Smoothed Normal Distribution Transform for Efficient Point Cloud Registration During Space Rendezvous

Renaut, Léo; Frei, Heike; Nüchter, Andreas

doi:10.5220/0011616300003417

Cited by 3 publications

(4 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The smoothed NDT is a variant of the NDT that we introduced in [42]. It aims at mitigating the discontinuity issues of the NDT cost function mentioned in Section 2.1 without affecting the computation time of the algorithm.…”

Section: Smoothed Normal Distribution Transformmentioning

confidence: 99%

“…where σ is the standard deviation of the chosen Gaussian blur. It is typically chosen to be close to the minimal cell size of the kd-tree [42], while the smoothing radius for considering neighboring distributions can be chosen to equal 3σ. Finally, registration of a source point cloud (z 1 , .…”

Section: Smoothed Normal Distribution Transformmentioning

confidence: 99%

“…Compared to the classical NDT, the smoothed NDT only requires the additional smoothing step, which is performed as a pre-processing step. Because the smoothing can be performed efficiently using the tree structure, the additional computation time is minor [42]. In the case where a reference 3D model of the satellite is known beforehand, the construction of the smoothed NDT map only has to be performed once with this model point cloud.…”

Section: Smoothed Normal Distribution Transformmentioning

confidence: 99%

See 2 more Smart Citations

Lidar Pose Tracking of a Tumbling Spacecraft Using the Smoothed Normal Distribution Transform

2023

Self Cite

View full text Add to dashboard Cite

Lidar sensors enable precise pose estimation of an uncooperative spacecraft in close range. In this context, the iterative closest point (ICP) is usually employed as a tracking method. However, when the size of the point clouds increases, the required computation time of the ICP can become a limiting factor. The normal distribution transform (NDT) is an alternative algorithm which can be more efficient than the ICP, but suffers from robustness issues. In addition, lidar sensors are also subject to motion blur effects when tracking a spacecraft tumbling with a high angular velocity, leading to a loss of precision in the relative pose estimation. This work introduces a smoothed formulation of the NDT to improve the algorithm’s robustness while maintaining its efficiency. Additionally, two strategies are investigated to mitigate the effects of motion blur. The first consists in un-distorting the point cloud, while the second is a continuous-time formulation of the NDT. Hardware-in-the-loop tests at the European Proximity Operations Simulator demonstrate the capability of the proposed methods to precisely track an uncooperative spacecraft under realistic conditions within tens of milliseconds, even when the spacecraft tumbles with a significant angular rate.

show abstract

Section: Smoothed Normal Distribution Transformmentioning

confidence: 99%

Section: Smoothed Normal Distribution Transformmentioning

confidence: 99%

Section: Smoothed Normal Distribution Transformmentioning

confidence: 99%

See 1 more Smart Citation

Lidar Pose Tracking of a Tumbling Spacecraft Using the Smoothed Normal Distribution Transform

2023

Self Cite

View full text Add to dashboard Cite

show abstract

“…The second proposed modification of NDT addresses the discontinuity issue of the NDT map presented in Section 2. In [24], we introduced a smoothing method of the NDT map that we summarize here. The target point cloud is split into m cells using a kd-tree partition.…”

Section: Smoothed Ndtmentioning

confidence: 99%

LiDAR based pose tracking of an uncooperative spacecraft using the smoothed normal distribution transform

Renaut,

Frei,

Nüchter

2023

Papers of ESA GNC-ICATT 2023

View full text Add to dashboard Cite

Performing an autonomous space rendezvous with an uncooperative spacecraft requires a precise relative pose estimation in close range, whether it is in the context of an on-orbit servicing or active debris removal mission. In such contexts, LiDAR sensors are of great interest. They provide a depth image of the uncooperative spacecraft or object independently from the illumination conditions, and have a large working range, making them also suitable for use while transitioning from mid to close-range. Yet LiDAR sensors also have relatively low framerates, what makes them sensitive to motion blur or motion distortion effects when tracking faster objects such as a satellite rotating with an important angular rate. Most tracking algorithms using LiDAR point clouds developed in the space context are based on a variant of the iterative closest point (ICP) algorithm. However, the normal distribution transform (NDT) algorithm is also widely used in multiple fields of mobile robotics, and is considered a second standard next to ICP. Using a condensed representation of the point clouds, the NDT algorithm achieves better processing times than ICP while obtaining the same precision. Especially for space applications, where the computing hardware sometimes has limited capabilities compared to what is achieved on ground, the use of an efficient algorithm is crucial. Likewise, if the number of points contained in each acquired point cloud is important, it becomes challenging to perform pose tracking in real time. Despite being efficient, the NDT algorithm in its classical version presents discontinuity issues that can alter its robustness. Specifically, the initial guess has to be quite close to the actual solution for the algorithm to successfully converge. To mitigate this problem, a customized smoothed NDT algorithm is used in this work. This modified NDT algorithm relies on a Gaussian smoothing of the NDT map as a pre-processing step, which leads to a better robustness of the method to larger errors in the initial pose estimate. The smoothing technique is coupled with a kd-tree representation of the NDT map and a relaxed formulation of the optimization problem to speed up the convergence of the algorithm. The smoothed NDT algorithm is applied to the problem of LiDAR based pose tracking of an uncooperative spacecraft in close range. For scenarios where the uncooperative spacecraft has fast rotation rates, a strategy to motion compensate the point clouds is further investigated. The resulting pose estimation system is integrated within a GNC system and tested in closed loop at the European Proximity Operations Simulator (EPOS). EPOS is a hardware-in-the-loop test facility maintained by the German Aerospace Center (DLR), where realistic conditions for space rendezvous can be reproduced and tested in closed loop. The pose tracking system is tested for a rendezvous scenario comprising a fly-around, inspection and approach of an uncooperative satellite. Using solely the LiDAR, the servicer satellite is able to perform an approach up to immediate proximity to the target, at a distance where robotic servicing or de-orbiting operations could take place. During the whole phase of proximity operations, the pose estimation is precise up to a few degrees and centimeters, even when the target satellite is only partially visible in the LiDAR’s field of view. More challenging scenarios are also investigated, where the uncooperative spacecraft spins with a higher rotation rate. In these cases, it becomes necessary to account for the motion blur induced by the movement of the satellite during the scanning. Again, the pose tracking system is able to track the target satellite with a good precision throughout the whole approach, and converges within few iterations.

show abstract

Robust Localization Approach Using Hybrid Correspondence NDT and Real-Time Uncertainty Estimation

Aoki,

Takahashi,

Sato

et al. 2024

2024 IEEE/SICE International Symposium on System Integration (SII)

View full text Add to dashboard Cite

Smoothed Normal Distribution Transform for Efficient Point Cloud Registration During Space Rendezvous

Cited by 3 publications

References 0 publications

Lidar Pose Tracking of a Tumbling Spacecraft Using the Smoothed Normal Distribution Transform

Lidar Pose Tracking of a Tumbling Spacecraft Using the Smoothed Normal Distribution Transform

LiDAR based pose tracking of an uncooperative spacecraft using the smoothed normal distribution transform

Robust Localization Approach Using Hybrid Correspondence NDT and Real-Time Uncertainty Estimation

Contact Info

Product

Resources

About