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Real-world autonomous systems often employ probabilistic predictive models ofhuman behavior during planning to reason about their future motion. Sinceaccurately modeling human behavior a priori is challenging, such models areoften parameterized, enabling the robot to adapt predictions based onobservations by maintaining a distribution over the model parameters. Althoughthis enables data and priors to improve the human model, observation models aredifficult to specify and priors may be incorrect, leading to erroneous statepredictions 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 andpriors, but can still leverage human behavioral data online to reduceconservatism in a safe way. To do this, we cast human motion prediction as aHamilton-Jacobi reachability problem in the joint state space of the human andthe belief over the model parameters. We construct a new continuous-timedynamical system, where the inputs are the observations of human behavior, andthe dynamics include how the belief over the model parameters change. Theresults of this reachability computation enable us to both analyze the effectof incorrect priors on future predictions in continuous state and time, as wellas to make predictions of the human state in the future. We compare ourapproach to the worst-case forward reachable set and a stochastic predictorwhich uses Bayesian inference and produces full future state distributions. Ourcomparisons in simulation and in hardware demonstrate how our framework canenable robust planning while not being overly conservative, even when the humanmodel is inaccurate.

A Hamilton-Jacobi Reachability-Based Framework for Predicting and Analyzing Human Motion for Safe Planning