  Continued great efforts have been dedicated towards high-quality trajectory
generation based on optimization methods, however, most of them do not suitably
and effectively consider the situation with moving obstacles; and more
particularly, the future position of these moving obstacles in the presence of
uncertainty within some possible prescribed prediction horizon. To cater to
this rather major shortcoming, this work shows how a variational Bayesian
Gaussian mixture model (vBGMM) framework can be employed to predict the future
trajectory of moving obstacles; and then with this methodology, a trajectory
generation framework is proposed which will efficiently and effectively address
trajectory generation in the presence of moving obstacles, and also
incorporating presence of uncertainty within a prediction horizon. In this
work, the full predictive conditional probability density function (PDF) with
mean and covariance is obtained, and thus a future trajectory with uncertainty
is formulated as a collision region represented by a confidence ellipsoid. To
avoid the collision region, chance constraints are imposed to restrict the
collision probability, and subsequently a nonlinear MPC problem is constructed
with these chance constraints. It is shown that the proposed approach is able
to predict the future position of the moving obstacles effectively; and thus
based on the environmental information of the probabilistic prediction, it is
also shown that the timing of collision avoidance can be earlier than the
method without prediction. The tracking error and distance to obstacles of the
trajectory with prediction are smaller compared with the method without
prediction.
