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Summary: IEEE TRANSACTIONS ON ROBOTICS, VOL. 24, NO. 1, FEBRUARY 2008 211
Proximity Queries Between Convex Objects:
An Interior Point Approach for Implicit Surfaces
Nilanjan Chakraborty, Student Member, IEEE, Jufeng Peng, Srinivas Akella, Member, IEEE, and John E. Mitchell
Abstract--This paper presents a general method for exact dis-
tance computation between convex objects represented as intersec-
tions of implicit surfaces. Exact distance computation algorithms
are particularly important for applications involving objects that
make intermittent contact, such as in dynamic simulations and in
haptic interactions. They can also be used in the narrow phase
of hierarchical collision detection. In contrast to geometric ap-
proaches developed for polyhedral objects, we formulate the dis-
tance computation problem as a convex optimization problem. We
use an interior point method to solve the optimization problem
and demonstrate that, for general convex objects represented as
implicit surfaces, interior point approaches are globally conver-
gent, and fast in practice. Further, they provide polynomial-time
guarantees for implicit surface objects when the implicit surfaces
have self-concordant barrier functions. We use a primal-dual inte-
rior point algorithm that solves the KarushKuhnTucker (KKT)
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