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Path Integral Particle Filtering for Hybrid Systems via Saltation Matrices

Karthik Shaji, Sreeranj Jayadevan, Bo Yuan, Hongzhe Yu, Yongxin Chen

TL;DR

This work presents an optimal-control-based particle filtering method for state estimation in hybrid systems that undergo intermittent contact with their environments that offers a computationally efficient and reliable estimation algorithm for hybrid systems with stochastic dynamics.

Abstract

We present an optimal-control-based particle filtering method for state estimation in hybrid systems that undergo intermittent contact with their environments. We follow the path integral filtering framework that exploits the duality between the smoothing problem and optimal control. We leverage saltation matrices to map out the uncertainty propagation during contact events for hybrid systems. The resulting path integral optimal control problem allows for a state estimation algorithm robust to outlier effects, flexible to non-Gaussian noise distributions, that also handles the challenging contact dynamics in hybrid systems. This work offers a computationally efficient and reliable estimation algorithm for hybrid systems with stochastic dynamics. We also present extensive experimental results demonstrating that our approach consistently outperforms strong baselines across multiple settings.

Path Integral Particle Filtering for Hybrid Systems via Saltation Matrices

TL;DR

This work presents an optimal-control-based particle filtering method for state estimation in hybrid systems that undergo intermittent contact with their environments that offers a computationally efficient and reliable estimation algorithm for hybrid systems with stochastic dynamics.

Abstract

We present an optimal-control-based particle filtering method for state estimation in hybrid systems that undergo intermittent contact with their environments. We follow the path integral filtering framework that exploits the duality between the smoothing problem and optimal control. We leverage saltation matrices to map out the uncertainty propagation during contact events for hybrid systems. The resulting path integral optimal control problem allows for a state estimation algorithm robust to outlier effects, flexible to non-Gaussian noise distributions, that also handles the challenging contact dynamics in hybrid systems. This work offers a computationally efficient and reliable estimation algorithm for hybrid systems with stochastic dynamics. We also present extensive experimental results demonstrating that our approach consistently outperforms strong baselines across multiple settings.
Paper Structure (21 sections, 63 equations, 8 figures, 3 algorithms)

This paper contains 21 sections, 63 equations, 8 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Notation and Preliminaries
  3. Smooth Path Integral Particle Filtering
  4. Hybrid Systems and the Linearization of Jump Dynamics
  5. Hybrid Dynamical Systems
  6. Stochastic Optimal Control with Hybrid Transitions
  7. Problem Formulation
  8. Smoothing for Hybrid Dynamical Systems
  9. Solving Hybrid Filtering Through Hybrid Optimal Control
  10. Hybrid Path Integral Smoothing and Filtering
  11. Hybrid Particle Filtering
  12. Algorithm and Implementation
  13. Numerical Examples and Results
  14. Bouncing Ball System
  15. Spring Loaded Inverted Pendulum (SLIP) System
  16. ...and 6 more sections

Figures (8)

  • Figure 1: Hybrid automaton with two modes
  • Figure 2: Bouncing Ball Visualization
  • Figure 3: SLIP Visualization
  • Figure 4: Results from Changing Particle Count
  • Figure 5: Results from Changing Sliding Window Size
  • ...and 3 more figures