  We present a novel approach for long-term human trajectory prediction, which
is essential for long-horizon robot planning in human-populated environments.
State-of-the-art human trajectory prediction methods are limited by their focus
on collision avoidance and short-term planning, and their inability to model
complex interactions of humans with the environment. In contrast, our approach
overcomes these limitations by predicting sequences of human interactions with
the environment and using this information to guide trajectory predictions over
a horizon of up to 60s. We leverage Large Language Models (LLMs) to predict
interactions with the environment by conditioning the LLM prediction on rich
contextual information about the scene. This information is given as a 3D
Dynamic Scene Graph that encodes the geometry, semantics, and traversability of
the environment into a hierarchical representation. We then ground these
interaction sequences into multi-modal spatio-temporal distributions over human
positions using a probabilistic approach based on continuous-time Markov
Chains. To evaluate our approach, we introduce a new semi-synthetic dataset of
long-term human trajectories in complex indoor environments, which also
includes annotations of human-object interactions. We show in thorough
experimental evaluations that our approach achieves a 54% lower average
negative log-likelihood (NLL) and a 26.5% lower Best-of-20 displacement error
compared to the best non-privileged baselines for a time horizon of 60s.
