  We present a path planning framework that takes into account the human's
safety perception in the presence of a flying robot. The framework addresses
two objectives: (i) estimation of the uncertain parameters of the proposed
safety perception model based on test data collected using Virtual Reality (VR)
testbed, and (ii) offline optimal control computation using the estimated
safety perception model. Due to the unknown factors in the human tests data, it
is not suitable to use standard regression techniques that minimize the mean
squared error (MSE). We propose to use a Hidden Markov model (HMM) approach
where human's attention is considered as a hidden state to infer whether the
data samples are relevant to learn the safety perception model. The HMM
approach improved log-likelihood over the standard least squares solution. For
path planning, we use Bernstein polynomials for discretization, as the
resulting path remains within the convex hull of the control points, providing
guarantees for deconfliction with obstacles at low computational cost. An
example of optimal trajectory generation using the learned human model is
presented. The optimal trajectory generated using the proposed model results in
reasonable safety distance from the human. In contrast, the paths generated
using the standard regression model have undesirable shapes due to overfitting.
The example demonstrates that the HMM approach has robustness to the unknown
factors compared to the standard MSE model.
