Formulation and Structure of the SLAM problem
The trajectories of the robot as well as the locations of the landmarks are estimated without prior knowledge, this allows for the robot to be placed in an unknown environment. Figure 11: Simultaneous estimate of both robot and landmark association [35]
Figure 10 shows a robot moving through an environment, observing landmarks with a sensor. One can see that the robots estimated location is not its exact location (Clear triangle), and the same for the landmarks, this is obvious as these locations are estimates and need to be corrected as much as possible over time. At a time instant k, the following variables are defined [35], [36]: xk: State vector which contain the location and orientation …show more content…
The map building may be formatted by computing P(m|X_(0:k),X_(0:k,) Z_(0:k,) U_(0:k)) which, for all times k, it is assumed that the location is either known or deterministic. Conversely, the localization of the robot is computed with P(x_k |Z_(0:k,) U_(0:k),m) in which, for all times, k, it is assumed that the landmark locations are known. The landmarks form the basis for estimating the location [35], [36].
Structure of Probabilistic SLAM:
By referring to Figure 10, it is clear that the error in the landmark locations is correlated, and is in fact due to a single source which is the robots estimated location. From this it is observed that the relative locations between two landmarks that may actually be accurately known (mi-mj). Furthermore, this correlation increases monotonically as more and more observations are made (for the linear Gaussian case). This is an important insight to SLAM as this implies that the relative location of landmarks never diverges but rather improves. This can be conceptually seen by observing a point in Figure 10 where two landmarks are observed the same instance in time (m¬j and m¬i,) due to this it is clear that the relative location is independent of the coordinate frame of the
The trajectories of the robot as well as the locations of the landmarks are estimated without prior knowledge, this allows for the robot to be placed in an unknown environment. Figure 11: Simultaneous estimate of both robot and landmark association [35]
Figure 10 shows a robot moving through an environment, observing landmarks with a sensor. One can see that the robots estimated location is not its exact location (Clear triangle), and the same for the landmarks, this is obvious as these locations are estimates and need to be corrected as much as possible over time. At a time instant k, the following variables are defined [35], [36]: xk: State vector which contain the location and orientation …show more content…
The map building may be formatted by computing P(m|X_(0:k),X_(0:k,) Z_(0:k,) U_(0:k)) which, for all times k, it is assumed that the location is either known or deterministic. Conversely, the localization of the robot is computed with P(x_k |Z_(0:k,) U_(0:k),m) in which, for all times, k, it is assumed that the landmark locations are known. The landmarks form the basis for estimating the location [35], [36].
Structure of Probabilistic SLAM:
By referring to Figure 10, it is clear that the error in the landmark locations is correlated, and is in fact due to a single source which is the robots estimated location. From this it is observed that the relative locations between two landmarks that may actually be accurately known (mi-mj). Furthermore, this correlation increases monotonically as more and more observations are made (for the linear Gaussian case). This is an important insight to SLAM as this implies that the relative location of landmarks never diverges but rather improves. This can be conceptually seen by observing a point in Figure 10 where two landmarks are observed the same instance in time (m¬j and m¬i,) due to this it is clear that the relative location is independent of the coordinate frame of the