# A Succinct Control Theory Derivation and New Experiments with the Square-Root Variant of Fitts' Law for Heterogeneous Targets

### Siamak Faridani

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/EECS-2013-39

May 1, 2013

### http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-39.pdf

In this work, we present a succinct derivation for the Square-Root model based on an explicit model from optimal control theory. Our derivation is intuitive and exact, makes fewer assumptions, and requires far fewer steps than the two-submovement derivation presented in Meyer et al. To compare the Square-Root model with statistical significance, we performed two extensive experiments with homogeneous and heterogeneous targets that appear in sequence on a plane. Later, we extend the two-parameter model to a more accurate three-parameter that increases the accuracy of the model over the two-parameter formulation. The succinct and intuitive derivation and new experimental results may enhance the appeal of the Square-Root model for design of systems and interfaces with heterogeneous targets.

**Advisor:** Ken Goldberg

BibTeX citation:

@mastersthesis{Faridani:EECS-2013-39, Author = {Faridani, Siamak}, Title = {A Succinct Control Theory Derivation and New Experiments with the Square-Root Variant of Fitts' Law for Heterogeneous Targets}, School = {EECS Department, University of California, Berkeley}, Year = {2013}, Month = {May}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-39.html}, Number = {UCB/EECS-2013-39}, Abstract = {In this work, we present a succinct derivation for the Square-Root model based on an explicit model from optimal control theory. Our derivation is intuitive and exact, makes fewer assumptions, and requires far fewer steps than the two-submovement derivation presented in Meyer et al. To compare the Square-Root model with statistical significance, we performed two extensive experiments with homogeneous and heterogeneous targets that appear in sequence on a plane. Later, we extend the two-parameter model to a more accurate three-parameter that increases the accuracy of the model over the two-parameter formulation. The succinct and intuitive derivation and new experimental results may enhance the appeal of the Square-Root model for design of systems and interfaces with heterogeneous targets.} }

EndNote citation:

%0 Thesis %A Faridani, Siamak %T A Succinct Control Theory Derivation and New Experiments with the Square-Root Variant of Fitts' Law for Heterogeneous Targets %I EECS Department, University of California, Berkeley %D 2013 %8 May 1 %@ UCB/EECS-2013-39 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/2013/EECS-2013-39.html %F Faridani:EECS-2013-39