The Uncertainty Aware Salted Kalman Filter: State Estimation for Hybrid Systems with Uncertain Guards

In this paper, we present a method for updating robotic state belief through contact with uncertain surfaces and apply this update to a Kalman filter for more accurate state estimation. Examining how guard surface uncertainty affects the time spent in each mode, we derive a novel guard saltation matrix- which maps perturbations prior to hybrid events to perturbations after - accounting for additional variation in the resulting state. Additionally, we propose the use of parame-terized reset functions - capturing how unknown parameters change how states are mapped from one mode to the next - the Jacobian of which accounts for additional uncertainty in the resulting state. The accuracy of these mappings is shown by simulating sampled distributions through uncertain transition events and comparing the resulting covariances. Finally, we integrate these additional terms into the “uncertainty aware Salted Kalman Filter”, uaSKF, and show a peak reduction in average estimation error by 24–60% on a variety of test conditions and systems.

I. Introduction

Making and breaking contact is critical for robots as they often need to physically interact with their environment to accomplish their tasks. For a legged robot to navigate to a desired location - for search and rescue, mapping, remote surveying, etc. - its feet will need to repeatedly impact the ground as it walks or runs. Manipulation robots must grasp, push, pull, etc, the objects they need to manipulate. In order to safely and reliably operate during these changing contact conditions, robots need to have an accurate estimation of their state in order to generate reasonable plans and complete their tasks. However, when dealing with these intermittent contacts, the robot's dynamics become non-smooth and even discontinuous, which presents a challenge for classic meth-ods that assume smoothness [1]–[4].