+ Bharath Gopalakrishnan1 + Arun Singh2 + K. Madhava Krishna1 + Dinesh Manocha3 +
++ 1 IIIT Hyderabad + 2 TUT, AUT, Finland + 3 University of Maryland +
++In this paper, we present a computationally efficient +algorithm for solving a class of chance constrained optimization +under non-parametric uncertainty. Our algorithm is built on the +possibility of representing arbitrary distributions as functions +in Reproducing Kernel Hilbert Space (RKHS). We use this +foundation to formulate chance constrained optimization as one +of minimizing the distance between a desired distribution and the +distribution of the constraint functions in the RKHS. We provide +a systematic way of constructing the desired distribution based +on the notion of scenario approximation. Furthermore, we use the +kernel trick to show that the computational complexity of our +reformulated optimization problem is comparable to solving a +deterministic variant of the chance constrained optimization. We +validate our formulation on two important robotic applications: +(i) reactive collision avoidance of mobile robots in uncertain +dynamic environments and (ii) inverse dynamics based path +tracking of manipulators under perception uncertainty. In both +these applications, the underlying chance constraints are defined +over non-linear and non-convex functions of the uncertain pa- +rameters and possibly also decision variables. We also benchmark +our formulation with the existing approaches in terms of sample +complexity and the achieved optimal cost highlighting significant +improvements in both these metrics. +
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