Title: Continuous-Time Gaussian Process Motion Planning via Probabilistic Inference,
Abstract: We introduce a novel formulation of motion planning, for continuous-time
trajectories, as probabilistic inference. We first show how smooth
continuous-time trajectories can be represented by a small number of states
using sparse Gaussian process (GP) models. We next develop an efficient
gradient-based optimization algorithm that exploits this sparsity and GP
interpolation. We call this algorithm the Gaussian Process Motion Planner
(GPMP). We then detail how motion planning problems can be formulated as
probabilistic inference on a factor graph. This forms the basis for GPMP2, a
very efficient algorithm that combines GP representations of trajectories with
fast, structure-exploiting inference via numerical optimization. Finally, we
extend GPMP2 to an incremental algorithm, iGPMP2, that can efficiently replan
when conditions change. We benchmark our algorithms against several
sampling-based and trajectory optimization-based motion planning algorithms on
planning problems in multiple environments. Our evaluation reveals that GPMP2
is several times faster than previous algorithms while retaining robustness. We
also benchmark iGPMP2 on replanning problems, and show that it can find
successful solutions in a fraction of the time required by GPMP2 to replan from
scratch.