State and Unknown Terrain Estimation for Planetary Rovers via Interval Observers

Abstract

Herein, the problem of state and unknown terrain estimation is considered, where the unknown planetary terrain parameters, e.g., terrain stiffness and ground height, are inferred from how it affects rover motion through vehicle‐terrain interaction. In particular, an alternative framework for terrain estimation based on set‐valued or set‐membership estimation is proposed, where the goal is to find set‐valued estimates (in the form of hyper‐rectangles or intervals) of the states and unknown terrain parameters. For this purpose, a state and model interval observer is designed for partially unknown nonlinear systems with bounded noise. By leveraging a combination of nonlinear bounding/decomposition functions, affine abstractions, and a data‐driven function abstraction method (to overestimate the unknown dynamics model from noisy input–output data), the proposed observer is capable of simultaneously estimating the states and learning the unknown dynamics. Further, a tractable sufficient condition is derived for guaranteeing the stability of the designed observer, i.e., such that the sequence of interval estimate widths are uniformly bounded. When applied to the state and unknown terrain estimation problem, the simulation results indicate that our approach can more reliably find the range of possible terrain parameters when compared with the cubature Kalman filter.

Keywords

• State and model interval observers
• Terrain estimations
• Vehicle–terrain interaction