  This work addresses the problem of predicting the motion trajectories of
dynamic objects in the environment. Recent advances in predicting motion
patterns often rely on machine learning techniques to extrapolate motion
patterns from observed trajectories, with no mechanism to directly incorporate
known rules. We propose a novel framework, which combines probabilistic
learning and constrained trajectory optimisation. The learning component of our
framework provides a distribution over future motion trajectories conditioned
on observed past coordinates. This distribution is then used as a prior to a
constrained optimisation problem which enforces chance constraints on the
trajectory distribution. This results in constraint-compliant trajectory
distributions which closely resemble the prior. In particular, we focus our
investigation on collision constraints, such that extrapolated future
trajectory distributions conform to the environment structure. We empirically
demonstrate on real-world and simulated datasets the ability of our framework
to learn complex probabilistic motion trajectories for motion data, while
directly enforcing constraints to improve generalisability, producing more
robust and higher quality trajectory distributions.

Robotics;Machine Learning