Xinyan Yan

Gaussian Process Motion planning

Motion planning is a fundamental tool in robotics, used to generate collision-free, smooth, trajectories, while satisfying task-dependent constraints. In this paper, we present a novel approach to motion planning using Gaussian processes. In contrast to most existing trajectory optimization algorithms, which rely on a discrete state parameterization in practice, we represent the continuous-time trajectory as a sample from a Gaussian process (GP) generated by a linear time-varying stochastic differential equation. We then provide a gradient-based optimization technique that optimizes continuous-time trajectories with respect to a cost functional. By exploiting GP interpolation, we develop the Gaussian Process Motion Planner (GPMP), that finds optimal trajectories parameterized by a small number of states. We benchmark our algorithm against recent trajectory optimization algorithms by solving 7-DOF robotic arm planning problems in simulation and validate our approach on a real 7-DOF WAM arm.

Incremental sparse GP regression for continuous-time trajectory estimation and mapping

Recent work on simultaneous trajectory estimation and mapping (STEAM) for mobile robots has used Gaussian processes (GPs) to efficiently represent the robots trajectory through its environment. GPs have several advantages over discrete-time trajectory representations: they can represent a continuous-time trajectory, elegantly handle asynchronous and sparse measurements, and allow the robot to query the trajectory to recover its estimated position at any time of interest. A major drawback of the GP approach to STEAM is that it is formulated as a batch trajectory estimation problem. In this paper we provide the critical extensions necessary to transform the existing GP-based batch algorithm for STEAM into an extremely efficient incremental algorithm. In particular, we are able to vastly speed up the solution time through efficient variable reordering and incremental sparse updates, which we believe will greatly increase the practicality of Gaussian process methods for robot mapping and localization. Finally, we demonstrate the approach and its advantages on both synthetic and real datasets. An incremental sparse GP regression algorithm for STEAM problems is proposed.The benefits of GP-based approaches and incremental smoothing are combined.The approach elegantly handles asynchronous and sparse measurements.Results indicate significant speed-up in performance with little loss in accuracy.

Approximately optimal continuous-time motion planning and control via Probabilistic Inference

The problem of optimal motion planing and control is fundamental in robotics. However, this problem is intractable for continuous-time stochastic systems in general and the solution is difficult to approximate if non-instantaneous nonlinear performance indices are present. In this work, we provide an efficient algorithm, PIPC (Probabilistic Inference for Planning and Control), that yields approximately optimal policies with arbitrary higher-order nonlinear performance indices. Using probabilistic inference and a Gaussian process representation of trajectories, PIPC exploits the underlying sparsity of the problem such that its complexity scales linearly in the number of nonlinear factors. We demonstrate the capabilities of our algorithm in a receding horizon setting with multiple systems in simulation.