Elsevier

Automatica

Volume 97, November 2018, Pages 161-166
Automatica

Brief paper
Monte Carlo localisation of a mobile robot using a Doppler–Azimuth radar

https://doi.org/10.1016/j.automatica.2018.08.012Get rights and content

Abstract

This paper investigates the moving robot localisation problem using a Doppler–Azimuth radar array. The solution is formulated in the framework of nonlinear/non-Gaussian estimation using a particle filter and a random finite set (RFS) model of measurements. The proposed approach assumes the availability of a feature-based map, radar measurements and robot odometry data. The associations between the measurements and the features of the map (landmarks) are unknown. The RFS model is adopted to deal with false and missed detections and uses Murty’s algorithm to reduce computation when solving the association problem. The proposed particle filter incorporates the Kullback–Leibler Distance (KLD)-Sampling to reduce computational time. Monte-Carlo simulation results demonstrate the efficacy of the proposed algorithm.

Introduction

Successful deployment of a mobile robot requires the ability to localise and orient itself as it moves through an environment. In this paper we consider robotic applications where satellite navigation is not available, such as indoor, underground, undersea or extraterrestrial environments. Furthermore, the sensor available for robot navigation is a Doppler radar. Since frequency measurements can be easily obtained at low cost and with high accuracy, Doppler radars have the advantage over traditional robot navigation sensors: they are cheaper and lighter than LIDAR sensors, and potentially have a greater range than both LIDAR and ultrasound sensors. However, using Doppler shifts for navigation is difficult, because of the poor information content of such measurements.

In the past, Doppler-shift frequencies have been used for the purpose of target localisation and tracking Battistelli et al. (2015), Ristic and Farina (2013), Shames et al. (2013). The problem of robot navigation using Doppler-shift frequencies is novel and very different from target tracking. The robot, equipped with a Doppler radar, has to estimate its own position and heading (also known as the robot pose) using the measured Doppler-shifts. The Doppler-shift on the transmitted radar wave occurs due to the movement of a robot relative to the static features (landmarks) at known locations. The paper builds on our previous work (Guan, Ristic, Wang, Moran, & Evans, 2016). In particular, it relaxes the following assumptions made in Guan et al. (2016): knowledge of the robot’s initial pose distribution, perfect Doppler radar detection and known landmark to measurement associations.

The main feature of the proposed method is that it is based on the particle filter and models the measurements at each scan as random finite sets (Mahler, 2007). A collective term for particle-filter based robot navigation algorithms is Monte Carlo localisation (MCL) Kootstra and De Boer (2009), Liu et al. (2008), Thrun et al. (2001). The novelty of our MCL algorithm is that it is using realistic Doppler radar measurements, characterised by false and missed detections as well as poor accuracy of azimuth measurements. The RFS modelling allows us to formulate robot localisation as a particle filter which can elegantly deal with false and missed radar detections. RFS models have previously been used for feature-based simultaneous localisation and mapping (SLAM) using range-azimuth measurements (Adams, Vo, Mahler, & Mullane, 2014). While in this paper we focus on robot localisation only (i.e. the feature-based map is assumed known), the solution is proposed for less informative measurements of Doppler-shifts and azimuth. The theoretical formulations of a general RFS particle filter can be found in Ristic (2013) and Vo, Singh, and Doucet (2005).

The RFS particle filter that we propose incorporates Murty’s algorithm (Murty, 1968) along with the Kullback–Leibler Distance (KLD)-Sampling algorithm (Fox, 2003) to reduce computational time. The assumptions are that a feature-based map is known and that the robot odometry data are available. In summary, this paper includes the following contributions: (a) application of RFS particle filters to mobile robot localisation on a feature-based map with a Doppler radar; (b) realistic Doppler radar measurements modelled with false and missed-detections and unknown measurement-to-landmark association; (c) incorporation of KLD-Sampling with RFS particle filters.

The remainder of this paper is organised as follows. Section 2 introduces the robot motion model and the sensor measurement model. Section 3 proposes a likelihood function based on RFS modelling, followed by the RFS particle filter with KLD sampling. Numerical simulation studies are presented in Section 4 and conclusions are drawn in Section 5.

Section snippets

Robot motion model

The robot’s pose at discrete-time k is a vector xk=xk,yk,θkT, where (xk,yk) are Cartesian coordinates of robot location and θk is its heading. Let the control input applied from k1 to k be comprised of a translational and rotational velocity and denoted uk=vk,wkT. Robot motion is described by equation (Thrun, Burgard, & Fox, 2006, Ch.7): xk=f(xk1,uk)+ek, where ekN(0(3×1),Qk) is the Gaussian process noise with zero mean and the covariance matrix Qk, and f(xk1,uk) is a three-dimensional

Theoretical framework

Recursive pose estimation can be carried out in the Bayesian framework through the prediction and update steps. Suppose the posterior probability density function (PDF) of pose at time k1 is p(xk1|Z1:k1,u1:k1), where x1:k1x1,x2,,xk1 and so forth. The prediction equation, using uk and the transition density, is given by p(xk|Z1:k1,u1:k)=π(xk|xk1,uk)p(xk1|Z1:k1,u1:k1)dxk1while the update equation, using the measurement set Zk, applies the Bayes rule: p(xk|Z1:k,u1:k)=φ(Zk|xk,m)p(xk|

