    • ...
  • Example(s):
    • the fan-out of a simulated search team of robots, measured to validate the fan-out equation (Olsen & Wood, 2004).
    • a fan-out of one for driving a car, whose very short neglect time means a person cannot drive more than one car at once.
    • the high fan-out of manufacturing robots, which run for days or months after a day of setup (Olsen & Wood, 2004).
    • ...
  • Counter-Example(s):
    • a Robot Attention Demand Measure, which is the fraction of an operator's time one robot consumes rather than the number of robots one operator can run.
    • a software fan-out count, which is the number of modules a software module calls.
    • a span of control, which is the number of subordinates one manager supervises.
  • See: Neglect Tolerance (Human-Robot Interaction), Robot Attention Demand Measure, Human-Robot Interaction Task, Agent Autonomy Measure, Attention Expenditure Measure.

References

2025

  • (Perkins et al., 2025) ⇒ Lawrence Dale Perkins, Matthew Johnson, Hakkı Erhan Sevil, and Michael A. Goodrich. (2025). “Fan-Out Revisited: The Impact of the Human Element on Scalability of Human Multi-Robot Teams.” In: Proceedings of the 2025 IEEE International Conference on Robotics and Automation (ICRA).
    • ABSTRACT: ... Previous research indicates fan-out is often overestimated. This work explains why robot ability provides an upper bound to fan-out, but that actual achieved fan-out is influenced by both the human and robot abilities. We conduct a study to validate this new model and show improved performance over the two most common fan-out models. The results show that both previous models overestimate as predicted. ...

2005

  • (Crandall et al., 2005) ⇒ Jacob W. Crandall, Michael A. Goodrich, Dan R. Olsen, and Curtis W. Nielsen. (2005). “Validating Human-Robot Interaction Schemes in Multitasking Environments.” In: IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 35(4).
    • ABSTRACT: ... We use neglect tolerance to 1) identify the maximum number of robots that can be managed; 2) identify feasible configurations of multirobot teams; and 3) predict performance of multirobot teams under certain independence assumptions. ...

2004

  • (Olsen & Wood, 2004) ⇒ Dan R. Olsen, and Stephen Bart Wood. (2004). “Fan-out: Measuring Human Control of Multiple Robots.” In: Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (CHI 2004).
    • ABSTRACT: A goal of human-robot interaction is to allow one user to operate multiple robots simultaneously. In such a scenario the robots provide leverage to the user’s attention. The number of such robots that can be operated is called the fan-out of a human-robot team. Robots that have high neglect tolerance and lower interaction time will achieve higher fan-out. We define an equation that relates fan-out to a robot’s activity time and its interaction time. We describe how to measure activity time and fan-out. We then use the fan-out equation to compute interaction effort. ...
    • QUOTE: ... the robot will run for days or months after a day of setup. Thus AT is many times larger than IT and the fan-out is quite high. ...
    • QUOTE: ... neglect time for a car is very small, therefore AT is not much larger than IT. Plugging this into the fan-out equation we see that a person cannot drive more than one car at once. ...

2003

  • (Olsen & Goodrich, 2003) ⇒ Dan R. Olsen, and Michael A. Goodrich. (2003). “Metrics for Evaluating Human-Robot Interactions.” In: Proceedings of the Performance Metrics for Intelligent Systems Workshop (PERMIS 2003).
    • QUOTE: ... Fan-out is an estimate of the number of robots that a user and [sic] effectively operate at once. The fan-out metric is defined in terms of RAD as [equation: FO = 1.0 / RAD = (IE + NT) / IE]. From the FO equation we see that FO increases as neglect tolerance becomes large relative to interaction effort. ... There are two ways of measuring fan-out that yield similar results, but on different scales. The first approach measures the performance plateau. ... A second approach to measuring fan-out is the average robot activity. In this approach, the user is given more robots than they can realistically use. ...
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