Estimation-Aware Trajectory Optimization with Set-Valued Measurement Uncertainties

TL;DR

This paper introduces an optimization framework for generating trajectories that are aware of estimation uncertainties, especially set-valued and state-dependent, improving planning for vision-based and satellite rendezvous systems.

Contribution

It develops a novel estimation-aware trajectory generation method using set-valued uncertainties and introduces the concept of regularity for set-valued output maps, applicable to broad system classes.

Findings

Effective trajectory planning with vision-based estimation demonstrated.

Estimation-aware planning applied to satellite rendezvous with ML-based estimation.

Set-valued observability measure maximization improves estimation accuracy.

Abstract

In this paper, an optimization-based framework for generating estimation-aware trajectories is presented. In this setup, measurement (output) uncertainties are state-dependent and set-valued. Enveloping ellipsoids are employed to characterize state-dependent uncertainties with unknown distributions. The concept of regularity for set-valued output maps is then introduced, facilitating the formulation of the estimation-aware trajectory generation problem. Specifically, it is demonstrated that for output-regular maps, one can utilize a set-valued observability measure that is concave with respect to the finite horizon state trajectories. By maximizing this measure, estimation-aware trajectories can then be synthesized for a broad class of systems. Trajectory planning routines are also examined in this work, by which the observability measure is optimized for systems with locally linearized dynamics. To illustrate the effectiveness of the proposed approach, representative examples in the context of trajectory planning with vision-based estimation are presented. Moreover, the paper presents estimation-aware planning for an uncooperative Target-Rendezvous problem, where an Ego-satellite employs an onboard machine learning (ML)-based estimation module to realize the rendezvous trajectory.