  This paper deals with motion planning for multiple agents by representing the
problem as a simultaneous optimization of every agent's trajectory. Each
trajectory is considered as a sample from a one-dimensional continuous-time
Gaussian process (GP) generated by a linear time-varying stochastic
differential equation driven by white noise. By formulating the planning
problem as probabilistic inference on a factor graph, the structure of the
pertaining GP can be exploited to find the solution efficiently using numerical
optimization. In contrast to planning each agent's trajectory individually,
where only the current poses of other agents are taken into account, we propose
simultaneous planning of multiple trajectories that works in a predictive
manner. It takes into account the information about each agent's whereabouts at
every future time instant, since full trajectories of each agent are found
jointly during a single optimization procedure. We compare the proposed method
to an individual trajectory planning approach, demonstrating significant
improvement in both success rate and computational efficiency.
