Learning-based Moving Horizon Estimation through Differentiable Convex Optimization Layers

To control a dynamical system it is essential to obtain an accurate estimate of the current system state based on uncertain sensor measurements and existing system knowledge. An optimization-based moving horizon estimation (MHE) approach uses a dynamical model of the system, and further allows for integration of physical constraints on system states and uncertainties, to obtain a trajectory of state estimates. In this work, we address the problem of state estimation in the case of constrained linear systems with parametric uncertainty. The proposed approach makes use of differentiable convex optimization layers to formulate an MHE state estimator for systems with uncertain parameters. This formulation allows us to obtain the gradient of a squared and regularized output error, based on sensor measurements and state estimates, with respect to the current belief of the unknown system parameters. The parameters within the MHE problem can then be updated online using stochastic gradient descent (SGD) to improve the performance of the MHE. In a numerical example of estimating temperatures of a group of manufacturing machines, we show the performance of tuning the unknown system parameters and the benefits of integrating physical state constraints in the MHE formulation.Comment: This paper was accepted for presentation at the 4th Annual Conference on Learning for Dynamics and Control. The extended version here contains an additional appendix with more details on the numerical exampl

Incorporating delayed and multi-rate measurements in navigation filter for autonomous space rendezvous

In the scope of space missions involving rendezvous between a chaser and a target, vision based navigation relies on the use of optical sensors coupled with image processing and computer vision algorithms to obtain a measurement of the target relative pose. These algorithms usually have high latency time, implying that the chaser navigation filter has to fuse delayed and multi-rate measurements. This article has two main contributions: it provides a detailed modelization of the relative dynamics within the estimation filter, and it proposes a comparison of two delay management techniques suitable for this application. The selected methods are the Filter Recalculation method -which always provides an optimal estimation at the expense of a high computational load- and the Larsen’s method -which provides a faster solution whose optimality lies on stronger requirements. The application of these techniques to the space rendezvous problem is discussed and formalized. Finally, the current article proposes a comparison of the methods based on a Monte-Carlo campaign, aimed at demonstrating whether the loss of performance of Larsen’s method due to its sub-optimality still enables target state robust tracking

Tightly Coupled 3D Lidar Inertial Odometry and Mapping

Ego-motion estimation is a fundamental requirement for most mobile robotic applications. By sensor fusion, we can compensate the deficiencies of stand-alone sensors and provide more reliable estimations. We introduce a tightly coupled lidar-IMU fusion method in this paper. By jointly minimizing the cost derived from lidar and IMU measurements, the lidar-IMU odometry (LIO) can perform well with acceptable drift after long-term experiment, even in challenging cases where the lidar measurements can be degraded. Besides, to obtain more reliable estimations of the lidar poses, a rotation-constrained refinement algorithm (LIO-mapping) is proposed to further align the lidar poses with the global map. The experiment results demonstrate that the proposed method can estimate the poses of the sensor pair at the IMU update rate with high precision, even under fast motion conditions or with insufficient features.Comment: Accepted by ICRA 201