Path Integral Particle Filtering for Hybrid Systems via Saltation Matrices

TL;DR

This paper introduces a novel particle filtering method for hybrid systems with contact dynamics, using saltation matrices within a path integral framework to improve robustness and flexibility in state estimation.

Contribution

It presents a new optimal-control-based particle filter that effectively propagates uncertainty during contact events in hybrid systems using saltation matrices.

Findings

Outperforms baseline methods on bouncing ball simulations

Handles non-Gaussian noise effectively

Robust to contact-induced uncertainty propagation

Abstract

State estimation for hybrid systems that undergo intermittent contact with their environments, such as extraplanetary robots and satellites undergoing docking operations, is difficult due to the discrete uncertainty propagation during contact. To handle this propagation, this paper presents an optimal-control-based particle filtering method that leverages saltation matrices to map out uncertainty propagation during contact events. By exploiting a path integral filtering framework that exploits the duality between smoothing and optimal control, the resulting state estimation algorithm is robust to outlier effects, flexible to non-Gaussian noise distributions, and handles challenging contact dynamics in hybrid systems. To evaluate the validity and consistency of the proposed approach, this paper tests it against strong baselines on the stochastic dynamics generated by a bouncing ball and spring loaded inverted pendulum.