Mapping Walls of Indoor Environment using RGB-D Sensor

TL;DR

This paper presents a real-time method for inferring indoor wall configurations using a moving RGB-D sensor, aiding robots in environment understanding without relying on Manhattan assumptions.

Contribution

The paper introduces a fast, online wall detection approach from RGB-D data that does not depend on Manhattan World assumptions, enabling better robot navigation.

Findings

Achieved accurate wall detection in real-time

Demonstrated effectiveness on MIT Stata Center Dataset

Method operates efficiently without Manhattan assumptions

Abstract

Inferring walls configuration of indoor environment could help robot "understand" the environment better. This allows the robot to execute a task that involves inter-room navigation, such as picking an object in the kitchen. In this paper, we present a method to inferring walls configuration from a moving RGB-D sensor. Our goal is to combine a simple wall configuration model and fast wall detection method in order to get a system that works online, is real-time, and does not need a Manhattan World assumption. We tested our preliminary work, i.e. wall detection and measurement from moving RGB-D sensor, with MIT Stata Center Dataset. The performance of our method is reported in terms of accuracy and speed of execution.

Tables

Table 1. TABLE I: Softwares and hardwares used in experiments

Soft/Hardwares	Specifications
Dataset	MIT Stata Center Dataset
Processor	Intel i5-3330 3GHz processor
RAM	16GB
Pointclouds library	pcl
Software framework	ROS

Equations

$$\mathbf{h}=\left[\begin{array}{c}{u}^{\prime }\\ v^{\prime }\\ 1\end{array}\right]=\left[\begin{array}{ccc}c(\theta )& s(\theta )& -xc(\theta )-ys(\theta )\\ -s(\theta )& c(\theta )& xs(\theta )-yc(\theta )\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]$$

$${\mathbf{h}}^{-1}=\left[\begin{array}{c}u\\ v\\ 1\end{array}\right]=\left[\begin{array}{ccc}c(\theta )& -s(\theta )& x\\ s(\theta )& c(\theta )& y\\ 0& 0& 1\end{array}\right]\left[\begin{array}{c}{u}^{\prime }\\ v^{\prime }\\ 1\end{array}\right]$$

$$\mathbf{H}=\left[\begin{array}{cc}c(\theta )& s(\theta )\\ -s(\theta )& c(\theta )\end{array}\right]$$

$$u$$

$$v$$

$$p({\mathbf{w}}_{1:M}|{\mathbf{x}}_{1:t},{\mathbf{z}}_{1:t})$$

$$p({\mathbf{w}}_{1:M}|{\mathbf{x}}_{1:t},{\mathbf{z}}_{1:t})=\prod _{i=1}^{M}p({\mathbf{w}}_i|{\mathbf{x}}_{1:t},{\mathbf{z}}_{1:t})$$

$${\mathbf{w}}_i$$

$${\Sigma }_{\mathbf{w}}$$

$$\mathbf{K}={\Sigma }_{\mathbf{w}}{\mathbf{H}}^T(\mathbf{R}+\mathbf{H}{\Sigma }_{\mathbf{w}}{\mathbf{H}}^T{)}^{-1}$$

$$L$$

$$\propto \exp (-0.5\times (\mathbf{z}-\mathbf{h}{)}^T{\Sigma }_{\mathbf{w}}^{-1}(\mathbf{z}-\mathbf{h}))$$

Full text

I Introduction

A mobile robot that operates in indoor environment, (e.g., a service robot), needs a high-level map to help the robot executing a task, e.g., picking up an object in the kitchen. Providing such a map before operation might be impractical because the map should be changed whenever the robot is placed in other environments.

Simultaneous localization and mapping (SLAM) is a set of methods to mapping unknown environment from unknown robot’s poses. While SLAM releases the robot from the need of a prior map, most of SLAMs only provide robot with the capability of creating a low-level map, e.g., occupancy grid map or feature map.

Producing high-level map within SLAM framework means intregating method such as object detection and recognition into the incremental map building step. This is shown in works such as [1] [2] [3] [4] [5] [6]. This approach is example of how semantic helps SLAM, [7].

Other approach is just the reverse, i.e., SLAM helps semantic, [7]. Here, SLAM construcs a low-level map which in turn supplied to object detection and recognition module to building a high-level (semantic) map.

In this work, we present an approach to building a high-level map of indoor environment from RGB-D sensor. Specifically, we build a map of indoor structure, i.e., walls configuration within a floor of a building. This kind of map helps robot to navigating itself from room to room within the building.

The following section describes works most related to ours. Next to it, we show approaches we took followed by experiment results. Finally, this paper ends by conclusions and some works we like to pursue in the future.

II Related Works

In computer vision community, indoor scene understanding usually means extracting objects and boundaries of a room from a single image, [8] [9] [10], or several images, [11]. On the contrary, in robotics, sensors are keep in motion. While this gives robot more informations about the surrounding, it sets a limit of time to processng those informations. Therefore, in robotics, the “understanding” never goes into finer details. The followings are several works on walls configuration reconstruction with moving sensors.

Within GTSAM framework, [3] uses door signs and walls as landmarks in SLAM. Door-signs are detected by a SVM-based classifier upon Histogram of Oriented Gradient (HOG) features. Walls are extracted from laser data using RANSAC. It is important to note that the SLAM works offline, i.e., it works after all observations data available. This is understandable regarding the SLAM works only with small number of landmarks (i.e., walls and door-signs) which is insufficient to make GTSAM framework works accurately online.

