LiDAR based pose tracking of an uncooperative spacecraft using the smoothed normal distribution transform
Authors:   German Aerospace Center (DLR), Weßlling, Germany, Renaut Leo , Frei Heike , Nüchter Andreas 
Published: January 2024

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.