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.
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