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 Gaussian process 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 samplingbased 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.

Abstract-With the increased use of high degree-of-freedom robots that must perform tasks in real-time, there is a need for fast algorithms for motion planning. In this work, we view motion planning from a probabilistic perspective. We consider smooth continuous-time trajectories as samples from a Gaussian process (GP) and formulate the planning problem as probabilistic inference. We use factor graphs and numerical optimization to perform inference quickly, and we show how GP interpolation can further increase the speed of the algorithm. Our framework also allows us to incrementally update the solution of the planning problem to contend with changing conditions. We benchmark our algorithm against several recent trajectory optimization algorithms on planning problems in multiple environments. Our evaluation reveals that our approach is several times faster than previous algorithms while retaining robustness. Finally, we demonstrate the incremental version of our algorithm on replanning problems, and show that it often can find successful solutions in a fraction of the time required to replan from scratch.

We develop a novel policy synthesis algorithm, RMPflow, based on geometrically consistent transformations of Riemannian Motion Policies (RMPs). RMPs are a class of reactive motion policies designed to parameterize non-Euclidean behaviors as dynamical systems in intrinsically nonlinear task spaces. Given a set of RMPs designed for individual tasks, RMPflow can consistently combine these local policies to generate an expressive global policy, while simultaneously exploiting sparse structure for computational efficiency. We study the geometric properties of RMPflow and provide sufficient conditions for stability. Finally, we experimentally demonstrate that accounting for the geometry of task policies can simplify classically difficult problems, such as planning through clutter on high-DOF manipulation systems.