Warped Gaussian Processes Occupancy Mapping With Uncertain Inputs

Abstract

Abstract-In this paper, we study extensions to the Gaussian Processes (GPs) continuous occupancy mapping problem. There are two classes of occupancy mapping problems that we particularly investigate. The first problem is related to mapping under pose uncertainty and how to propagate pose estimation uncertainty into the map inference. We develop expected kernel and expected sub-map notions to deal with uncertain inputs. In the second problem, we account for the complication of the robot's perception noise using Warped Gaussian Processes (WGPs). This approach allows for non-Gaussian noise in the observation space and captures the possible nonlinearity in that space better than standard GPs. The developed techniques can be applied separately or concurrently to a standard GP occupancy mapping problem. According to our experimental results, although taking into account pose uncertainty leads, as expected, to more uncertain maps, by modeling the nonlinearities present in the observation space WGPs can improve the map quality.

An Improved Mixture Model of Gaussian Processes and Its Classification Expectation–Maximization Algorithm

“…For the optimization of the WGP, a spatial branching strategy was designed [44]. The WGP (being a useful generalization of the GP) has also been widely used in practical applications [45][46][47][48].…”

Sampling-based incremental information gathering with applications to robotic exploration and environmental monitoring

“…However, note that the hyperparameters of the covariance functions are learned using the training set which contains measurements; therefore, the knowledge of underlying process and measurements is incorporated into the GP through its hyperparameters. Once we established GP variance reduction (GPVR) algorithm, we then use the expected kernel notion (Ghaffari Jadidi et al, 2017) to propagate pose uncertainty into the covariance function resulting in uncertain GP variance reduction (UGPVR) algorithm. In particular, these two information functions are interesting for the following reasons.…”

“…Now it is clear that having an estimate of the robot pose posterior with long tails (yet exponentially bounded) reduces the MI even further owing to averaging. Furthermore, if the robot pose is not known and we have only access to its estimate, ignoring the distribution can lead to overconfident or inconsistent inference/prediction (Ghaffari Jadidi et al, 2017: Figure 2).…”