  We present a planning framework for minimising the deterministic worst-case
error in sparse Gaussian process (GP) regression. We first derive a universal
worst-case error bound for sparse GP regression with bounded noise using
interpolation theory on reproducing kernel Hilbert spaces (RKHSs). By
exploiting the conditional independence (CI) assumption central to sparse GP
regression, we show that the worst-case error minimisation can be achieved by
solving a posterior entropy minimisation problem. In turn, the posterior
entropy minimisation problem is solved using a Gaussian belief space planning
algorithm. We corroborate the proposed worst-case error bound in a simple 1D
example, and test the planning framework in simulation for a 2D vehicle in a
complex flow field. Our results demonstrate that the proposed posterior entropy
minimisation approach is effective in minimising deterministic error, and
outperforms the conventional measurement entropy maximisation formulation when
the inducing points are fixed.