Numerical results

The top-down view of the scenario used for algorithm evaluation is shownin Fig. 1 (a). The (given) map covers an area of 12m×12 m, and includes M=7 landmarks. The map is specified with m=74513667554303The duration of the scenario is 30 s, with the sampling interval of Δt=1 s. The true initial robot pose is x0=[4m,2m,70π180rad]T; the control vector is constant throughout the duration of the scenario with uk=[0.3,6π180]T, for k=1,2,,30. For matrix Dk in (1), the following parameters

Conclusions

The paper considered Monte Carlo localisation of a moving robot equipped with a Doppler–azimuth radar array and a known map of landmarks. A realistic model of radar detections, including Pd<1, false alarms and unknown detection-to-landmark associations, is applied and formulated using random finite sets. A RFS particle filter for this problem is developed, which combinesKLD-sampling for adaptive number of particles and Murty’salgorithm for selecting the best measurement-to-landmark association

Robin Ping Guan obtained his Masters degree in Electrical Engineering from the University of Melbourne, Australia. He is a PhD candidate in the School of Engineering at RMIT University, Melbourne, Australia. His research work focuses on signal processing, and robotics. He is currently a tutor and laboratory demonstrator in the field of Control Systems at RMIT University, Australia.

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Robin Ping Guan obtained his Masters degree in Electrical Engineering from the University of Melbourne, Australia. He is a PhD candidate in the School of Engineering at RMIT University, Melbourne, Australia. His research work focuses on signal processing, and robotics. He is currently a tutor and laboratory demonstrator in the field of Control Systems at RMIT University, Australia.

Branko Ristic received PhD degree from QUT in 1995. In 1996 he joined the Defence Science and Technology (DST) organisation, where he stayed until 2015. His role in DST was to carry out research, develop new capabilities and provide technical advice to the Australian Defence Organisation on topics of target tracking, multi-sensor fusion and reasoning under uncertainty. During 2003/2004 he spent a year in IRIDIA (Université libre de Bruxelles, Belgium) on a study leave. In 2015 he joined RMIT University as a Principal Research Fellow. Dr Ristic co-authored two books (“Beyond the Kalman filter”, Artech House, 2004 and “Particle filters for Random set models”, Springer, 2013). He published over 80 journal articles, of which seven won best-paper awards. His research interests include statistical signal processing, information fusion, reasoning under uncertainty, sensor control and navigation, with emphasis on defence and security applications.

Liuping Wang received her PhD degree in 1989 from the Department of Automatic Control and Systems Engineering, University of Sheffield, UK. Upon completion of her PhD degree, she worked in the Department of Chemical Engineering at the University of Toronto, Canada for eight years in the field of process control. From 1998 to 2002, she worked in the Center for Integrated Dynamics and Control, University of Newcastle, Australia. In February 2002, she joined the School of Electrical and Computer Engineering, RMIT University, Australia where she is a Professor of Control Engineering. She has authored and co-authored more than 200 scientific papers in the field of system identification, PID control, adaptive control, model predictive control, electrical drive control and control technology application to industrial processes. She co-authored a book with Professor Will Cluett entitled From Process Data to Process Control—Ideas for Process Identification and PID control (Taylor and Francis, 2000). She co-edited two books with Professor Hugues Garnier entitled ‘Continuous time model identification from sampled data’ (Springer-Verlag, 2008) and ‘System identification, environmental modelling and control’ (Springer-Verlag, 2011). Her book entitled ‘Model Predictive Control Design and Implementation using MATLAB ®’ was published by Springer-Verlag in 2009. She is the lead author of the book entitled ‘PID and predictive control of electrical drives and power converters using using MATLAB ®’ published by Wiley-IEEE Press in 2015. She is an associate editor of International Journal of Control, Journal of Process Control and IEEE Transactions on Control System Technologies, and a Fellow of Institute of Engineers Australia.

Rob Evans was born in Melbourne, Australia, in 1947. After completing a BE degree in Electrical Engineering at the University of Melbourne in 1969, he worked as a radar systems engineering officer with the Royal Australian Airforce. He completed his PhD in 1975 at the University of Newcastle followed by postdoctoral studies at the Laboratory for Information and Decision Systems, MIT, USA and the Control and Management Department, Cambridge University, UK.

In 1977 he took up an academic position at the University of Newcastle, where he served as Head of the Department of Electrical and Computer Engineering from 1986 until 1991 and Chief Investigator and Co-Director of the ARC Centre of Excellence on Industrial Control Systems between 1988 and 1991.

In 1992 he moved to the University of Melbourne, where he has served in many roles including Head of the Department of Electrical and Electronic Engineering for the periods 1993–1996 and 2013–2017, Research Leader for the Cooperative Research Centre for Sensor Signal and Information Processing 1992–2000, Director of the DSTO Centre for Networked Decision and Sensor Systems 2001–2004, Director of the Victoria Research Laboratory of National ICT Australia 2004–2012, Executive Dean of Engineering during 2007 and Director of the Defence Sciences Institute 2014–2017. He is currently a Melbourne University Laureate Professor and a Chief Investigator in the ARC Centre of Excellence for Gravity Wave Detection. He served on the IFAC Council from 2002–2008.

His research and industry engagement has ranged across many areas including theory and applications in control systems, industrial electronics, radar systems, signal processing and telecommunications. He is a Fellow of the Australian Academy of Science, a Fellow of the Australian Academy of Technological Sciences and Engineering, a Life Fellow of the Institution of Electrical and Electronic Engineers, and a Fellow of the Institution of Engineers Australia.

The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Tianshi Chen under the direction of Editor Torsten Söderström.

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