### robotics代写|SLAM定位算法代写Simultaneous Localization and Mapping|Multi-hypothesis Data Association

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## robotics代写|SLAM定位算法代写Simultaneous Localization and Mapping|Multi-hypothesis Data Association

Sampling over robot paths also has an important repercussion for determining the correct data associations. Since each FastSLAM particle represents a specific robot path, the same data association need not be applied to every particle. Data association decisions in FastSLAM can be made on a perparticle basis. Particles that predict the correct data association will tend to receive higher weights and be more likely to be resampled in the future. Particles that pick incorrect data associations will receive low weights and be removed. Sampling over data associations enables FastSLAM to revise past data associations as new evidence becomes available.

This same process also applies to the addition and removal of landmarks. Often, per-particle data association will lead to situations in which the particles build maps with differing numbers of landmarks. While this complicates the issue of computing the most probable map, it allows FastSLAM to remove spurious landmarks when more evidence is accumulated. If an observation leads to the creation a new landmark in a particular particle, but further observations suggest that the observation belonged to an existing landmark, then the particle will receive a low weight. This landmark will be removed from the filter when the improbable particle is not replicated in future resamplings. This process is similar in spirit to the “candidate lists” employed by EKF SLAM algorithms to test the stability of new landmarks $[19,50]$. Unlike candidate lists, however, landmark testing in FastSLAM happens at no extra cost as a result of sampling over data associations.

## robotics代写|SLAM定位算法代写Simultaneous Localization and Mapping|Outline

This book presents an overview of the FastSLAM algorithm. Quantitative experiments will compare the performance of FastSLAM and the EKF on a variety of simulated and real world data sets. In Chapter 2 , we formulate the SLAM problem and describe prior work in the field, concentrating primarily on EKF-based approaches. In Chapter 3, we describe the simplest version of the FastSLAM algorithm given both known and unknown data association. This version, which is called FastSLAM 1.0, is the simplest FastSLAM algorithm to implement and works well in typical SLAM environments. In Chapter 4 , we present an improved version of the FastSLAM algorithm, called FastSLAM $2.0$, that produces better results than the original algorithm. FastSLAM $2.0$ incorporates the current observation into the proposal distribution of the particle filter and consequently produces more accurate results when motion noise is high relative to sensor noise. Chapter 4 also contains a proof of convergence for FastSLAM $2.0$ in linear-Gaussian worlds. In Chapter 5 , we describe a dynamic tracking problem that shares the same structure as the SLAM problem. We will show how a variation of the FastSLAM algorithm can be used to track dynamic objects from an imprecisely localized robot.

## robotics代写|SLAM定位算法代写Simultaneous Localization and Mapping|Problem Definition

Consider a mobile robot moving through an unknown, static environment. The robot executes controls and collects observations of features in the world. Both the controls and the observations are corrupted by noise. Simultaneous Localization and Mapping (SLAM) is the process of recovering a map of the environment and the path of the robot from a set of noisy controls and observations.

If the path of the robot were known with certainty, then mapping would be a straightforward problem. The positions of objects in the robot’s environment could be estimated using independent filters. However, when the path of the robot is unknown, error in the robot’s path correlates errors in the map. As a result, the state of the robot and the map must be estimated simultaneously.
The correlation between robot pose error and map error can be seen graphically in Figure 2.1(a). A robot is moving along the path specified by the dashed line, observing nearby landmarks, drawn as circles. The shaded ellipses represent the uncertainty in the pose of the robot, drawn over time. As a result of control error, the robot’s pose becomes more uncertain as the robot moves. The estimates of the landmark positions are shown as unshaded ellipses. Clearly, as the robot’s pose becomes more uncertain, the uncertainty in the estimated positions of newly observed landmarks also increases.

In Figure 2.1(b), the robot completes the loop and revisits a previously observed landmark. Since the position of this first landmark is known with high accuracy, the uncertainty in the robot’s pose estimate will decrease significantly. This newly discovered information about the robot’s pose increases

the certainty with which past poses of the robot are known as well. This, in turn, reduces the uncertainty of landmarks previously observed by the robot. The reader may notice that the shaded ellipses before the loop closure in Figure $2.1$ (b) do not shrink because they depict a time series of the robot’s pose uncertainty and not revised estimates of the robot’s past poses.

The effect of the observation on all of the landmarks around the loop is a consequence of the correlated nature of the SLAM problem. Errors in the map are correlated through errors in the robot’s path. Any observation that provides information about the pose of the robot, will necessarily provide information about all previously observed landmarks.

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