[12] creates a model of a local indoor environment (i.e., walls configuration) by generating a set of hypotheses of walls perpendicular to a known ground-plane. Each hypothesis is evaluated using observation of several points from frame to frame basis given known camera poses. EKF is then used to estimate posterior of each hypothesis.

[13] uses SLAM to generating sparse 3D point cloud and camera pose estimate. A large number of planes (considered as walls, floors, or ceilings) are generated and scored its fitness by RANSAC. Random combinations of available set of planes are then scored by particle-filter based inference engine. The highest-scored combination are likely the correct estimate of the walls configuration.

[14] uses walls configuration as a help to preventing SLAM reobserved landmarks which are occluded by walls whenever the robot move outside a room. This work reconstructs walls configuration by relying on vanishing point detection on several images taken from several robot’s poses. These vanishing points are then projected into 3D world to estimating planes normals. 3D point clouds from SLAM are then aligned to these normals. Space is then equally divided parallel to this normals. The furthest spaces in opposite directions (with number of points above a threshold) are set as walls configuration.

Our work is aimed at combining model of walls configuration as in [12] and the simple wall detection method as in [3]. The goals are

to drop box-shaped assumption (as in [14]), 2. 2.

online (not as in [3]), and 3. 3.

real-time (not just near real-time as in [13])

III Methods

Our target is to building a system that can map walls and objects in indoor environment from moving RGB-D sensor. The overall system is shown in Fig. 1. In this paper, we only present wall detector and mapping part of the system. As for SLAM, we used gmapping [15] although our system should be agnostic of any kind of SLAM implementation since we only need sensor pose estimation from it.

III-A Wall and Sensor Model

We model a wall by a 2D line i.e., line on the ground-plane. Further, we assume walls are perpendicular to ground-plane. Wall is parameterized by its closest point to origin, $\mathbf{w}=(u,v)$. (Fig. 2).

We use the same line parameterization both in observation space and in state space. Therefore, sensor model works like point translation/rotation in 2D space $(c=\cos,s=\sin)$:

[TABLE]

where $(x,y,\theta)$ is robot’s pose from where the wall is observed.

The inverse sensor model is

[TABLE]

Jacobian of sensor model w.r.t walls state space is

[TABLE]

III-B Wall Detector

To detect walls ($\mathcal{L}$) from RGB-D Sensor, we use line fitting (RANSAC) on a specific row in point cloud data ($\mathcal{P}$). We choose it to be a row in upper part of the point cloud to avoid occlusion by objects. wall_detector() is shown in Algorithm 1.

RANSAC returns wall in parameter $m$ and $c$. It is straightforward to change it to point closest to origin.

[TABLE]

III-C Mapping Wall with EKF

Our goal is to calculating probability density function of walls given observations ($\mathbf{z}_{1:t}$) and robot’s poses ($\mathbf{x}_{1:t}$):

[TABLE]

From Dynamic Bayesian Network (Fig. 3) and using concept of conditional independence, Equation 5 could be factored as

[TABLE]

It means we could calculate the posterior of landmarks from product of posteriors for individual landmark.

Within Recursive Bayesian Framework, with the Gaussian assumption of posterior ($\mathbf{w}\sim\mathcal{N}(\mathbf{\bar{w}},\Sigma_{\mathbf{w}})$), each individual landmark could be estimated using Extended Kalman Filter.

[TABLE]

with $\mathbf{K}$ is Kalman Gain

[TABLE]

$\mathbf{R}$ is covariance of measurement noise.

III-D Data Association

We use maximum likelihood to find whether a given observation is coming from the already observed wall. The likelihood function is defined

[TABLE]

Because there are a small number of walls in environment, we use exhaustive search to do data association. A sensor observes a new wall whenever the maximum likelihood falls below a certain threshold.

IV Experiments

We use ROS package of grid mapping as an underlying SLAM system. We tested our system in MIT Stata Center Dataset [16].

MIT Stata Center Dataset is a very challenging dataset because it consists of indoor environment with irregular shape of rooms. There are numerous rooms without clear boundaries and walls with large windows (Fig. 4). This frequently makes wall detector fail to detect walls. Furthermore, the room sometimes have a large dimension which makes RGB-D sensor fail to reach the furthest side of its wall. This gives rather scarce wall detection rate as seen in Fig. 11 and Fig. 12.

Our wall detection method is simple but it has acceptable detection performance. Fig. 7 shows detection performance of our method. Fig. 5 and Fig. 6 shows result of wall detector algorithm to two frames in dataset.

Other critical component in our system is data association. Although we used exhaustive search, the number of walls never grows very large. Fig. 8 shows performance of the method.

In EKF-based SLAM, updating the covariance matrix would be the most time consuming process. Here, our EKF is in small and constant dimension. It does not depend on the number of landmarks (Fig. 9).

Overall, Fig. 10 show the execution time of our method plotted in timesteps. This excludes time consumed by gmapping as underlying component of our method. For the mapping result, it is shown in Fig. 11.

In our experiments, we use software and hardware as listed in Table I.

V Conclusion and Future Work

We seek to building a method to mapping walls in indoor environment which

has a simple model to represents walls configuration 2. 2.

has the capability of working online 3. 3.

has no assumption about the shape of the room

In this paper, we showed our preliminary work on wall detector from moving RGB-D sensor and showed the performance in terms of speed of execution.

Our future works would be to improve the accuracy of wall detection and implementing model of walls configurations. Further, we seek to develop a method to also map objects in environment.