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This work addresses the problem of predicting the motion trajectories ofdynamic objects in the environment. Recent advances in predicting motionpatterns often rely on machine learning techniques to extrapolate motionpatterns from observed trajectories, with no mechanism to directly incorporateknown rules. We propose a novel framework, which combines probabilisticlearning and constrained trajectory optimisation. The learning component of ourframework provides a distribution over future motion trajectories conditionedon observed past coordinates. This distribution is then used as a prior to aconstrained optimisation problem which enforces chance constraints on thetrajectory distribution. This results in constraint-compliant trajectorydistributions which closely resemble the prior. In particular, we focus ourinvestigation on collision constraints, such that extrapolated futuretrajectory distributions conform to the environment structure. We empiricallydemonstrate on real-world and simulated datasets the ability of our frameworkto learn complex probabilistic motion trajectories for motion data, whiledirectly enforcing constraints to improve generalisability, producing morerobust and higher quality trajectory distributions.

Probabilistic Trajectory Prediction with Structural Constraints