Control theoretic models of pointing

Jörg Müller, Antti Oulasvirta, Roderick Murray-Smith

Research output: Contribution to journalArticleScientificpeer-review

46 Citations (Scopus)
381 Downloads (Pure)


This article presents an empirical comparison of four models from manual control theory on their ability to model targeting behaviour by human users using a mouse: McRuer's Crossover, Costello's Surge, secondorder lag (2OL), and the Bang-bang model. Such dynamic models are generative, estimating not only movement time, but also pointer position, velocity, and acceleration on a moment-to-moment basis. We describe an experimental framework for acquiring pointing actions and automatically fitting the parameters of mathematical models to the empirical data.We present the use of time-series, phase space, and Hooke plot visualisations of the experimental data, to gain insight into human pointing dynamics. We find that the identified control models can generate a range of dynamic behaviours that captures aspects of human pointing behaviour to varying degrees. Conditions with a low index of difficulty (ID) showed poorer fit because their unconstrained nature leads naturally to more behavioural variability. We report on characteristics of human surge behaviour (the initial, ballistic sub-movement) in pointing, as well as differences in a number of controller performance measures, including overshoot, settling time, peak time, and rise time. We describe trade-offs among the models. We conclude that control theory offers a promising complement to Fitts' law based approaches in HCI, with models providing representations and predictions of human pointing dynamics, which can improve our understanding of pointing and inform design.

Original languageEnglish
Article number27
Number of pages36
JournalACM Transactions on Computer-Human Interaction
Issue number4
Publication statusPublished - 1 Aug 2017
MoE publication typeA1 Journal article-refereed


  • Aimed movements
  • Control theory
  • Dynamics
  • Fitts' law
  • Modelling
  • Pointing
  • Targeting


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