# A Robust Localization, Slip Estimation, and Compensation System for WMR in the Indoor Environments

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## Abstract

**:**

## 1. Introduction

## 2. Basic Theory and Background Knowledge

#### 2.1. Bayes Filter

#### 2.1.1. Prediction

#### 2.1.2. Process Updating

#### 2.2. Sequential Monte Carlo Estimation (Particle Filters)

#### 2.3. Sequential Importance Sampling (SIS)

## 3. DecaWave-Based RTLS

#### 3.1. Wheeled Mobile Robot

#### 3.1.1. Differential Steering

#### 3.1.2. Ackermann Steering

#### 3.2. Simulation Environment

## 4. Results and Discussion

#### 4.1. Distance Noise Effect on PF Performance

#### 4.2. Angular Noise Effect on PF Localization Performance

#### 4.3. WMR Heading Estimation with RL

#### DQN Parameters

#### 4.4. Location-based Heading Estimation (LHE)

#### 4.5. RL and LHE Heading Estimation in Large Dimensions

#### 4.6. Location-Based Slip Estimation and Compensation

## 5. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**(

**a1**) Real-Time Location System (RTLS) with fixed two dimensional infrastructure, and localization of a tag (${T}_{1}$) with three fixed anchors (${A}_{1},{A}_{2}$, and ${A}_{3}$). (

**a2**) Wheeled mobile robot (WMR) with the differential steering system; (

**b**–

**e**) shows a sample data from the RTLS experiments.

**Figure 2.**Y-axis shows an average error in particle filter estimated position (PFEP) induced by the distance noise, while X-axis shows noise added in distance between moving object and the nearest landmark.

**Figure 3.**White square surrounded by the gray squares is $Object2$; arrows represent the eight possible actions in a state for moving to the next state, and the dark-blue square is $Object1$ that needs to be tracked.

**Figure 4.**(

**a**) (${X}_{r}$, ${Y}_{r}$) is a random point from a 30 cm${}^{2}$ region, (${X}_{m}$, ${Y}_{m}$) is the current weighted mean of the particle filter (PF), and [0–7] is the output of Deep Q-Network (DQN). (

**b**) Y-axis shows number of steps (NOS) in a single episode, while X-axis shows number of episodes (NOE).

**Figure 5.**The red lines show moving-object real position (MORP), while the green line shows the particle filter estimated position (PFEP) when there was (

**a**) 0°, and (

**b**) $0.1$° of noise added to the angle of the moving object at each motion step. (

**c**) The red line shows MORP, while the green line shows the PFEP when reinforcement learning (RL) was used to estimate the heading from MORP with noise added to it, as well as PFEP. (

**d**) The red line shows the exponential error growth because of cumulative angular error, the green line shows the RL angular error mitigation, and the blue line shows error in PFEP when there was 0° of error in the moving object angle.

**Figure 6.**Red circle shows moving object’s noisy position, blue circle shows the current weighted mean of the particle filter (PF), and arrows show the direction of moving object relative to the current weighted mean of the PF.

**Figure 7.**(

**a**) A comparative picture of moving object’s real position (MORP) and particle filter estimated position (PFEP). (

**b**) Cumulative angular noise versus distance. (

**c**) A clear picture of MORP with noise and PFEP. A zoomed-in portion of (

**c**) is shown in (

**d**). (

**e**) The noise added in MORP, a zoomed-in a portion of which is shown in (

**f**).

**Figure 8.**Black lines show original path followed by a wheeled mobile robot (WMR); green lines show the particle filter (PF) location estimation. (

**a**,

**a1**) Zero angular noise. (

**b**,

**c**) Green lines show PF location estimation of the paths followed by WMR in the presence of cumulative angular noise. (

**d1**,

**e1**) Shows PF location estimation of the paths in (

**d**,

**e**) followed by WMR through the application of reinforcement learning (RL) and Location-based Heading Estimation (LHE) in the presence of angular noise.

**Figure 9.**(

**a**) Green line is the particle filter (PF) location estimation of the wheeled mobile robot (WMR), and red line shows the desired path. (

**b**) The X-axis is similar to the X-axis of (

**a**); ${X}_{error}$ and ${Y}_{error}$ are the WMR’s slip from the desired path along X- and Y-axes, respectively. The red line shows the absolute value of the angle the WMR should move with to return back along the desired path.

**Table 1.**Comparison of distance and angular noise effects on particle filter (PF) performance. PF performance enhancement using Reinforcement Learning (RL) and a Location-based Heading Estimation (LHE) for angular noise mitigation.

Angular Noise (°) | Distance Noise (cm) | |||
---|---|---|---|---|

Noise (°) | Average Error (cm) | Noise (cm) | Average Error (cm) | |

Without noise | 0 | 9.93 | 5 | 4.23 |

With noise | 0.1–54.6 | 108.34 | 10 | 4.13 |

RL mitigation | 0.1–54.6 | 9.78 | 15 | 5.85 |

LHE mitigation | 0.1–60.4 | 14.99 | 20 | 5.70 |

25 | 5.73 |

**Table 2.**Methods and approaches adopted for vehicle sideslip angle (VSA) estimation. SMO: sliding-mode observer; KF: Kalman filter; EKF extended Kalman filter; CS: current sensing; IS: inertial sensors; RL & LHE: reinforcement learning & Location-based Heading Estimation.

Method | Method details | Robustness | Model |
---|---|---|---|

KF | Simple to be implemented, only those sensor’s output can be used, that results in Gaussian form output. It can be applied to systems with know initial state. Can only be applied to linear problems. | Low against changes of parameters | Kinematic |

EKF | It is simple to be implemented, stable, and able to deal with nonlinear input and measurement noise. The high computational effort required in the definition of the Jacobian matrices suffer from the intrinsic linearization errors. | High against input and measurement noise. | Dynamic—linear or non-linear |

IS | VSA estimated by fusing data from IS and GPS. It typically suffers from accumulated error, not good for indoor because of GPS signal weak coverage. | High robustness against changes of conditions, but low against measurement noise. | Kinematic |

SMO | VSA estimated using this observer in its linear or non-linear form, according to the type of vehicle model adopted. SMO features a faster convergence speed than EKF because it does not need to deal with massive matrix computation. | High robustness to model uncertainty and system noise | Dynamic—both linear and non-linear |

CS | Estimates wheel slippage from motor current. Works only in the direction of motion, but not laterally, and it requires some knowledge of the terrain. | High against changes in parameters | Kinematic |

RL+LHE | Simple to implement, robust, stable, deal with input and measurement noise, suitable for both indoor and outdoor. Independent of the number of WMR’s Wheels and shape. Not suffer from accumulated error. | High robustness to model uncertainty and system noise. | Both linear and non-linear |

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## Share and Cite

**MDPI and ACS Style**

Ullah, Z.; Xu, Z.; Lei, Z.; Zhang, L.
A Robust Localization, Slip Estimation, and Compensation System for WMR in the Indoor Environments. *Symmetry* **2018**, *10*, 149.
https://doi.org/10.3390/sym10050149

**AMA Style**

Ullah Z, Xu Z, Lei Z, Zhang L.
A Robust Localization, Slip Estimation, and Compensation System for WMR in the Indoor Environments. *Symmetry*. 2018; 10(5):149.
https://doi.org/10.3390/sym10050149

**Chicago/Turabian Style**

Ullah, Zakir, Zhiwei Xu, Zhang Lei, and Libo Zhang.
2018. "A Robust Localization, Slip Estimation, and Compensation System for WMR in the Indoor Environments" *Symmetry* 10, no. 5: 149.
https://doi.org/10.3390/sym10050149