  Real-world autonomous systems often employ probabilistic predictive models of
human behavior during planning to reason about their future motion. Since
accurately modeling human behavior a priori is challenging, such models are
often parameterized, enabling the robot to adapt predictions based on
observations by maintaining a distribution over the model parameters. Although
this enables data and priors to improve the human model, observation models are
difficult to specify and priors may be incorrect, leading to erroneous state
predictions that can degrade the safety of the robot motion plan. In this work,
we seek to design a predictor which is more robust to misspecified models and
priors, but can still leverage human behavioral data online to reduce
conservatism in a safe way. To do this, we cast human motion prediction as a
Hamilton-Jacobi reachability problem in the joint state space of the human and
the belief over the model parameters. We construct a new continuous-time
dynamical system, where the inputs are the observations of human behavior, and
the dynamics include how the belief over the model parameters change. The
results of this reachability computation enable us to both analyze the effect
of incorrect priors on future predictions in continuous state and time, as well
as to make predictions of the human state in the future. We compare our
approach to the worst-case forward reachable set and a stochastic predictor
which uses Bayesian inference and produces full future state distributions. Our
comparisons in simulation and in hardware demonstrate how our framework can
enable robust planning while not being overly conservative, even when the human
model is inaccurate.
