Real-time nonparametric reactive navigation of mobile robots in dynamic environments

Highlights

• A motion controller using for autonomous navigation in a dynamic environment is proposed.

• Limited sensing capabilities of a robot are effectively handled using the proposed motion model.

• An efficient method to approximate the learning curve of Gaussian process regression is proposed.

Abstract

In this paper, we propose a nonparametric motion controller using Gaussian process regression for autonomous navigation in a dynamic environment. Particularly, we focus on its applicability to low-cost mobile robot platforms with low-performance processors. The proposed motion controller predicts future trajectories of pedestrians using the partially-observable egocentric view of a robot and controls a robot using both observed and predicted trajectories. Furthermore, a hierarchical motion controller is proposed by dividing the controller into multiple sub-controllers using a mixture-of-experts framework to further alleviate the computational cost. We also derive an efficient method to approximate the upper bound of the learning curve of Gaussian process regression, which can be used to determine the required number of training samples for the desired performance. The performance of the proposed method is extensively evaluated in simulations and validated experimentally using a Pioneer 3DX mobile robot with two Microsoft Kinect sensors. In particular, the proposed baseline and hierarchical motion controllers show over $65\text{\%}$ and $51\text{\%}$ improvements over a reactive planner and predictive vector field histogram, respectively, in terms of the collision rate.

Introduction

The use of robots has been extending steadily from structured industrial factories to unstructured and cluttered daily living spaces. To reflect this trend, numerous navigation algorithms for dynamic environments have been studied [1], [2], [3], [4], [5], [6], [7]. While motion planning in a static environment can be done relatively easily using existing algorithms, such as sampling-based path planning or model predictive control, not all methods are applicable for more realistic dynamic environment. One important reason behind this discrepancy is that most of the algorithms assume structured environments, e.g., positions and dynamics of moving obstacles are assumed to be given beforehand. Moreover, considering the real-time constraint of navigation algorithms, computationally heavy methods such as sampling-based or optimization-based methods are often intractable for low-cost mobile robots. On the other hand, reactive control algorithms, such as the potential field method [4], dynamic window approach (DWA) [8], and vector field histogram (VFH) [9], [10], are computationally efficient, and thus, suitable for real-time navigation applications. However, these methods are vulnerable to noises and changes in dynamic environments as they only consider current measurements.

In this paper, we propose a nonparametric motion controller suitable for low-cost mobile robots operating in a dynamic environment to overcome issues, such as structured environments assumption and heavy computational loads. The proposed motion model predicts future positions of objects using an autoregressive Gaussian process motion model to overcome the limitations of the partially-observable view of a robot. In particular, the future position of an object is predicted given three previous consecutive positions. The prediction performance of the proposed motion model is shown to be more robust against measurement noises compared to existing linear model approaches, e.g., a constant velocity or acceleration model, often used in practice. The proposed motion controller using Gaussian process regression learns how to act from exhaustive offline simulations (training phase) using a receding time horizon control and achieves the state-of-the-art navigation performance in real-time in the test phase. Moreover, in order to further reduce the computational complexity, the motion controller is divided into multiple sub-controllers using a mixture-of-experts framework for a mixture of Gaussian processes. The overall control process takes less than $4\mathrm{ms}$ making it suitable for low-cost or embedded processors. An efficient method of approximating the upper bound of the generalization error of Gaussian process regression, which is known as a learning curve [11], is also proposed. Using this learning curve, we can efficiently determine the required number of training samples for a desirable level of performance of the proposed algorithm.

A preliminary version of this work appeared in [7]. The current work extends [7] by incorporating a learning method using Hamiltonian Monte Carlo, and introducing a hierarchical Gaussian process motion controller using mixture-of-experts framework to further reduce the computational complexity and an approximation to the learning curve of Gaussian process regression for estimating a required number of training samples for the desired accuracy of the proposed motion model and motion controller. A more extensive set of experiments is also included in the current work.

The remainder of this paper is organized as follows. In Section 2, related work is discussed. In Section 3, Gaussian processes and a mixture of Gaussian processes are described. The proposed motion model and motion controller are described in Sections 4 Autoregressive Gaussian process motion model, 5 Nonparametric Bayesian motion controller, respectively. The performance of the proposed algorithm is extensively validated both in simulations and real-world experiments. The results are shown in Sections 6 Simulation, 7 Experiments.